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Widely expected to depart London soon, I couldn't pass up the opportunity to get a shot of Arriva London VDL DB300/Wright Gemini 2 DW268 (LJ59LXZ), pictured in Coulsdon on route 60.
With route 194 being one of the routes to be gaining new Wright Electroliners very soon, the 59 reg DW's at South Croydon, originally new to route 38 are expected to leave the fleet, most likely once the 194 moves to Thornton Heath.
Apparently this is a replica of Noah's Ark, though I' m not sure how they know what the original looked like. It's a floating museum that is full of models depicting bible stories. The entry fee is incredibly steep so these two photos are all you'll get to see of it on my photo stream
We expected to leave the forested path and come upon an ocean view (per the trail sign). It may be out there but we hiked over a few dunes and never saw the view. No thanks to Dune Hiking! We can see an ocean view any day of the week.
Wasn't expecting to see this in Hadlow near Tunbridge today!, and this was the best I could do of this vehicle as the Arriva Route 7 Bus I was ridding back to Maidstone was moving, and this vehicle is now used by Hugh Lowes Farms to transport farm workers around Mereworth near Maidstone in Kent, and is is one 13! vehicles in use at Mereworth, and they are not the only ex Stagecoach Vehicles in Farms use in the Maidstone Area, and acording to Google Maps Satalite Imagery several others can be found around Five Wents, Langley, Sutton Valence and Coxheath.
And be sure to check by my other acount: www.flickr.com/photos_user.gne?path=&nsid=77145939%40..., to see what else I saw Very Recently!!
In a future post apocalyptic world not very far from now, justice has a new name The Druidess Of Midian!
A bit of fun shoot at Coalhouse Fort, Tilbury, Essex, with C-Imagery.
Model: The Druidess Of Midian
Photography © C-Imagery
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No unauthorised use without prior written consent.
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Not a great composition, objects are too near the border of the image .... but I like the color here and the idea !!!
Inspired by Sylvain Latouche, a great photographer ..I greatly encourage you to visit his stream
Setup:
Camera Canon 5DIII | Exposure 1/160 sec | Aperture f/5.6| Focal Length 85 mm | ISO Speed 100
One bottle of '' PINK CHAMPAGNE"
One flash 430 EXII with a home-made snoot for the background
One flash 580 EXII with a softbox @8h00
and another flash (but i don't remember where is it ).
I did not expect to find this V8V in the delivery area of a shopping center, but it made for a really cool backdrop. I think the clear taillights are a nice touch.
Hi. Not having a Pro account is the worst feeling. I wasn't expecting to get one, but I just thought someone would purchase me one 'cause I've done it for other's in the past. I'm not saying that I bought them for Olivia and Juliana just so other people would buy me one, but ugh, I just want one :(
-This is old, I don't love it, but I don't hate it(: School and cross country is great!(: I wish I could see all six-hundred of my pictures here again...My first meet is this Saturday!! :D I cannot wait to wear my flats againnnn(: I hope who ever reads this is doing great!!<3
-You know what I'm really sick and tired of though? When girls take pictures that I took the same exact things of, the same idea, the same, UGH everything! And they take a picture, edit it just like one of mine, and then post it without saying anything that it was inspired. I mean, OHMYGOSH. I just can't even take it sometimes. Its the exact same picture!!!!!!
My youth group leader-I've mentioned him here before- Mike is leaving...He won't be my leader any more. I can't explain what I feel other than happy and sad at the same time, but isn't that pretty obvious?
When Jaimie and I went to Youth Week rather than going to Young Life summer camp, it was sad we wouldn't be with our friends, but we grew in God more. Mike hasn't had his own leader so to speak, no one has been filling him up with Jesus, you could say. He hasn't had a church for a long time. So, even though it is terribly sad that he won't be my leader anymore, I'm happy that he'll be going on mission trips to do bigger and better things and be more of a solider for our Lord.
I mean, yes its awesome that he's Asian, but he's so much more than that. I find it so much easier to follow his lesson's at bible study rather than anyone else's, honestly. He can explain things like Jaimie can, in a way that you would have never thought of but when you hear it, you're blown away and become excited because you would have never thought of to look at a verse like that before, or something. When Mike found out that I had a "thing" with this boy named James, he told Lisa, my other leader to make sure I didn't date him because Mike new he wasn't a Christian. He thought of me instantly when Shannon was coming to Long Island and needed a photographer's assistant and helped me out so much. He's just...He rock's so much. Two of my Young Life leaders have now left while I've been in Young Life, my two favorites.
Maybe you think its weird that I'm talking about my youth group leader, especially since he's a guy, but I don't really care because countless times, he's amazed me, surprised me, said incredible things. He's going to save more unsaved people, and I cannot wait to hear about it; he's changed me life and I'm just so grateful and blessed to having known him.
Let God and God only define you.
Join my Facebook!
Do not steal my pictures or blog my pictures without my permission.
Wasn't expecting to see this vehicle in Dover today, and this vehicle had just dropped off a large student group for "Student Group Day" which is every Wednesday afternoon and can sometimes bring up to 15! vehicles from all Local Operators, and I saw at least 10 vehicles here today.
And be sure to check by my other acount: www.flickr.com/photos_user.gne?path=&nsid=77145939%40..., to see what else I saw Very Recently!!
Yes I'm back again.
However due to my main computer on which I edit my work being struck down with a big bad virus, this picture and all the others I am uploading, were Unedited but have now been replaced with Edited versions. So enjoy and Thanks for your patience and understanding.
I do still hate everything about this shit that is new Flickr and always will, but an inability to find another outlet for my work that is as easy for me to use as the Old BETTER Flickr was, has forced me back to Flickr, even though it goes against everything I believe in.
I don't generally have an opinion on my own work, I prefer to leave that to other people and so based on the positive responses to my work from the various friends I had made on Flickr prior to the changes I have decided to upload some more of my work as an experiment and to see what happens.
So make the most of me before they delete my acount: www.flickr.com/photos/69558134@N05/?details=1, to stop me complaining!!
Youghal, Cork
Fuji GW670III camera
(after repair of the shutter)
Ilford Delta 3200 film
Red25 filter attached, but not too sure
Developed in TMAX (20%, 20 C, 8.5')
The roses in the People's Garden
Plan
Rosarium History - Classification
Floribunda - new color range - Casting
Tree roses - new plantings - Pests - Winter Care
Rambling Roses - fertilizing, finishes
Shrub Roses - Rose Renner - Sponsorship - variety name
The history of roses in the People's Garden
The People's Garden, located between the Imperial Palace and the ring road is famous for its beautiful roses:
1000 standard roses
4000 Floribunda,
300 rambling roses,
(Also called Rose Park) 200 shrub roses.
Noteworthy is the diversity: there are about 400 varieties, including very old plants:
1859 - Rubens
1913 - Pearl of the Vienna Woods
1919 - Jean C.N. Forestier
The above amounts are from the Federal Gardens. My own count has brought other results:
730 tree roses
2300 Floribunda
132 rambling roses
100 shrub roses
That's about 3300 roses in total. Approx. 270 species I was able to verify. Approx. 50 rose bushes were not labeled. Some varieties come very often, others only once or twice.
Molineux 1994
Rubens 1859
Medialis 1993
Swan lake 1968
Once flourished here Lilac and Rhododendron bushes
1823 People's Garden was opened with the Temple of Theseus. Then made multiple extensions.
The part of today's "Rosarium" along the Ring Road was built in 1862. (Picture fence 1874)
What is so obvious to today's Vienna, was not always so: most of the beds in the People's Garden originally were planted with lilac and rhododendron.
Only after the second World War II it was converted to the present generous rose jewelry.
Since then grow along the ring side creepers, high stem and floribunda roses. On the side of Heroes Square, with the outputs, shrub roses were placed, among which there are also some wild roses.
1889 emerged the Grillparzer Monument.
(All the pictures you can see by clicking the link at the end of the side!)
Rhododendrons, output Sisi Avenue, 1930
Classifications of roses
(Wild roses have 7 sheets - prize roses 5 sheets)
English Rose
Florybunda
Hybrid Tea Rose
Rambling Rose
At the Roses in the People´s Garden are hanging labels (if they do not fall victim to vandals or for souvenirs) with the year indication of breeding, the name of breeding and botanical description:
Hybrid Tea Rose (TB): 1 master, 1 flower;
Florybunda (Flb): 1 strain, many flowers;
English Rose (Engl): mixture of old and modern varieties Tb and Flb.
Called Schlingrose, also climbing rose
Florybunda: 1 strain, many flowers (Donauprinzessin)
Shrub Roses - Floribunda - Tree roses - Climbing Roses
Even as a child, we hear the tale of Sleeping Beauty, but roses have no thorns, but spines. Thorns are fused directly to the root and can not be easily removed as spines (upper wooden containers called).
All roses belong to the bush family (in contrast to perennials that "disappear" in the winter). Nevertheless, there is the term Shrub Rose: It's a chronological classification of roses that were on the market before 1867. They are very often planted as a soloist in a garden, which them has brought the name "Rose Park".
Hybrid Tea Rose: 1 master, 1 flower (rose Gaujard )
Other classifications are:
(High) standard roses: roses are not grafted near the ground, but at a certain strain level. With that, the rose gardener sets the height of the crown.
Floribunda roses : the compact and low bushy roses are ideal for group planting on beds
Crambling roses: They have neither roots nor can they stick up squirm. Their only auxiliary tool are their spines with which they are entangled in their ascent into each other
English Rose: mixture of old varieties, hybrid tea and Florybunda (Tradescanth)
4000 Floribunda
Floribunda roses are hardy, grow compact, knee-high and bushy, are durable and sturdy
There are few smelling varieties
Polyantha classification: a tribe, many small flowers; Florybunda: a tribe, many big blossoms
New concept of color: from red to light yellow
The thousands Floribunda opposite of Grillparzer Monument shimmer (still) in many colors. From historical records, however, is indicated that there was originally a different color scheme for the Floribunda than today: At the entrance of the Burgtheater side the roses were dark and were up to Grillparzer monument ever brighter - there they were then already white.
This color range they want again, somewhat modified, resume with new plantings: No white roses in front of the monument, but bright yellow, so that Grillparzer monument can better stand out. It has already begun, there was heavy frost damage during the winter 2011/12.
Colorful roses
2011: white and pink roses
2012: after winter damage new plantings in shades of yellow .
Because the domestic rose production is not large enough, the new, yellow roses were ordered in Germany (Castor).
Goldelse, candlelight, Hanseatic city of Rostock.
Watering
Waterinr of the Floribunda in the morning at 11 clock
What roses do not like at all, and what attracts pests really magically, the foliage is wet. Therefore, the Floribunda roses are in the People's Garde poured in the morning at 11 clock, so that the leaves can dry thoroughly.
Ground sprinklers pouring only the root crown, can not be used because the associated hoses should be buried in the earth, and that in turn collide with the Erdanhäufung (amassing of earth) that is made for winter protection. Choosing the right time to do it, it requires a lot of sense. Is it too early, so still too warm, the bed roses begin to drive again, but this young shoots freeze later, inevitably, because they are too thin.
1000 Tree roses
Most standard roses are found in the rose garden.
During the renovation of the Temple of Theseus the asphalt was renewed in 2011, which was partially only a few centimeters thick, and so was the danger that trucks with heavy transports break into. Due to this construction site the entire flower bed in front had to be replaced.
Now the high-stem Rose Maria Theresia is a nice contrast to the white temple, at her feet sits the self-cleaning floribunda aspirin. Self-cleaning means that withered flowers fall off and rarely maintenance care is needed.
Pink 'Maria Theresa' and white 'aspirin' before the temple of Theseus
Standard tree rose Maria Theresa
Floribunda aspirin
The concept of the (high) standard roses refers to a special type of rose decoration. Suitable varieties of roses are not grafted near the ground, but at a certain height of the trunk. With that the rose gardener sets the height of the crown fixed (60 cm, 90 cm, 140 cm)
Plantings - Pests - Winter Care
Normally about 50 roses in the People's Garden annually have to be replaced because of winter damages and senility. Till a high standard rose goes on sale, it is at least 4 years old. With replantings the soil to 50 cm depth is completely replaced (2/3 basic soil, 1/3 compost and some peat ).
Roses have enemies, such as aphids. Against them the Pirimor is used, against the Buchsbaumzünsler (Box Tree Moth, Cydalima perspectalis) Calypso (yet - a resistance is expected).
In popular garden roses are sprayed with poison, not only when needed, but also as a precaution, since mildew and fire rose (both are types of fungi) also overwinter.
Therefore it is also removed as far as possible with the standard roses before packing in winter the foliage.
Pest Control with Poison
The "Winter Package " first is made with paper bags, jute bags, then it will be pulled (eg cocoa or coffee sacks - the commercially available yard goods has not proven).
They are stored in the vault of the gardener deposit in the Burggarten (below the Palm House). There namely also run the heating pipes. Put above them, the bags after the winter can be properly dried.
Are during the winter the mice nesting into the packaged roses, has this consequences for the crows want to approach the small rodents and are getting the packaging tatty. It alreay has happened that 500 standard roses had to be re-wrapped.
"Winter Package" with paper and jute bags
300 ambling roses
The Schlingrosen (Climbing Roses) sit "as a framing" behind the standard roses.
Schlingrose pearl from the Vienna Woods
Schlingrose Danube
Schlingrose tenor
Although climbing roses are the fastest growing roses, they get along with very little garden space.
They have no rootlets as the evergreen ivy, nor can they wind up like a honeysuckle. Their only auxiliary tool are their spines with which they are entangled in their ascent mesh.
Climbing roses can reach stature heights of 2 to 3 meters.
4 x/year fertilizing
4 times a year, the soil is fertilized. From August, but no more, because everything then still new drives would freeze to death in winter. Well-rotted horse manure as fertilizer was used (straw mixed with horse manure, 4 years old). It smelled terrible, but only for 2 days.
Since the City of Vienna may only invest more plant compost heap (the EU Directive prohibits animal compost heap on public property), this type of fertilization is no longer possible to the chagrin of gardeners, and roses.
In the people garden in addition is foliar fertilizer used (it is sprayed directly on the leaves and absorbed about this from the plant).
Finishes in the Augarten
Old rose varieties are no longer commercially available. Maybe because they are more sensitive, vulnerable. Thus, the bud of Dr. F. Debat already not open anymore, if it has rained twice.
Roses need to be replaced in the People's Garden, this is sometimes done through an exchange with the Augarten Palace or the nursery, where the finishes are made. Previously there were roses in Hirschstetten and the Danube Park, but the City of Vienna has abandoned its local rose population (not to say destroyed), no exchange with these institutions is possible anymore.
Was formerly in breeding the trend to large flowers, one tends to smell roses again today. Most varieties show their resplendent, lush flowers only once, early in the rose-year, but modern varieties are more often blooming.
200 shrub roses
Some shrub roses bloom in the rose garden next to the Grillparzer Monument
Most of the shrub or park roses can be found along the fence to Heroes' Square. These types are so old, and there are now so many variations that even a species of rose connoisseurs assignment is no longer possible in many cases.
The showy, white, instensiv fragrant wild rose with its large umbels near des Triton Fountain is called Snow White.
Shrub roses are actually "Old Garden Roses" or "old roses", what a time
classification of roses is that were on the market before 1867.
Shrub roses are also called park roses because they are often planted as a soloist in a park/garden.
They grow shrubby, reaching heights up to 2 meters and usually bloom only 1 x per year.
The Renner- Rose
The most famous bush rose sits at the exit to Ballhausplatz before the presidential office.
It is named after the former Austrian President Dr. Karl Renner
When you enter, coming from the Ballhausplatz, the Viennese folk garden of particular note is a large rose bush, which is in full bloom in June.
Before that, there is a panel that indicates that the rose is named after Karl Renner, founder of the First and Second Republic. The history of the rose is a bit of an adventure. President Dr. Karl Renner was born on 14 in December 1870 in the Czech village of Untertannowitz as the last of 18 children of a poor family.
Renner output rose at Ballhausplatz
He grew up there in a small house, in the garden, a rose bush was planted.
In summer 1999, the then Director of the Austrian Federal Gardens, Peter Fischer Colbrie was noted that Karl Renner's birthplace in Untertannowitz - Dolni Dunajovice today - and probably would be demolished and the old rosebush as well fall victim to the demolition.
High haste was needed, as has already been started with the removal of the house.
Misleading inscription " reconstruction"?
The Federal Gardens director immediately went to a Rose Experts on the way to Dolni Dunajovice and discovered "as only bright spot in this dismal property the at the back entrance of the house situated, large and healthy, then already more than 80 year old rose bush".
After consultation with the local authorities Peter Fischer Colbrie received approval, to let the magnificent rose bush dig-out and transport to Vienna.
Renner Rose is almost 100 years old
A place had been found in the Viennese People´s Garden, diagonal vis-à-vis the office where the president Renner one resided. On the same day, the 17th August 1999 the rosebush was there planted and in the following spring it sprouted already with flowers.
In June 2000, by the then Minister of Agriculture Molterer and by the then Mayor Zilk was a plaque unveiled that describes the origin of the rose in a few words. Meanwhile, the "Renner-Rose" is far more than a hundred years old and is enjoying good health.
Memorial Dr. Karl Renner : The Registrar in the bird cage
Georg Markus , Courier , 2012
Sponsorships
For around 300 euros, it is possible to assume a Rose sponsorship for 5 years. A tree-sponsorship costs 300 euros for 1 year. Currently, there are about 60 plates. Behind this beautiful and tragic memories.
If you are interested in sponsoring people garden, please contact:
Master gardener Michaela Rathbauer, Castle Garden, People's Garden
M: 0664/819 83 27 volksgarten@bundesgaerten.at
Varieties
Abraham Darby
1985
English Rose
Alec 's Red
1970
Hybrid Tea Rose
Anni Däneke
1974
Hybrid Tea Rose
aspirin
Florybunda
floribunda
Bella Rosa
1982
Florybunda
floribunda
Candlelight
Dagmar Kreizer
Danube
1913
Schlingrose
Donauprinzessin
Doris Thystermann
1975
Hybrid Tea Rose
Dr. Waldheim
1975
Hybrid Tea Rose
Duftwolke
1963
Eiffel Tower
1963
English Garden
Hybrid Tea Rose
Gloria Dei
1945
Hybrid Tea Rose
Goldelse
gold crown
1960
Hybrid Tea Rose
Goldstar
1966
deglutition
Greeting to Heidelberg
1959
Schlingrose
Hanseatic City of Rostock
Harlequin
1985
Schlingrose
Jean C.N. Forestier
1919
Hybrid Tea Rose
John F. Kennedy
1965
Hybrid Tea Rose
Landora
1970
Las Vegas
1956
Hybrid Tea Rose
Mainzer Fastnacht
1964
Hybrid Tea Rose
Maria Theresa
medial
Moulineux
1994
English Rose
national pride
1970
Hybrid Tea Rose
Nicole
1985
Florybunda
Olympia 84
1984
Hybrid Tea Rose
Pearl of the Vienna Woods
1913
Schlingrose
Piccadilly
1960
Hybrid Tea Rose
Rio Grande
1973
Hybrid Tea Rose
Rose Gaujard
1957
Hybrid Tea Rose
Rubens
1859
English Rose
Rumba
snowflake
1991
Florybunda
snow white
shrub Rose
Swan
1968
Schlingrose
Sharifa Asma
1989
English Rose
city of Vienna
1963
Florybunda
Tenor
Schlingrose
The Queen Elizabeth Rose
1954
Florybunda
Tradescanth
1993
English Rose
Trumpeter
1980
Florybunda
floribunda
Virgo
1947
Hybrid Tea Rose
Winchester Cathedral
1988
English Rose
Source: Federal leadership Gardens 2012
Historic Gardens of Austria, Vienna, Volume 3 , Eva Berger, Bohlau Verlag, 2004 (Library Vienna)
Index Volksgartenstraße
www.viennatouristguide.at/Altstadt/Volksgarten/volksgarte...
Really wasn't expecting to see this in Dover today!, and this vehicle had brought School Groups to Dover Castle, which in winter still opens on Tuesdays and Thursdays for School Groups, and a thank you to Regents Coaches Bus Driver Mark Smith for the tip off that this was up here.
And be sure to check by my other acount: www.flickr.com/photos_user.gne?path=&nsid=77145939%40..., to see what else I saw Last Week!
Yes I'm back again.
However due to my main computer on which I edit my work being struck down with a big bad virus, this picture and all the others I am uploading, were Unedited but have now been replaced with Edited versions. So enjoy and Thanks for your patience and understanding.
I do still hate everything about this shit that is new Flickr and always will, but an inability to find another outlet for my work that is as easy for me to use as the Old BETTER Flickr was, has forced me back to Flickr, even though it goes against everything I believe in.
I don't generally have an opinion on my own work, I prefer to leave that to other people and so based on the positive responses to my work from the various friends I had made on Flickr prior to the changes I have decided to upload some more of my work as an experiment and to see what happens.
So make the most of me before they delete my acount: www.flickr.com/photos/69558134@N05/?details=1, to stop me complaining!!
Life is still busy and nervous.Wanna have a cup of coffee at a quiet coffee shop.
Expect our next trip.
I miss those days we walked together in Tokyo, shared everything, books, music, every great view, and happy moment with each other!
I bought an amazing biography of a female artist, will share with you later.
♥ Thank 蜜茶不加蜜 for the lovely testimonial, you made my day!
Wasn't expecting to see this in Dover tonight!, and this vehicle was on SouthEastern Trains Emergency Rail Replacement Service to Ramsgate, and had also driven past my house in Dover about 12:15AM, and so yeah I went out for a shot again, and this was the best I could do in the light rain and winds, but still not that bad considering the conditions I had to work with, plus the fact that vehicles interior lighting didn't help in my opinion, and besides I've done worse night shots right?
But yes your probably still thinking I'm crazy for going out at night like this, especially when John Lee Hooker sang that "Night Time is the Right Time to be with the Woman You Love!", however I still don't have any of that...
And be sure to check by my other acount: www.flickr.com/photos_user.gne?path=&nsid=77145939%40..., to see what else I saw this week!!
Well, this is NOT the kind of news I was expecting during Comic-con! Because of some pretty horrible Tweets Gunn made that have resurfaced today, Disney has cut all ties with the director.
This news has been a roller coaster for me. For starters, I read most of his controversial tweets and they're flat out disgusting and horrible. We've also seen that the Guardians can work without Gunn given their appearance in Infinity War. At the same time, the Guardians of the Galaxy are Gunn's babies and it'll be really hard for someone to convince me that someone else can capture the heart and the complex emotions the characters brought in the past two films.
Overall, it may have been for the best. The things Gunn tweeted about is inexcusable, even if those ideas and jokes have never been anywhere near his Guardians films.
Well, there no really debate of what should be done because he's officially been fired. So, this means what's going to happen to Guardians of the Galaxy Vol. 3? Gunn has already submitted the script for the film, and it was planning to shoot this fall, but I wouldn't be surprised if they either make some rewrites by someone else and give them the script credit and Gunn the story credit, or throw out the script all together.
Anyways, I thought I'd throw in some suitable replacements in the meantime. My first pick would obviously be Taika Waititi as the director. He's my favorite director of all time (spoilers for tomorrow's top ten), and he's proven he can make something awesome in the cosmic universe. My second pick for both script and possibly directing would be Nicole Perlman. Now for those of you who don't know, Nicole Perlman spent two years researching and writing the first Guardians of the Galaxy script, only to have Gunn do a last minute rewrite and direct. I think she'd be a perfect for wrapping up this Guardians trilogy, plus more female talent behind the scenes is great.
Anyways, those are my thoughts. I'd really like to hear everyone's perspective on this so leave your thoughts in the comments below!
Young Timmy was in absolute heaven!
Although he didn't expect to be.
Earlier in the day, when his parents said they'd be taking him to Times Square to see the Fleet Week activities, he wasn't exactly thrilled. Wasn't that the Navy? Didn't they just sail around in boats and stuff? His cousin Fred, whom he idolized, had joined the Army -- now THAT was cool! The video game he played at home -- the one where he got to blow up stuff and kill people -- that was the Army. That's what he wanted to be a part of.
Bobby from down the block also told him that the Navy was filled with "a bunch of homos." Timmy didn't know what that meant, but he knew whatever it was, it must be bad...right? He didn't want to be around homos. He wasn't looking forward to this Fleet Week thing at all.
But when he and his parent got to Times Square, it was filled with not just regular sailors, but Navy guys and Marines in cool camouflage outfits. They were doing self-defense demonstrations, and he watched as guys wrestled each other on the mat. Now that was awesome! And even cooler was the amount of weapons being shown. Rifles, bazookas...you name it!
When one of the soldier guys asked Timmy if he wanted to hold his big gun, he was thrilled! He didn't know if his mom would let him, so he looked up at her for her approval. But she just smiled, and nodded her head "ok"...
This was the best day ever!!!
Times Square, NYC
Taken with a 1st gen. iPhone
Commentary.
Expecting the white Chalk cliffs
and grey limestone, the dark flint
and inter-tidal sand and shingle,
it came as a pleasant surprise to see this
lush, verdant scene, just yards from Lulworth Cove.
A pure-water Chalk stream, lined by
water-irises, shrubs, flowers and trees.
This Jurassic Coast is an amazing place.
For all its superb features……
truly World Heritage!
Expecting to fly
While I laughed, I wondered whether
I could wave goodbye
Knowin' that you'd gone
Bella strikes a strong pose. She is amazing in all ways, both physically and personally.
Lyrics: Expecting to Fly by Buffalo Springfield
Monday, 2 September 2024: we are back to hot weather after a few cooler days, 30C today. Water restrictions outdoor and indoor ongoing and expected to end on 23 September. People are still using too much water and if it doesn't improve, boil-water may result!
Another five images taken on 22 August 2024, when I drove a long way SE of Calgary, to visit a familiar old ghost town.
This ghost town is only tiny. You can walk anywhere, right up to each building. There is usually information posted about what you are seeing. I never go inside these old structures (only the restored church), but you can look through the windows.
On 22 August 2024, I made a long trip SE of Calgary. My destination was a small, almost-ghost town that I had visited three (?) times before. If I remember correctly, this was my fourth visit - the others were in July 2020, August 2022 and 18 September 2023.
Basically, my day was pretty much similar to the day I last went out there, on 18 September 2023, so I am going to use the description I wrote under last year's photos, with a few changes.
On 22 August 2024, the weather forecast was pretty good and turned out to be unusually correct. Sunny, blue sky, and puffy, white clouds.
Most of my driving was on the main roads, in order to get to my destination as quickly as possible. The total drive of 489 kms took me just over 9 and a half hours, between 8:35 am and 6:00 pm. Much as I would have loved to check out a few back roads, I knew I absolutely had to get home before my car ran out of gas. The only time I left the highway was to quickly keep an eye open for any Common Nighthawks - none.
Last year, the small ghost town, that I was so keen to revisit yet again, had to be seen from my car, because it was too windy to walk, which was a shame. A challenge to take photos, sitting in a car that is being rocked by the extreme wind.
Once I reached the ghost town, I was the only person there. It is only a small place with a handful of old buildings, but very nicely kept. One of its main buildings is a small, country United Church, kept in great condition both inside and out. I had read online beforehand that people can go inside the church and sign their Guest Book, otherwise I probably would not have gone in. Really like the door knobs to the front door. The link below gives a very interesting, detailed history, including an old photo of the church in 1980, before restoration. I would love to have seen it back then.
www.facebook.com/LethbridgeHistoricalSociety/posts/retlaw...
As well as the old ghost town, I also wanted to check on a favourite abandoned house - simple, old and leaning. It was a relief to find that it was still standing. When I had slowed down to take a few photos, a truck came from the opposite direction and stopped. I was delighted when the driver said she was the owner of the old house! So interesting. She gave me permission to go closer, with a warning that there are pit holes, so to be careful. I thanked her, but told her that I always take photos of old barns/houses from the road, anyway.
From there, I took more or less the same route home. Rather late in the season for wildflowers, but I was happy to spot one little cluster of Chicory growing at a road edge. Very few birds to be seen, too, apart from a few hawks, Horned Larks, and a Vesper Sparrow. Fortunately, I still had a little gas left in the gas tank. Always a concern when I do a long drive.
It was a great day. and my timing was good, as the other evening, we had a huge storm! Lots of rain, thunder, continuous lightning in all directions for quite a while. I have rarely seen a lightning storm like that.
Different forms of fluctuations of the terrestrial gravity field are observed by gravity experiments. For example, atmospheric pressure fluctuations generate a gravity-noise foreground in measurements with super-conducting gravimeters. Gravity changes caused by high-magnitude earthquakes have been detected with the satellite gravity experiment GRACE, and we expect high-frequency terrestrial gravity fluctuations produced by ambient seismic fields to limit the sensitivity of ground-based gravitational-wave (GW) detectors. Accordingly, terrestrial gravity fluctuations are considered noise and signal depending on the experiment. Here, we will focus on ground-based gravimetry. This field is rapidly progressing through the development of GW detectors. The technology is pushed to its current limits in the advanced generation of the LIGO and Virgo detectors, targeting gravity strain sensitivities better than 10−23 Hz−1/2 above a few tens of a Hz. Alternative designs for GW detectors evolving from traditional gravity gradiometers such as torsion bars, atom interferometers, and superconducting gradiometers are currently being developed to extend the detection band to frequencies below 1 Hz. The goal of this article is to provide the analytical framework to describe terrestrial gravity perturbations in these experiments. Models of terrestrial gravity perturbations related to seismic fields, atmospheric disturbances, and vibrating, rotating or moving objects, are derived and analyzed. The models are then used to evaluate passive and active gravity noise mitigation strategies in GW detectors, or alternatively, to describe their potential use in geophysics. The article reviews the current state of the field, and also presents new analyses especially with respect to the impact of seismic scattering on gravity perturbations, active gravity noise cancellation, and time-domain models of gravity perturbations from atmospheric and seismic point sources. Our understanding of terrestrial gravity fluctuations will have great impact on the future development of GW detectors and high-precision gravimetry in general, and many open questions need to be answered still as emphasized in this article.
Keywords: Terrestrial gravity, Newtonian noise, Wiener filter, Mitigation
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Introduction
In the coming years, we will see a transition in the field of high-precision gravimetry from observations of slow lasting changes of the gravity field to the experimental study of fast gravity fluctuations. The latter will be realized by the advanced generation of the US-based LIGO [1] and Europe-based Virgo [7] gravitational-wave (GW) detectors. Their goal is to directly observe for the first time GWs that are produced by astrophysical sources such as inspiraling and merging neutron-star or black-hole binaries. Feasibility of the laser-interferometric detector concept has been demonstrated successfully with the first generation of detectors, which, in addition to the initial LIGO and Virgo detectors, also includes the GEO600 [119] and TAMA300 [161] detectors, and several prototypes around the world. The impact of these projects onto the field is two-fold. First of all, the direct detection of GWs will be a milestone in science opening a new window to our universe, and marking the beginning of a new era in observational astronomy. Second, several groups around the world have already started to adapt the technology to novel interferometer concepts [60, 155], with potential applications not only in GW science, but also geophysics. The basic measurement scheme is always the same: the relative displacement of test masses is monitored by using ultra-stable lasers. Progress in this field is strongly dependent on how well the motion of the test masses can be shielded from the environment. Test masses are placed in vacuum and are either freely falling (e.g., atom clouds [137]), or suspended and seismically isolated (e.g., high-quality glass or crystal mirrors as used in all of the detectors listed above). The best seismic isolations realized so far are effective above a few Hz, which limits the frequency range of detectable gravity fluctuations. Nonetheless, low-frequency concepts are continuously improving, and it is conceivable that future detectors will be sufficiently sensitive to detect GWs well below a Hz [88].
Terrestrial gravity perturbations were identified as a potential noise source already in the first concept laid out for a laser-interferometric GW detector [171]. Today, this form of noise is known as “terrestrial gravitational noise”, “Newtonian noise”, or “gravity-gradient noise”. It has never been observed in GW detectors, but it is predicted to limit the sensitivity of the advanced GW detectors at low frequencies. The most important source of gravity noise comes from fluctuating seismic fields [151]. Gravity perturbations from atmospheric disturbances such as pressure and temperature fluctuations can become significant at lower frequencies [51]. Anthropogenic sources of gravity perturbations are easier to avoid, but could also be relevant at lower frequencies [163]. Today, we only have one example of a direct observation of gravity fluctuations, i.e., from pressure fluctuations of the atmosphere in high-precision gravimeters [128]. Therefore, almost our entire understanding of gravity fluctuations is based on models. Nonetheless, potential sensitivity limits of future large-scale GW detectors need to be identified and characterized well in advance, and so there is a need to continuously improve our understanding of terrestrial gravity noise. Based on our current understanding, the preferred option is to construct future GW detectors underground to avoid the most dominant Newtonian-noise contributions. This choice was made for the next-generation Japanese GW detector KAGRA, which is currently being constructed underground at the Kamioka site [17], and also as part of a design study for the Einstein Telescope in Europe [140, 139]. While the benefit from underground construction with respect to gravity noise is expected to be substantial in GW detectors sensitive above a few Hz [27], it can be argued that it is less effective at lower frequencies [88].
Alternative mitigation strategies includes coherent noise cancellation [42]. The idea is to monitor the sources of gravity perturbations using auxiliary sensors such as microphones and seismometers, and to use their data to generate a coherent prediction of gravity noise. This technique is successfully applied in gravimeters to reduce the foreground of atmospheric gravity noise using collocated pressure sensors [128]. It is also noteworthy that the models of the atmospheric gravity noise are consistent with observations. This should give us some confidence at least that coherent Newtonian-noise cancellation can also be achieved in GW detectors. It is evident though that a model-based prediction of the performance of coherent noise cancellation schemes is prone to systematic errors as long as the properties of the sources are not fully understood. Ongoing experiments at the Sanford Underground Research Facility with the goal to characterize seismic fields in three dimensions are expected to deliver first data from an underground seismometer array in 2015 (see [89] for results from an initial stage of the experiment). While most people would argue that constructing GW detectors underground is always advantageous, it is still necessary to estimate how much is gained and whether the science case strongly profits from it. This is a complicated problem that needs to be answered as part of a site selection process.
More recently, high-precision gravity strainmeters have been considered as monitors of geophysical signals [83]. Analytical models have been calculated, which allow us to predict gravity transients from seismic sources such as earthquakes. It was suggested to implement gravity strainmeters in existing earthquake-early warning systems to increase warning times. It is also conceivable that an alternative method to estimate source parameters using gravity signals will improve our understanding of seismic sources. Potential applications must still be investigated in greater detail, but the study already demonstrates that the idea to use GW technology to realize new geophysical sensors seems feasible. As explained in [49], gravitational forces start to dominate the dynamics of seismic phenomena below about 1 mHz (which coincides approximately with a similar transition in atmospheric dynamics where gravity waves start to dominate over other forms of oscillations [164]). Seismic isolation would be ineffective below 1 mHz since the gravitational acceleration of a test mass produced by seismic displacement becomes comparable to the seismic acceleration itself. Therefore, we claim that 10 mHz is about the lowest frequency at which ground-based gravity strainmeters will ever be able to detect GWs, and consequently, modelling terrestrial gravity perturbations in these detectors can focus on frequencies above 10 mHz.
This article is divided into six main sections. Section 2 serves as an introduction to gravity measurements focussing on the response mechanisms and basic properties of gravity sensors. Section 3 describes models of gravity perturbations from ambient seismic fields. The results can be used to estimate noise spectra at the surface and underground. A subsection is devoted to the problem of noise estimation in low-frequency GW detectors, which differs from high-frequency estimates mostly in that gravity perturbations are strongly correlated between different test masses. In the low-frequency regime, the gravity noise is best described as gravity-gradient noise. Section 4 is devoted to time domain models of transient gravity perturbations from seismic point sources. The formalism is applied to point forces and shear dislocations. The latter allows us to estimate gravity perturbations from earthquakes. Atmospheric models of gravity perturbations are presented in Section 5. This includes gravity perturbations from atmospheric temperature fields, infrasound fields, shock waves, and acoustic noise from turbulence. The solution for shock waves is calculated in time domain using the methods of Section 4. A theoretical framework to calculate gravity perturbations from objects is given in Section 6. Since many different types of objects can be potential sources of gravity perturbations, the discussion focusses on the development of a general method instead of summarizing all of the calculations that have been done in the past. Finally, Section 7 discusses possible passive and active noise mitigation strategies. Due to the complexity of the problem, most of the section is devoted to active noise cancellation providing the required analysis tools and showing limitations of this technique. Site selection is the main topic under passive mitigation, and is discussed in the context of reducing environmental noise and criteria relevant to active noise cancellation. Each of these sections ends with a summary and a discussion of open problems. While this article is meant to be a review of the current state of the field, it also presents new analyses especially with respect to the impact of seismic scattering on gravity perturbations (Sections 3.3.2 and 3.3.3), active gravity noise cancellation (Section 7.1.3), and timedomain models of gravity perturbations from atmospheric and seismic point sources (Sections 4.1, 4.5, and 5.3).
Even though evident to experts, it is worth emphasizing that all calculations carried out in this article have a common starting point, namely Newton’s universal law of gravitation. It states that the attractive gravitational force equation M1 between two point masses m1, m2 is given by
equation M21
where G = 6.672 × 10−11 N m2/kg2 is the gravitational constant. Eq. (1) gives rise to many complex phenomena on Earth such as inner-core oscillations [156], atmospheric gravity waves [157], ocean waves [94, 177], and co-seismic gravity changes [122]. Due to its importance, we will honor the eponym by referring to gravity noise as Newtonian noise in the following. It is thereby clarified that the gravity noise models considered in this article are non-relativistic, and propagation effects of gravity changes are neglected. While there could be interesting scenarios where this approximation is not fully justified (e.g., whenever a gravity perturbation can be sensed by several sensors and differences in arrival times can be resolved), it certainly holds in any of the problems discussed in this article. We now invite the reader to enjoy the rest of the article, and hope that it proves to be useful.
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Gravity Measurements
In this section, we describe the relevant mechanisms by which a gravity sensor can couple to gravity perturbations, and give an overview of the most widely used measurement schemes: the (relative) gravimeter [53, 181], the gravity gradiometer [125], and the gravity strainmeter. The last category includes the large-scale GW detectors Virgo [6], LIGO [91], GEO600 [119], KAGRA [17], and a new generation of torsion-bar antennas currently under development [13]. Also atom interferometers can potentially be used as gravity strainmeters in the future [62]. Strictly speaking, none of the sensors only responds to a single field quantity (such as changes in gravity acceleration or gravity strain), but there is always a dominant response mechanism in each case, which justifies to give the sensor a specific name. A clear distinction between gravity gradiometers and gravity strainmeters has never been made to our knowledge. Therefore the sections on these two measurement principles will introduce a definition, and it is by no means the only possible one. Later on in this article, we almost exclusively discuss gravity models relevant to gravity strainmeters since the focus lies on gravity fluctuations above 10 mHz. Today, the sensitivity near 10 mHz of gravimeters towards gravity fluctuations is still competitive to or exceeds the sensitivity of gravity strainmeters, but this is likely going to change in the future so that we can expect strainmeters to become the technology of choice for gravity observations above 10 mHz [88]. The following sections provide further details on this statement. Space-borne gravity experiments such as GRACE [167] will not be included in this overview. The measurement principle of GRACE is similar to that of gravity strainmeters, but only very slow changes of Earth gravity field can be observed, and for this reason it is beyond the scope of this article.
The different response mechanisms to terrestrial gravity perturbations are summarized in Section 2.1. While we will identify the tidal forces acting on the test masses as dominant coupling mechanism, other couplings may well be relevant depending on the experiment. The Shapiro time delay will be discussed as the only relativistic effect. Higher-order relativistic effects are neglected. All other coupling mechanisms can be calculated using Newtonian theory including tidal forces, coupling in static non-uniform gravity fields, and coupling through ground displacement induced by gravity fluctuations. In Sections 2.2 to 2.4, the different measurement schemes are explained including a brief summary of the sensitivity limitations (choosing one of a few possible experimental realizations in each case). As mentioned before, we will mostly develop gravity models relevant to gravity strainmeters in the remainder of the article. Therefore, the detailed discussion of alternative gravimetry concepts mostly serves to highlight important differences between these concepts, and to develop a deeper understanding of the instruments and their role in gravity measurements.
Gravity response mechanisms
Gravity acceleration and tidal forces We will start with the simplest mechanism of all, the acceleration of a test mass in the gravity field. Instruments that measure the acceleration are called gravimeters. A test mass inside a gravimeter can be freely falling such as atom clouds [181] or, as suggested as possible future development, even macroscopic objects [72]. Typically though, test masses are supported mechanically or magnetically constraining motion in some of its degrees of freedom. A test mass suspended from strings responds to changes in the horizontal gravity acceleration. A test mass attached at the end of a cantilever with horizontal equilibrium position responds to changes in vertical gravity acceleration. The support fulfills two purposes. First, it counteracts the static gravitational force in a way that the test mass can respond to changes in the gravity field along a chosen degree of freedom. Second, it isolates the test mass from vibrations. Response to signals and isolation performance depend on frequency. If the support is modelled as a linear, harmonic oscillator, then the test mass response to gravity changes extends over all frequencies, but the response is strongly suppressed below the oscillators resonance frequency. The response function between the gravity perturbation δg(ω) and induced test mass acceleration δa(ω) assumes the form
equation M32
where we have introduced a viscous damping parameter γ, and ω0 is the resonance frequency. Well below resonance, the response is proportional to ω2, while it is constant well above resonance. Above resonance, the supported test mass responds like a freely falling mass, at least with respect to “soft” directions of the support. The test-mass response to vibrations δα(ω) of the support is given by
equation M43
This applies for example to horizontal vibrations of the suspension points of strings that hold a test mass, or to vertical vibrations of the clamps of a horizontal cantilever with attached test mass. Well above resonance, vibrations are suppressed by ω−2, while no vibration isolation is provided below resonance. The situation is somewhat more complicated in realistic models of the support especially due to internal modes of the mechanical system (see for example [76]), or due to coupling of degrees of freedom [121]. Large mechanical support structures can feature internal resonances at relatively low frequencies, which can interfere to some extent with the desired performance of the mechanical support [173]. While Eqs. (2) and (3) summarize the properties of isolation and response relevant for this paper, details of the readout method can fundamentally impact an instrument’s response to gravity fluctuations and its susceptibility to seismic noise, as explained in Sections 2.2 to 2.4.
Next, we discuss the response to tidal forces. In Newtonian theory, tidal forces cause a relative acceleration δg12(ω) between two freely falling test masses according to
equation M54
where equation M6 is the Fourier amplitude of the gravity potential. The last equation holds if the distance r12 between the test masses is sufficiently small, which also depends on the frequency. The term equation M7 is called gravity-gradient tensor. In Newtonian approximation, the second time integral of this tensor corresponds to gravity strain equation M8, which is discussed in more detail in Section 2.4. Its trace needs to vanish in empty space since the gravity potential fulfills the Poisson equation. Tidal forces produce the dominant signals in gravity gradiometers and gravity strainmeters, which measure the differential acceleration or associated relative displacement between two test masses (see Sections 2.3 and 2.4). If the test masses used for a tidal measurement are supported, then typically the supports are designed to be as similar as possible, so that the response in Eq. (2) holds for both test masses approximately with the same parameter values for the resonance frequencies (and to a lesser extent also for the damping). For the purpose of response calibration, it is less important to know the parameter values exactly if the signal is meant to be observed well above the resonance frequency where the response is approximately equal to 1 independent of the resonance frequency and damping (here, “well above” resonance also depends on the damping parameter, and in realistic models, the signal frequency also needs to be “well below” internal resonances of the mechanical support).
Shapiro time delay Another possible gravity response is through the Shapiro time delay [19]. This effect is not universally present in all gravity sensors, and depends on the readout mechanism. Today, the best sensitivities are achieved by reflecting laser beams from test masses in interferometric configurations. If the test mass is displaced by gravity fluctuations, then it imprints a phase shift onto the reflected laser, which can be observed in laser interferometers, or using phasemeters. We will give further details on this in Section 2.4. In Newtonian gravity, the acceleration of test masses is the only predicted response to gravity fluctuations. However, from general relativity we know that gravity also affects the propagation of light. The leading-order term is the Shapiro time delay, which produces a phase shift of the laser beam with respect to a laser propagating in flat space. It can be calculated from the weak-field spacetime metric (see chapter 18 in [124]):
equation M95
Here, c is the speed of light, ds is the so-called line element of a path in spacetime, and equation M10. Additionally, for this metric to hold, motion of particles in the source of the gravity potential responsible for changes of the gravity potential need to be much slower than the speed of light, and also stresses inside the source must be much smaller than its mass energy density. All conditions are fulfilled in the case of Earth gravity field. Light follows null geodesics with ds2 = 0. For the spacetime metric in Eq. (5), we can immediately write
equation M116
As we will find out, this equation can directly be used to calculate the time delay as an integral along a straight line in terms of the coordinates equation M12, but this is not immediately clear since light bends in a gravity field. So one may wonder if integration along the proper light path instead of a straight line yields additional significant corrections. The so-called geodesic equation must be used to calculate the path. It is a set of four differential equations, one for each coordinate t, equation M13 in terms of a parameter λ. The weak-field geodesic equation is obtained from the metric in Eq. (5):
equation M147
where we have made use of Eq. (6) and the slow-motion condition equation M15. The coordinates equation M16 are to be understood as functions of λ. Since the deviation of a straight path is due to a weak gravity potential, we can solve these equations by perturbation theory introducing expansions equation M17 and t = t(0) +t(1) + …. The superscript indicates the order in ψ/c2. The unperturbed path has the simple parametrization
equation M188
We have chosen integration constants such that unperturbed time t(0) and parameter λ can be used interchangeably (apart from a shift by t0). Inserting these expressions into the right-hand side of Eq. (7), we obtain
equation M199
As we can see, up to linear order in equation M20, the deviation equation M21 is in orthogonal direction to the unperturbed path equation M22, which means that the deviation can be neglected in the calculation of the time delay. After some transformations, it is possible to derive Eq. (6) from Eq. (9), and this time we find explicitly that the right-hand-side of the equation only depends on the unperturbed coordinates1. In other words, we can integrate the time delay along a straight line as defined in Eq. (8), and so the total phase integrated over a travel distance L is given by
equation M2310
In static gravity fields, the phase shift doubles if the light is sent back since not only the direction of integration changes, but also the sign of the expression substituted for dt/dλ.
Gravity induced ground motion As we will learn in Section 3, seismic fields produce gravity perturbations either through density fluctuations of the ground, or by displacing interfaces between two materials of different density. It is also well-known in seismology that seismic fields can be affected significantly by self-gravity. Self-gravity means that the gravity perturbation produced by a seismic field acts back on the seismic field. The effect is most significant at low frequency where gravity induced acceleration competes against acceleration from elastic forces. In seismology, low-frequency seismic fields are best described in terms of Earth’s normal modes [55]. Normal modes exist as toroidal modes and spheroidal modes. Spheroidal modes are influenced by self-gravity, toroidal modes are not. For example, predictions of frequencies and shapes of spheroidal modes based on Earth models such as PREM (Preliminary Reference Earth Model) [68] are inaccurate if self-gravity effects are excluded. What this practically means is that in addition to displacement amplitudes, gravity becomes a dynamical variable in the elastodynamic equations that determine the normal-mode properties. Therefore, seismic displacement and gravity perturbation cannot be separated in normal-mode formalism (although self-gravity can be neglected in calculations of spheroidal modes at sufficiently high frequency).
In certain situations, it is necessary or at least more intuitive to separate gravity from seismic fields. An exotic example is Earth’s response to GWs [67, 49, 47, 30, 48]. Another example is the seismic response to gravity perturbations produced by strong seismic events at large distance to the source as described in Section 4. It is more challenging to analyze this scenario using normal-mode formalism. The sum over all normal modes excited by the seismic event (each of which describing a global displacement field) must lead to destructive interference of seismic displacement at large distances (where seismic waves have not yet arrived), but not of the gravity amplitudes since gravity is immediately perturbed everywhere. It can be easier to first calculate the gravity perturbation from the seismic perturbation, and then to calculate the response of the seismic field to the gravity perturbation at larger distance. This method will be adopted in this section. Gravity fields will be represented as arbitrary force or tidal fields (detailed models are presented in later sections), and we simply calculate the response of the seismic field. Normal-mode formalism can be avoided only at sufficiently high frequencies where the curvature of Earth does not significantly influence the response (i.e., well above 10 mHz). In this section, we will model the ground as homogeneous half space, but also more complex geologies can in principle be assumed.
Gravity can be introduced in two ways into the elastodynamic equations, as a conservative force −∇ψ [146, 169], or as tidal strain The latter method was described first by Dyson to calculate Earth’s response to GWs [67]. The approach also works for Newtonian gravity, with the difference that the tidal field produced by a GW is necessarily a quadrupole field with only two degrees of freedom (polarizations), while tidal fields produced by terrestrial sources are less constrained. Certainly, GWs can only be fully described in the framework of general relativity, which means that their representation as a Newtonian tidal field cannot be used to explain all possible observations [124]. Nonetheless, important here is that Dyson’s method can be extended to Newtonian tidal fields. Without gravity, the elastodynamic equations for small seismic displacement can be written as
equation M2411
where equation M25 is the seismic displacement field, and equation M26 is the stress tensor [9]. In the absence of other forces, the stress is determined by the seismic field. In the case of a homogeneous and isotropic medium, the stress tensor for small seismic displacement can be written as
equation M2712
The quantity equation M28 is known as seismic strain tensor, and λ, μ are the Lamé constants (see Section 3.1). Its trace is equal to the divergence of the displacement field. Dyson introduced the tidal field from first principles using Lagrangian mechanics, but we can follow a simpler approach. Eq. (12) means that a stress field builds up in response to a seismic strain field, and the divergence of the stress field acts as a force producing seismic displacement. The same happens in response to a tidal field, which we represent as gravity strain equation M29. A strain field changes the distance between two freely falling test masses separated by equation M30 by equation M312. For sufficiently small distances L, the strain field can be substituted by the second time integral of the gravity-gradient tensor equation M32. If the masses are not freely falling, then the strain field acts as an additional force. The corresponding contribution to the material’s stress tensor can be written
equation M3313
Since we assume that the gravity field is produced by a distant source, the local contribution to gravity perturbations is neglected, which means that the gravity potential obeys the Laplace equation, equation M34. Calculating the divergence of the stress tensor according to Eq. (11), we find that the gravity term vanishes! This means that a homogeneous and isotropic medium does not respond to gravity strain fields. However, we have to be more careful here. Our goal is to calculate the response of a half-space to gravity strain. Even if the half-space is homogeneous, the Lamé constants change discontinuously across the surface. Hence, at the surface, the divergence of the stress tensor reads
equation M3514
In other words, tidal fields produce a force onto an elastic medium via gradients in the shear modulus (second Lamé constant). The gradient of the shear modulus can be written in terms of a Dirac delta function, equation M36, for a flat surface at z = 0 with unit normal vector equation M37. The response to gravity strain fields is obtained applying the boundary condition of vanishing surface traction, equation M38:
equation M3915
Once the seismic strain field is calculated, it can be used to obtain the seismic stress, which determines the displacement field equation M40 according to Eq. (11). In this way, one can for example calculate that a seismometer or gravimeter can observe GWs by monitoring surface displacement as was first calculated by Dyson [67].
Coupling in non-uniform, static gravity fields If the gravity field is static, but non-uniform, then displacement equation M41 of the test mass in this field due to a non-gravitational fluctuating force is associated with a changing gravity acceleration according to
equation M4216
We introduce a characteristic length λ, over which gravity acceleration varies significantly. Hence, we can rewrite the last equation in terms of the associated test-mass displacement ζ
equation M4317
where we have neglected directional dependence and numerical factors. The acceleration change from motion in static, inhomogeneous fields is generally more significant at low frequencies. Let us consider the specific case of a suspended test mass. It responds to fluctuations in horizontal gravity acceleration. The test mass follows the motion of the suspension point in vertical direction (i.e., no seismic isolation), while seismic noise in horizontal direction is suppressed according to Eq. (3). Accordingly, it is possible that the unsuppressed vertical (z-axis) seismic noise ξz(t) coupling into the horizontal (x-axis) motion of the test mass through the term ∂xgz = ∂zgx dominates over the gravity response term in Eq. (2). Due to additional coupling mechanisms between vertical and horizontal motion in real seismic-isolation systems, test masses especially in GW detectors are also isolated in vertical direction, but without achieving the same noise suppression as in horizontal direction. For example, the requirements on vertical test-mass displacement for Advanced LIGO are a factor 1000 less stringent than on the horizontal displacement [22]. Requirements can be set on the vertical isolation by estimating the coupling of vertical motion into horizontal motion, which needs to take the gravity-gradient coupling of Eq. (16) into account. Although, because of the frequency dependence, gravity-gradient effects are more significant in low-frequency detectors, such as the space-borne GW detector LISA [154].
Next, we calculate an estimate of gravity gradients in the vicinity of test masses in large-scale GW detectors, and see if the gravity-gradient coupling matters compared to mechanical vertical-to-horizontal coupling.
One contribution to gravity gradients will come from the vacuum chamber surrounding the test mass. We approximate the shape of the chamber as a hollow cylinder with open ends (open ends just to simplify the calculation). In our calculation, the test mass can be offset from the cylinder axis and be located at any distance to the cylinder ends (we refer to this coordinate as height). The gravity field can be expressed in terms of elliptic integrals, but the explicit solution is not of concern here. Instead, let us take a look at the results in Figure Figure1.1. Gravity gradients ∂zgx vanish if the test mass is located on the symmetry axis or at height L/2. There are also two additional ∂zgx = 0 contour lines starting at the symmetry axis at heights ∼ 0.24 and ∼0.76. Let us assume that the test mass is at height 0.3L, a distance 0.05L from the cylinder axis, the total mass of the cylinder is M = 5000 kg, and the cylinder height is L = 4 m. In this case, the gravity-gradient induced vertical-to-horizontal coupling factor at 20 Hz is
equation M4418
This means that gravity-gradient induced coupling is extremely weak, and lies well below estimates of mechanical coupling (of order 0.001 in Advanced LIGO3). Even though the vacuum chamber was modelled with a very simple shape, and additional asymmetries in the mass distribution around the test mass may increase gravity gradients, it still seems very unlikely that the coupling would be significant. As mentioned before, one certainly needs to pay more attention when calculating the coupling at lower frequencies. The best procedure is of course to have a 3D model of the near test-mass infrastructure available and to use it for a precise calculation of the gravity-gradient field.
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Figure 1
Gravity gradients inside hollow cylinder. The total height of the cylinder is L, and M is its total mass. The radius of the cylinder is 0.3L. The axes correspond to the distance of the test mass from the symmetry axis of the cylinder, and its height above one of the cylinders ends. The plot on the right is simply a zoom of the left plot into the intermediate heights.
Gravimeters
Gravimeters are instruments that measure the displacement of a test mass with respect to a non-inertial reference rigidly connected to the ground. The test mass is typically supported mechanically or magnetically (atom-interferometric gravimeters are an exception), which means that the test-mass response to gravity is altered with respect to a freely falling test mass. We will use Eq. (2) as a simplified response model. There are various possibilities to measure the displacement of a test mass. The most widespread displacement sensors are based on capacitive readout, as for example used in superconducting gravimeters (see Figure Figure22 and [96]). Sensitive displacement measurements are in principle also possible with optical readout systems; a method that is (necessarily) implemented in atom-interferometric gravimeters [137], and prototype seismometers [34] (we will explain the distinction between seismometers and gravimeters below). As will become clear in Section 2.4, optical readout is better suited for displacement measurements over long baselines, as required for the most sensitive gravity strain measurements, while the capacitive readout should be designed with the smallest possible distance between the test mass and the non-inertial reference [104].
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Figure 2
Sketch of a levitated sphere serving as test mass in a superconducting gravimeter. Dashed lines indicate magnetic field lines. Coils are used for levitation and precise positioning of the sphere. Image reproduced with permission from [96]; copyright by Elsevier.
Let us take a closer look at the basic measurement scheme of a superconducting gravimeter shown in Figure Figure2.2. The central part is formed by a spherical superconducting shell that is levitated by superconducting coils. Superconductivity provides stability of the measurement, and also avoids some forms of noise (see [96] for details). In this gravimeter design, the lower coil is responsible mostly to balance the mean gravitational force acting on the sphere, while the upper coil modifies the magnetic gradient such that a certain “spring constant” of the magnetic levitation is realized. In other words, the current in the upper coil determines the resonance frequency in Eq. (2).
Capacitor plates are distributed around the sphere. Whenever a force acts on the sphere, the small signal produced in the capacitive readout is used to immediately cancel this force by a feedback coil. In this way, the sphere is kept at a constant location with respect to the external frame. This illustrates a common concept in all gravimeters. The displacement sensors can only respond to relative displacement between a test mass and a surrounding structure. If small gravity fluctuations are to be measured, then it is not sufficient to realize low-noise readout systems, but also vibrations of the surrounding structure forming the reference frame must be as small as possible. In general, as we will further explore in the coming sections, gravity fluctuations are increasingly dominant with decreasing frequency. At about 1 mHz, gravity acceleration associated with fluctuating seismic fields become comparable to seismic acceleration, and also atmospheric gravity noise starts to be significant [53]. At higher frequencies, seismic acceleration is much stronger than typical gravity fluctuations, which means that the gravimeter effectively operates as a seismometer. In summary, at sufficiently low frequencies, the gravimeter senses gravity accelerations of the test mass with respect to a relatively quiet reference, while at higher frequencies, the gravimeter senses seismic accelerations of the reference with respect to a test mass subject to relatively small gravity fluctuations. In superconducting gravimeters, the third important contribution to the response is caused by vertical motion ξ(t) of a levitated sphere against a static gravity gradient (see Section 2.1.4). As explained above, feedback control suppresses relative motion between sphere and gravimeter frame, which causes the sphere to move as if attached to the frame or ground. In the presence of a static gravity gradient ∂zgz, the motion of the sphere against this gradient leads to a change in gravity, which alters the feedback force (and therefore the recorded signal). The full contribution from gravitational, δa(t), and seismic, equation M45, accelerations can therefore be written
equation M4619
It is easy to verify, using Eqs. (2) and (3), that the relative amplitude of gravity and seismic fluctuations from the first two terms is independent of the test-mass support. Therefore, vertical seismic displacement of the reference frame must be considered fundamental noise of gravimeters and can only be avoided by choosing a quiet measurement site. Obviously, Eq. (19) is based on a simplified support model. One of the important design goals of the mechanical support is to minimize additional noise due to non-linearities and cross-coupling. As is explained further in Section 2.3, it is also not possible to suppress seismic noise in gravimeters by subtracting the disturbance using data from a collocated seismometer. Doing so inevitably turns the gravimeter into a gravity gradiometer.
Gravimeters target signals that typically lie well below 1 mHz. Mechanical or magnetic supports of test masses have resonance frequencies at best slightly below 10 mHz along horizontal directions, and typically above 0.1 Hz in the vertical direction [23, 174]4. Well below resonance frequency, the response function can be approximated as equation M47. At first, it may look as if the gravimeter should not be sensitive to very low-frequency fluctuations since the response becomes very weak. However, the strength of gravity fluctuations also strongly increases with decreasing frequency, which compensates the small response. It is clear though that if the resonance frequency was sufficiently high, then the response would become so weak that the gravity signal would not stand out above other instrumental noise anymore. The test-mass support would be too stiff. The sensitivity of the gravimeter depends on the resonance frequency of the support and the intrinsic instrumental noise. With respect to seismic noise, the stiffness of the support has no influence as explained before (the test mass can also fall freely as in atom interferometers).
For superconducting gravimeters of the Global Geodynamics Project (GGP) [52], the median spectra are shown in Figure Figure3.3. Between 0.1 mHz and 1 mHz, atmospheric gravity perturbations typically dominate, while instrumental noise is the largest contribution between 1 mHz and 5 mHz [96]. The smallest signal amplitudes that have been measured by integrating long-duration signals is about 10−12 m/s2. A detailed study of noise in superconducting gravimeters over a larger frequency range can be found in [145]. Note that in some cases, it is not fit to categorize seismic and gravity fluctuations as noise and signal. For example, Earth’s spherical normal modes coherently excite seismic and gravity fluctuations, and the individual contributions in Eq. (19) have to be understood only to accurately translate data into normal-mode amplitudes [55].
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Figure 3
Median spectra of superconducting gravimeters of the GGP. Image reproduced with permission from [48]; copyright by APS.
Gravity gradiometers
It is not the purpose of this section to give a complete overview of the different gradiometer designs. Gradiometers find many practical applications, for example in navigation and resource exploration, often with the goal to measure static or slowly changing gravity gradients, which do not concern us here. For example, we will not discuss rotating gradiometers, and instead focus on gradiometers consisting of stationary test masses. While the former are ideally suited to measure static or slowly changing gravity gradients with high precision especially under noisy conditions, the latter design has advantages when measuring weak tidal fluctuations. In the following, we only refer to the stationary design. A gravity gradiometer measures the relative acceleration between two test masses each responding to fluctuations of the gravity field [102, 125]. The test masses have to be located close to each other so that the approximation in Eq. (4) holds. The proximity of the test masses is used here as the defining property of gradiometers. They are therefore a special type of gravity strainmeter (see Section 2.4), which denotes any type of instrument that measures relative gravitational acceleration (including the even more general concept of measuring space-time strain).
Gravity gradiometers can be realized in two versions. First, one can read out the position of two test masses with respect to the same rigid, non-inertial reference. The two channels, each of which can be considered a gravimeter, are subsequently subtracted. This scheme is for example realized in dual-sphere designs of superconducting gravity gradiometers [90] or in atom-interferometric gravity gradiometers [159].
It is schematically shown in Figure Figure4.4. Let us first consider the dual-sphere design of a superconducting gradiometer. If the reference is perfectly stiff, and if we assume as before that there are no cross-couplings between degrees of freedom and the response is linear, then the subtraction of the two gravity channels cancels all of the seismic noise, leaving only the instrumental noise and the differential gravity signal given by the second line of Eq. (4). Even in real setups, the reduction of seismic noise can be many orders of magnitude since the two spheres are close to each other, and the two readouts pick up (almost) the same seismic noise [125]. This does not mean though that gradiometers are necessarily more sensitive instruments to monitor gravity fields. A large part of the gravity signal (the common-mode part) is subtracted together with the seismic noise, and the challenge is now passed from finding a seismically quiet site to developing an instrument with lowest possible intrinsic noise.
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Figure 4
Basic scheme of a gravity gradiometer for measurements along the vertical direction. Two test masses are supported by horizontal cantilevers (superconducting magnets, …). Acceleration of both test masses is measured against the same non-inertial reference frame, which is connected to the ground. Each measurement constitutes one gravimeter. Subtraction of the two channels yields a gravity gradiometer.
The atom-interferometric gradiometer differs in some important details from the superconducting gradiometer. The test masses are realized by ultracold atom clouds, which are (nearly) freely falling provided that magnetic shielding of the atoms is sufficient, and interaction between atoms can be neglected. Interactions of a pair of atom clouds with a laser beam constitute the basic gravity gradiometer scheme. Even though the test masses are freely falling, the readout is not generally immune to seismic noise [80, 18]. The laser beam interacting with the atom clouds originates from a source subject to seismic disturbances, and interacts with optics that require seismic isolation. Schemes have been proposed that could lead to a large reduction of seismic noise [178, 77], but their effectiveness has not been tested in experiments yet. Since the differential position (or tidal) measurement is performed using a laser beam, the natural application of atom-interferometer technology is as gravity strainmeter (as explained before, laser beams are favorable for differential position measurements over long baselines). Nonetheless, the technology is currently insufficiently developed to realize large-baseline experiments, and we can therefore focus on its application in gradiometry. Let us take a closer look at the response of atom-interferometric gradiometers to seismic noise. In atom-interferometric detectors (excluding the new schemes proposed in [178, 77]), one can show that seismic acceleration δα(ω) of the optics or laser source limits the sensitivity of a tidal measurement according to
equation M4820
where L is the separation of the two atom clouds, and is the speed of light. It should be emphasized that the seismic noise remains, even if all optics and the laser source are all linked to the same infinitely stiff frame. In addition to this noise term, other coupling mechanisms may play a role, which can however be suppressed by engineering efforts. The noise-reduction factor ωL/c needs to be compared with the common-mode suppression of seismic noise in superconducting gravity gradiometers, which depends on the stiffness of the instrument frame, and on contamination from cross coupling of degrees-of-freedom. While the seismic noise in Eq. (20) is a fundamental noise contribution in (conventional) atom-interferometric gradiometers, the noise suppression in superconducting gradiometers depends more strongly on the engineering effort (at least, we venture to claim that common-mode suppression achieved in current instrument designs is well below what is fundamentally possible).
To conclude this section, we discuss in more detail the connection between gravity gradiometers and seismically (actively or passively) isolated gravimeters. As we have explained in Section 2.2, the sensitivity limitation of gravimeters by seismic noise is independent of the mechanical support of the test mass (assuming an ideal, linear support). The main purpose of the mechanical support is to maximize the response of the test mass to gravity fluctuations, and thereby increase the signal with respect to instrumental noise other than seismic noise. Here we will explain that even a seismic isolation of the gravimeter cannot overcome this noise limitation, at least not without fundamentally changing its response to gravity fluctuations. Let us first consider the case of a passively seismically isolated gravimeter. For example, we can imagine that the gravimeter is suspended from the tip of a strong horizontal cantilever. The system can be modelled as two oscillators in a chain, with a light test mass m supported by a heavy mass M representing the gravimeter (reference) frame, which is itself supported from a point rigidly connected to Earth. The two supports are modelled as harmonic oscillators. As before, we neglect cross coupling between degrees of freedom. Linearizing the response of the gravimeter frame and test mass for small accelerations, and further neglecting terms proportional to m/M, one finds the gravimeter response to gravity fluctuations:
equation M4921
Here, ω1, γ1 are the resonance frequency and damping of the gravimeter support, while ω2, γ2 are the resonance frequency and damping of the test-mass support. The response and isolation functions R(·), S(·) are defined in Eqs. (2) and (3). Remember that Eq. (21) is obtained as a differential measurement of test-mass acceleration versus acceleration of the reference frame. Therefore, δg1(ω) denotes the gravity fluctuation at the center-of-mass of the gravimeter frame, and δg2(ω) at the test mass. An infinitely stiff gravimeter suspension, ω1 → ∞, yields R(ω; ω1, γ1) = 0, and the response turns into the form of the non-isolated gravimeter. The seismic isolation is determined by
equation M5022
We can summarize the last two equations as follows. At frequencies well above ω1, the seismically isolated gravimeter responds like a gravity gradiometer, and seismic noise is strongly suppressed. The deviation from the pure gradiometer response ∼ δg2(ω) − δg1(ω) is determined by the same function S(ω; ω1, γ1) that describes the seismic isolation. In other words, if the gravity gradient was negligible, then we ended up with the conventional gravimeter response, with signals suppressed by the seismic isolation function. Well below ω1, the seismically isolated gravimeter responds like a conventional gravimeter without seismic-noise reduction. If the centers of the masses m (test mass) and M (reference frame) coincide, and therefore δg1(ω) = δg2(ω), then the response is again like a conventional gravimeter, but this time suppressed by the isolation function S(ω; ω1, γ1).
Let us compare the passively isolated gravimeter with an actively isolated gravimeter. In active isolation, the idea is to place the gravimeter on a stiff platform whose orientation can be controlled by actuators. Without actuation, the platform simply follows local surface motion. There are two ways to realize an active isolation. One way is to place a seismometer next to the platform onto the ground, and use its data to subtract ground motion from the platform. The actuators cancel the seismic forces. This scheme is called feed-forward noise cancellation. Feed-forward cancellation of gravity noise is discussed at length in Section 7.1, which provides details on its implementation and limitations. The second possibility is to place the seismometer together with the gravimeter onto the platform, and to suppress seismic noise in a feedback configuration [4, 2]. In the following, we discuss the feed-forward technique as an example since it is easier to analyze (for example, feedback control can be unstable [4]). As before, we focus on gravity and seismic fluctuations. The seismometer’s intrinsic noise plays an important role in active isolation limiting its performance, but we are only interested in the modification of the gravimeter’s response. Since there is no fundamental difference in how a seismometer and a gravimeter respond to seismic and gravity fluctuations, we know from Section 2.2 that the seismometer output is proportional to δg1(ω) − δα(ω), i.e., using a single test mass for acceleration measurements, seismic and gravity perturbations contribute in the same way. A transfer function needs to be multiplied to the acceleration signals, which accounts for the mechanical support and possibly also electronic circuits involved in the seismometer readout. To cancel the seismic noise of the platform that carries the gravimeter, the effect of all transfer functions needs to be reversed by a matched feed-forward filter. The output of the filter is then equal to δg1(ω) − δα(ω) and is added to the motion of the platform using actuators cancelling the seismic noise and adding the seismometer’s gravity signal. In this case, the seismometer’s gravity signal takes the place of the seismic noise in Eq. (3). The complete gravity response of the actively isolated gravimeter then reads
equation M5123
The response is identical to a gravity gradiometer, where ω2, γ2 are the resonance frequency and damping of the gravimeter’s test-mass support. In reality, instrumental noise of the seismometer will limit the isolation performance and introduce additional noise into Eq. (23). Nonetheless, Eqs. (21) and (23) show that any form of seismic isolation turns a gravimeter into a gravity gradiometer at frequencies where seismic isolation is effective. For the passive seismic isolation, this means that the gravimeter responds like a gradiometer at frequencies well above the resonance frequency ω1 of the gravimeter support, while it behaves like a conventional gravimeter below ω1. From these results it is clear that the design of seismic isolations and the gravity response can in general not be treated independently. As we will see in Section 2.4 though, tidal measurements can profit strongly from seismic isolation especially when common-mode suppression of seismic noise like in gradiometers is insufficient or completely absent.
Gravity strainmeters
Gravity strain is an unusual concept in gravimetry that stems from our modern understanding of gravity in the framework of general relativity. From an observational point of view, it is not much different from elastic strain. Fluctuating gravity strain causes a change in distance between two freely falling test masses, while seismic or elastic strain causes a change in distance between two test masses bolted to an elastic medium. It should be emphasized though that we cannot always use this analogy to understand observations of gravity strain [106]. Fundamentally, gravity strain corresponds to a perturbation of the metric that determines the geometrical properties of spacetime [124]. We will briefly discuss GWs, before returning to a Newtonian description of gravity strain.
Gravitational waves are weak perturbations of spacetime propagating at the speed of light. Freely falling test masses change their distance in the field of a GW. When the length of the GW is much larger than the separation between the test masses, it is possible to interpret this change as if caused by a Newtonian force. We call this the long-wavelength regime. Since we are interested in the low-frequency response of gravity strainmeters throughout this article (i.e., frequencies well below 100 Hz), this condition is always fulfilled for Earth-bound experiments. The effect of a gravity-strain field equation M52 on a pair of test masses can then be represented as an equivalent Newtonian tidal field
equation M5324
Here, equation M54 is the relative acceleration between two freely falling test masses, L is the distance between them, and equation M55 is the unit vector pointing from one to the other test mass, and equation M56 its transpose. As can be seen, the gravity-strain field is represented by a 3 × 3 tensor. It contains the space-components of a 4-dimensional metric perturbation of spacetime, and determines all properties of GWs5. Note that the strain amplitude h in Eq. (24) needs to be multiplied by 2 to obtain the corresponding amplitude of the metric perturbation (e.g., the GW amplitude). Throughout this article, we define gravity strain as h = ΔL/L, while the effect of a GW with amplitude aGW on the separation of two test mass is determined by aGW = 2ΔL/L.
The strain field of a GW takes the form of a quadrupole oscillation with two possible polarizations commonly denoted × (cross)-polarization and +(plus)-polarization. The arrows in Figure Figure55 indicate the lines of the equivalent tidal field of Eq. (24).
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Figure 5
Polarizations of a gravitational wave.
Consequently, to (directly) observe GWs, one can follow two possible schemes: (1) the conventional method, which is a measurement of the relative displacement of suspended test masses typically carried out along two perpendicular baselines (arms); and (2) measurement of the relative rotation between two suspended bars. Figure Figure66 illustrates the two cases. In either case, the response of a gravity strainmeter is obtained by projecting the gravity strain tensor onto a combination of two unit vectors, equation M57 and equation M58, that characterize the orientation of the detector, such as the directions of two bars in a rotational gravity strain meter, or of two arms of a conventional gravity strain meter. This requires us to define two different gravity strain projections. The projection for the rotational strain measurement is given by
equation M5925
where the subscript × indicates that the detector responds to the ×-polarization assuming that the x, y-axes (see Figure Figure5)5) are oriented along two perpendicular bars. The vectors equation M60 and equation M61 are rotated counter-clockwise by 90° with respect to equation M62 and equation M63. In the case of perpendicular bars equation M64 and equation M65. The corresponding projection for the conventional gravity strain meter reads
equation M6626
The subscript + indicates that the detector responds to the +-polarization provided that the x, y-axes are oriented along two perpendicular baselines (arms) of the detector. The two schemes are shown in Figure Figure6.6. The most sensitive GW detectors are based on the conventional method, and distance between test masses is measured by means of laser interferometry. The LIGO and Virgo detectors have achieved strain sensitivities of better than 10−22 Hz−1/2 between about 50 Hz and 1000 Hz in past science runs and are currently being commissioned in their advanced configurations [91, 7]. The rotational scheme is realized in torsion-bar antennas, which are considered as possible technology for sub-Hz GW detection [155, 69]. However, with achieved strain sensitivity of about 10−8 Hz−1/2 near 0.1 Hz, the torsion-bar detectors are far from the sensitivity we expect to be necessary for GW detection [88].
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Figure 6
Sketches of the relative rotational and displacement measurement schemes.
Let us now return to the discussion of the previous sections on the role of seismic isolation and its impact on gravity response. Gravity strainmeters profit from seismic isolation more than gravimeters or gravity gradiometers. We have shown in Section 2.2 that seismically isolated gravimeters are effectively gravity gradiometers. So in this case, seismic isolation changes the response of the instrument in a fundamental way, and it does not make sense to talk of seismically isolated gravimeters. Seismic isolation could in principle be beneficial for gravity gradiometers (i.e., the acceleration of two test masses is measured with respect to a common rigid, seismically isolated reference frame), but the common-mode rejection of seismic noise (and gravity signals) due to the differential readout is typically so high that other instrumental noise becomes dominant. So it is possible that some gradiometers would profit from seismic isolation, but it is not generally true. Let us now consider the case of a gravity strainmeter. As explained in Section 2.3, we distinguish gradiometers and strainmeters by the distance of their test masses. For example, the distance of the LIGO or Virgo test masses is 4 km and 3 km respectively. Seismic noise and terrestrial gravity fluctuations are insignificantly correlated between the two test masses within the detectors’ most sensitive frequency band (above 10 Hz). Therefore, the approximation in Eq. (4) does not apply. Certainly, the distinction between gravity gradiometers and strainmeters remains somewhat arbitrary since at any frequency the approximation in Eq. (4) can hold for one type of gravity fluctuation, while it does not hold for another. Let us adopt a more practical definition at this point. Whenever the design of the instrument places the test masses as distant as possible from each other given current technology, then we call such an instrument strainmeter. In the following, we will discuss seismic isolation and gravity response for three strainmeter designs, the laser-interferometric, atom-interferometric, and superconducting strainmeters. It should be emphasized that the atom-interferometric and superconducting concepts are still in the beginning of their development and have not been realized yet with scientifically interesting sensitivities.
Laser-interferometric strainmeters The most sensitive gravity strainmeters, namely the large-scale GW detectors, use laser interferometry to read out the relative displacement between mirror pairs forming the test masses. Each test mass in these detectors is suspended from a seismically isolated platform, with the suspension itself providing additional seismic isolation. Section 2.1.1 introduced a simplified response and isolation model based on a harmonic oscillator characterized by a resonance frequency ω0 and viscous damping γ6. In a multi-stage isolation and suspension system as realized in GW detectors (see for example [37, 121]), coupling between multiple oscillators cannot be neglected, and is fundamental to the seismic isolation performance, but the basic features can still be explained with the simplified isolation and response model of Eqs. (2) and (3). The signal output of the interferometer is proportional to the relative displacement between test masses. Since seismic noise is approximately uncorrelated between two distant test masses, the differential measurement itself cannot reject seismic noise as in gravity gradiometers. Without seismic isolation, the dominant signal would be seismic strain, i.e., the distance change between test masses due to elastic deformation of the ground, with a value of about 10−15 Hz−1/2 at 50 Hz (assuming kilometer-scale arm lengths). At the same time, without seismically isolated test masses, the gravity signal can only come from the ground response to gravity fluctuations as described in Section 2.1.3, and from the Shapiro time delay as described in Section 2.1.2.
Lighting: One CL-600 in a 120cm Jinbei BD w/ diffusion. I'm standing in front of the light.
First off... I like creating tension. The tension created by the man looking out of the frame and not being on the same plane as the main subject appeals to me.
This couple contacts me and says that they're getting married in December. They want to know if I'll do a couple's shoot. I decline... not really my thing. They are very persistent though and tell me how much they admire my photography. I finally tell them to come in for individual quick sessions. At the end of their individual sessions I told them we would "try" a few shots of the couple but stated very clearly that they shouldn't expect anything.
I thought about it for a couple of days. How can I make this different? I don't want them to be holding hands or gazing into each other's eyes... let the other photogs do that mess.
I had this idea to integrate my close-up headshot style into their shoot. I told Jeevan to stand in the back and look out of frame. I got Vinnie to do her thing with the camera. I even told them that Jeevan would be out of focus. They were all for it.
We took a few frames and when they looked at them they were floored. They enjoyed just how different it was. They stated that in India (where they'll wed) they will have to do silly stuff... like holding hands and gazing into each other's eyes. They ended up extremely happy.
Adding on the morning of 19 May 2021: just had a quick look at our weather forecast and I see that snow flurries are expected tonight, with scattered flurries tomorrow and wet snow for Friday. All my windows and door are being removed and reinstalled on Friday! If the snow does arrive, I wonder if the repair work will still continue. Typical Calgary, our high just four days ago was 24C. This morning, our temperature is 6C (windchill 3C). Sunrise is at 5:40 am and sunset is at 9:25 pm.
Tuesday, 18 May 2021: our temperature was PLUS 15C (windchill PLUS 13C) at 3:00 pm. Sunrise is at 5:42 am, and sunset is at 9:23 pm. Very windy today.
On 15 May 2021, I finally did a long drive that I had wanted to do the last few years, but never really been brave enough to do it. So glad I made myself do this, and it was a great day.
Much of the driving was on backroads that had a thick layer of loose, chunky gravel, making driving very unpleasant. It tends to push the wheels towards the side of the road, so one has to concentrate on trying to drive in a straight line. My arms and wrists ached like crazy from gripping the steering wheel.,
It looked a good day to go for a long drive to take my mind off all the repair work that has to be done. The forecast looked good, though it made no mention of the haze which made scenic shots useless. It felt so good to see quite a few birds for a change. The highlight of my day was briefly seeing a Swainson's Hawk perched on a fence post. I took a couple of shots, which had to be through my windshield. The hawk put its head down and that is when I realized that it had a snake held in its talons. It took a couple of pecks at the snake while I was watching (and taking a few seconds of video), and then off it flew. I wonder if it had a nest with babies in it nearby.
Another highlight for me, was to come across a beautiful female Merlin, also perched on a fence post. It had been quite a while since I last saw a Merlin.
At the beginning of my drive, I would have liked to call in for breakfast at the Saskatoon Farm, but I knew it would be really busy on a Saturday. Likewise at the end of the day, I would have liked to call in at Frank Lake, but I always try and avoid busy places. Makes no sense when someone has the weekdays in which to visit places like city parks. Some people are still working, so I prefer to usually leave the parks for them at the weekends.
I did call in at one of my favourite sloughs on the way home and enjoyed watching quite a few White-faced Ibis feeding and preening. So peaceful in a place with no other cars or people.
Of course, no day would be complete without spotting an old barn or two. These included one of my absolute favourite barns, photographed and posted previously, too.
The next two days, I have to get all sorts of things done because I know the repairmen will be taking out all my windows and putting them back, along with new frames on Friday, 21 May. I will have to be home, as they will need to have access to inside my place. It has now been just over six weeks that they have been replacing all sorts of rotten, wooden beams outside and adding two (?) layers of whatever material they use, before they eventually install new siding.
FORT LAUDERDALE, FLA. — Matthews Southwest has begun the final phase of the expansion and redevelopment of the Greater Fort Lauderdale/Broward County Convention Center, which includes the 29-story, 800-room Omni Fort Lauderdale hotel. The total cost of the project is about $1.3 billion and is expected to deliver in late 2025. Nunzio Marc DeSantis Architects designed the hotel, Fentress Architects designed the convention center expansion and Balfour Beatty is handling construction. The project is expected to generate 1,000 construction jobs and 1,300 permanent jobs.
Matthews Southwest opened Phase I of the convention center in October 2021. The expansion project will add an additional 600,000 square feet of flexible indoor event and meeting space and an additional 200,000 square feet of outdoor programming space, to create a total of more than 1.4 million square feet of event space that includes 350,000 square feet of contiguous exhibition space. The expanded center will also feature a new 65,000-square-foot waterfront ballroom, 50 meeting rooms, new dining concepts, pre-function space and modern décor and technologies. The new Omni hotel will feature a rooftop bar, grand and junior ballrooms, meeting spaces, yoga deck and a pool deck. The project will also include an onsite water taxi stop and charter boat dock, amphitheater, six-acre waterfront event plaza with public access, waterfront promenade, three additional restaurants and a 24,000-square-foot Convention & Visitors Bureau office building.
Credit for the data above is given to the following websites:
rebusinessonline.com/matthews-southwest-begins-final-phas...
www.pcma.org/on-the-waterfront-greater-fort-lauderdales-c...
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It's Expected I'm Gone · Minutemen
I don't wanna hurt
See, my position was here
I mean, as it was, I was