Seismology for Dummies: Guesstimating nuke test yields

[vkrishna]

In any case, the very fact that the seismic waves are of predominantly a single frequency, renders the argument of no interference invalid. If one has two signals of the same frequency, there is no question of a randomised phase relationship averaging out. Trivially, two single frequency signals always have a well defined phase relationship.

[A_Gupta]

It is apparently not true that simultaneous nuclear tests have not been conducted before.

Please go to

http://www.ldeo.columbia.edu/Monitoring/Data/Brv_arch_ex/brv_text_table.pdf

scroll down to page

Table A4: Borovoye archive data for underground nuclear test at Novaya Zemlya Test Sites,
1967–1990

There are many instances of multiple explosions as well as salvos (see the Comments column).

A map on page 7 of the document shows the Novoya Zemlya test sites.

----
or

http://www.ldeo.columbia.edu/Monitoring/Arch/nz/nz.html

and

http://www.ldeo.columbia.edu/Monitoring/Arch/nz/nz-map.html

-----

Also see :

http://www.thebulletin.org/issues/nukenotes/mj98nukenote.html

Also see

http://www.thebulletin.org/issues/nukenotes/mj98nukenote.html

What is not clear is how separated in space some of these explosions were. Two quotes follow :

Minatom adopted the definition developed in the 1990 Protocol to the Threshold Test Ban Treaty, the same one used by the U.S. Energy Department, in preparing its comprehensive list. A test is defined as either a single explosion, or two or more explosions fired within 0.1 second of one another within a circular area with a diameter of two kilometers. The yield is the aggregate of all of the explosions.

Explosions: The Soviets, like the Americans, had a practice of conducting simultaneous explosions; that is, placing more than one device in the same shaft, or firing two or more devices at the same time. For the period 1964–90, 146 Soviet tests used more than one device, resulting in 400 explosions. These are sometimes referred to as salvo explosions. Each salvo counts as one test since the multiple devices were detonated within 0.1 second of one another.

Sometimes as many as eight devices were placed in the same shaft or tunnel and detonated simultaneously. The total number of devices detonated in the 715 Soviet tests was 969. The total number of devices detonated in the 1,054 U.S. tests, (including 24 conducted with Britain) was 1,149.

( The Indian tests were 0.25 seconds apart as per Ramana).

Presumably either the devices were exploded exactly simultaneously, or else when they are 0.1 second apart, the devices were separated by at least a few hundred meters - unless they were testing the survivability of their arsenal after a first strike - otherwise would not one explosion destroy the other devices ?

http://www.thebulletin.org/issues/nukenotes/mj95nukenote.html

has some info on US simultaneous or near-simultaneous tests.

-Arun Gupta

[Kaushal]

A_Gupta Kaushal :

Once you have a wide spectrum rather than a a narrow frequency, interference tends to take a toss.

I don’t see the relevance of this statement to my earlier statement on non-sunusoidity of a wave, namely. Any wave can be represented as a sum of sunusoids . The wider the spectrum obviously the more it looks like ‘white noise’.

Your earlier statement was “These are not simple sinusoidal waves”. I guess to rephrase my earlier comment/question, why would you expect them to be sinusoids,

Kaushal

[A_Gupta]

Originally posted by Kaushal:
A_Gupta Kaushal :

Once you have a wide spectrum rather than a a narrow frequency, interference tends to take a toss.

I don’t see the relevance of this statement to my earlier statement on non-sunusoidity of a wave, namely. Any wave can be represented as a sum of sunusoids . The wider the spectrum obviously the more it looks like ‘white noise’.

Your earlier statement was “These are not simple sinusoidal waves”. I guess to rephrase my earlier comment/question, why would you expect them to be sinusoids,

Kaushal

If it looks like white noise, there is no interference. The BR analyis of interference linked to in the very first article in this thread is valid for tuning forks.

Anyway, here is an article that does not dispute the yields for May 11, and estimates the yields only to within a factor of 2.

http://www.thebulletin.org/issues/1998/ja98/ja98vanmoyland.html

[Sunil]

A_Gupta,

> If it looks like white noise there cannot be intereference.

Umm.. I don't think that's correct. You could have interference effects on the individual frequency components.

To `see' these in greater clarity it is best to look at the fourier transform of the signal as opposed to its time domain representations(which is what is shown in the paper).

A single seismograph will *not* "see" the entire interfernce fringe. It does not have the `aperture' to see the entire fringe, for that one would need a seismograph that is a 1-2 kilometers long. The seismograph merely records the seismic signal at one point along the wave path.

I have yet to see a clear explanation of what dephasing mechanisms you are alluding to. Whatever you have provided so far have been re-statements of your basic assertion that "there is no interference".

Unless that is cleared up, the BRM analysis is accurate.

[shiv]

From A_gupta's links:

http://www.ldeo.columbia.edu/Monitoring/Arch/nz/nz.html

salvo explosion means two or more separate explosions where a period of time between successive individual explosions does not exceed 5 seconds and where the burial points of all explosive devices can be connected by segments of straight lines, each of them connecting two burial points and does not exceed 40 kilometers in length.

http://www.thebulletin.org/issues/nukenotes/mj98nukenote.html

A test is defined as either a single explosion, or two or more explosions fired within 0.1 second of one another within a circular area with a diameter of two kilometers.

Funny "definitions" - just like in medicine - possibly arbitrary, based on "gut feeling". Don't know. It seems as though great problems can be caused to the definers by doing two tests 0.25 sec apart in shafts 2.5 Km apart - so the test/tests falls into the grey area not covered by these two definitions.

Or could the REAL reasons be the resolution of the detection mechanisms. Why 40 Km? Why less than 2 Km? Why 0.1 sec? Why worry about a straight line in >2 test - why not a triangle or polygon?

[Kuttan]

The interference theory would say that when one sets off these firecrackers simultaneously, one creates zones of relative silence. I don't think so but it would be interesting experiment to try.

As someone commented, this too has been tried, never fear. I could not hear anything for quite some time after the event - must be the wave interference

[A_Gupta]

Code: Select all

  
 http://nuketesting.enviroweb.org/hew/Usa/Tests/Nevada.html
 
 contains statistics for underground nuclear tests in the
 Nevada test site.
 
 The time of the explosion upto 0.01 second, the latitude and
 longitude upto 0.01 seconds of an arc are given, the depth
 of the device is given.  The yields are given sometimes
 precisely and sometimes as a range.
 
 From these it is possible to extract the following events
 that were separated very little in space and/or time.
 
 At 37 latitude, each second of an arc longitude corresponds
 to about 25 meters east-west distance; and each second of an
 arc latitude difference corresponds to about 31 meters
 north-south.
 
 ANNOUNCED_NAME Announced name for shot
 ZULU_DATE      Shot date (Greenwich) stored as YYMMDD. (integer)
 ZULU_TIME      Greenwich mean time of detonation of shot (decimal).
                Format is XXXX.YYZZ where X=hours, 
                Y=clock seconds, Z=decimal millisecond
 LATITUDE-LONGITUDE
                Geodetic coordinate of shot location (decimal).
                Format is DDD.MMSSHH where DDD=degrees,MM=minutes,
                SS=seconds, HH=hundredths of a second
 
 DOB            Depth of burial of device in meters (decimal).
 ANNOUNCED_YLD  What yield was announced for this shot? (text)
 
 
 
 announced_name|zulu_date |zulu_time |latitude  |longitude |dob       |announced_yld  |
 CASSELMAN     |    630208|1600.00160| 37.085590|116.030680|   302.970|LOW            |
 HATCHIE       |    630208|1600.01150| 37.073345|116.021913|    60.960|LOW            |
 
 FERRET        |    630208|1830.00000| 37.033002|116.014534|   325.690|LOW            |
 ACUSHI        |    630208|1830.00140| 37.024610|116.011590|   260.870|LOW            |
 
 KAWEAH        |    630221|1947.00140| 37.071310|116.024460|   227.080|LOW            |
 CARMEL        |    630221|1947.08630| 37.091730|116.044760|   163.370|LOW            |
 
 KOOTENAI      |    630424|1609.30141| 37.071415|116.021060|   181.970|LOW            |
 PAISANO       |    630424|1609.30142| 37.071389|116.021023|    56.690|LOW            |
 
 TEJON         |    630517|1455.00000| 37.025402|116.015648|    74.600|LOW            |
 HARKEE        |    630517|1455.00000| 37.023806|116.005628|   241.420|LOW            |
 
 BONEFISH      |    640218|1537.19120| 37.033378|116.015996|   300.760|LT 20 KT       |
 MACKEREL      |    640218|1537.37124| 37.054425|116.030259|   333.710|LT 20 KT       |
 
 CREPE         |    641205|2115.00100| 37.065190|116.031240|   404.200|20 TO 200 KT   |
 DRILL         |    641205|2115.00160| 37.080342|116.041110|   219.460|3.4 KT         |
 
 CASSOWARY     |    641216|2000.00000| 37.022240|116.012602|   150.140|LT 20 KT       |
 PARROT        |    641216|2000.00040| 37.020540|116.004420|   180.320|1.3 KT         |
  
 SIENNA        |    660118|1835.00000| 37.021438|116.010636|   275.010|LT 20 KT       |
 LAMPBLACK     |    660118|1835.00040| 37.053010|116.010730|   561.480|20 TO 200 KT   |
 
 COGNAC        |    671025|1430.00000| 37.025927|116.022247|   240.390|LT 20 KT       |
 SAZERAC       |    671025|1430.00060| 37.015380|116.013490|   301.340|LT 20 KT       |
 
 BUGGY         |    680312|1704.00110| 37.002700|116.221190|    50.290|1.08 KT        |
 BUGGY         |    680312|1704.00110| 37.002750|116.221361|    50.290|1.08 KT        |
 BUGGY         |    680312|1704.00110| 37.002802|116.221534|    50.290|1.08 KT        |
 BUGGY         |    680312|1704.00110| 37.002855|116.221707|    50.290|1.08 KT        |
 BUGGY         |    680312|1704.00110| 37.002908|116.221880|    50.290|1.08 KT        |
 
 FUNNEL        |    680625|1530.00000| 37.024686|116.014875|   118.700|LT 20 KT       |
 SEVILLA       |    680625|1530.00000| 37.022968|115.593247|   358.650|LT 20 KT       |
 
 BIT           |    681031|1830.00000| 37.024932|116.014608|   148.310|LT 20 KT       |
 FILE          |    681031|1830.00000| 37.010154|116.020863|   228.950|LT 20 KT       |
 
 WINCH         |    690204|1500.00000| 37.003398|116.023228|   240.630|LT 20 KT       |
 NIPPER        |    690204|1500.00000| 37.000960|116.003289|   240.730|LT 20 KT       |
 
 BLENTON       |    690430|1700.00040| 37.045340|116.005020|   557.730|20 TO 200 KT   |
 THISTLE       |    690430|1700.00040| 37.052500|116.002030|   560.470|20 TO 200 KT   |
 
 HOREHOUND     |    690827|1345.00000| 36.593373|115.594390|   331.830|LT 20 KT       |
 PLIERS        |    690827|1345.00040| 37.011740|116.021710|   238.870|LT 20 KT       |
 
 PLANER        |    691121|1452.00000| 37.025338|116.012184|   377.840|LT 20 KT       |
 PICCALILLI    |    691121|1452.00040| 37.015230|116.000740|   393.800|20 TO 200 KT   |
 
 BELEN         |    700204|1700.00000| 37.031807|116.021983|   420.800|20 TO 200 KT   |
 GRAPE B       |    700204|1700.00040| 37.055310|116.013540|   554.460|20 TO 200 KT   |
 
 
 PITON         |    700528|1200.00160| 37.081850|116.014770|   100.580|LT 20 KT       |
 PITON A       |    700528|1200.00164| 37.083832|116.015743|   236.220|LT 20 KT       |
 
 CANJILON      |    701216|1600.00000| 37.042108|116.012996|   302.190|LT 20 KT       |
 ARTESIA       |    701216|1600.00090| 37.060060|116.002860|   484.830|20 TO 200 KT   |
 CREAM         |    701216|1600.00170| 37.083440|116.020240|   292.910|LT 20 KT       |
 
 CHAENACTIS    |    711214|2109.59160| 37.072620|116.052240|   331.010|20 TO 200 KT   |
 YERBA         |    711214|2110.00040| 37.012370|116.033107|   331.990|LT 20 KT       |
 HOSPAH        |    711214|2110.01040| 37.013306|116.014493|   302.030|LT 20 KT       |
 
 TAJIQUE       |    720628|1630.00070| 37.041053|115.593159|   332.310|LT 20 KT       |
 HAPLOPAPPUS   |    720628|1630.02160| 37.080672|116.020696|   184.400|LT 20 KT       |
  
 TOPMAST       |    780323|1630.00114| 37.055590|116.011064|   457.810|LT 20 KT       |
 ICEBERG       |    780323|1630.00200| 37.061000|116.030000|   640.290|20 TO 150 KT   |
 
 WEXFORD       |    840830|1445.00000| 37.083800|116.073092|   314.000|LT 20 KT       |
 DOLCETTO      |    840830|1445.00102| 37.052326|115.595772|   365.150|LT 20 KT       |
 
 RHYOLITE      |    880622|1400.00079| 37.095817|116.042008|   207.300|LT 150 KT      |
 NIGHTINGALE   |    880622|1400.00079| 37.095817|116.042008|   237.700|LT 150 KT      |

[A_Gupta]

If we go to

http://www.bharat-rakshak.com/MONITOR/ISSUE3-6/ramana.html (The Indian Nuclear Tests - Summary paper)

and granting all the assumptions in the analysis in the linked document (quantitative analysis)

http://www.bharat-rakshak.com/MONITOR/ISSUE3-6/pok.pdf

and assuming that the two explosions produce waveforms which have the same shape (i.e., for each sinusoidal component the amplitudes are proportional and the phases are the same),

even then, table 2, showing frequency versus viewing angle is in error,

because one explosion is 0.25 seconds before the other, which introduces a phase difference - one oscillator got its start before the other.

The symmetry around the north-south axis is destroyed. Calling the time difference T,

the correct relationship is

2 Pi d sin(theta) / lambda = phi - 2 Pi c T/ lambda

or = phi + 2 Pi c T/ lambda

the sign depending on whether the east or the west explosion went off first.

For a 4 km/sec wave speed, frequency of 2 Hz, i.e., lambda of 2 km, c T /lambda = 0.5

This additional term can be neglected only for long wave length, i.e., low frequency waves. Long wavelength here means much larger than 1 kilometer ( 4 km/sec * 0.25 seconds) or frequency much less than 4 Hz. ( At 1 Hz, the additional term = 0.25)

Postscript : I edited to add in a factor of 2 Pi that I missed.

[Sunil]

Hi A_Gupta,

I don't think I follow what the point of that table in your post before last is.

[shiv]

Originally posted by A_Gupta:
( The Indian tests were 0.25 seconds apart as per Ramana).

It is not clear to me where ramana got this figure, because the following quote has been brought to my attention - taken from the first paragraph of the paper by S.K. Sikka, Falguni Roy and G.J.Nair, Current Science, vol 75, Sept 1998, pg. 486.

"At the Pokharan test site in Rajasthan, three nuclear explosions were
detonated by India on 11 May, 1998 at 1543 hrs IST. These explosions were
triggered SIMULTANEOUSLY and comprised a thermonuclear device, a fission
device and a sub-kiloton device emplaced in spatially separated shafts

[vsunder]

First of all I do not recall anywhere it being said that double explosions were a first for POK-2. The thread is full of unsubstantiated innuendos.
It can be said however that there are not that many articles analysing such explosions.
However, since there are so many "seismic experts" on this thread, let me ask you to explain to me the following. In a paper "Seeing Double" Douglas,R.C. Stewart, P. D. Marshall, Geophysical J. of the Royal astronomical Society, v92, 335-338 analyse two shots fired 10km apart at Nova Zelmya in the FSU. They show that this test exhibited very strong interference patterns and thus the title of the article. Now regarding POK-2, Douglas claims that this double shot cannot exhibit interference patterns like the one at Nova Zelmya though he has not presented the ANY evidence as in his earlier paper for or against,like detailed evaluation of the seismograms from several detectors. No Physics reason is given by Douglas except that the sources in POK-2 were too close(1 km apart) and the explosions SIMULTANEOUS(<0.1 second apart). In fact he goes on to suggest in his Current Science article that interference for the source geometry of POK-2 would only be possible for waves >5Hz. He claims that such was not observed. He gives no Physics explanation as to why he makes such a statement. Neither does he quantify what is TOO close. However, in 1999,Harsh Gupta, D. Sarkar et al in Current Science, v76, 1117-1121 display the spectrum for POK-2 that is plot frequency along the x-axis and the energy content in that frequency along the y-axis. It is clearly seen that the energy from POK-2 peaks in the 5Hz frequency. This paper is also referred to in the BRM article. So why does Douglas say no 5hz waves were detected. So tell me why in one case they(Douglas/Marshall) agree interference has occurred and in the other it cannot occur. You know you can look up the relevant papers in a decent library and Current Science is on the web.

[A_Gupta]

The point is that there is potentially plenty of data available to validate (or invalidate) interference of near simultaneous, close to each other, nuclear explosions.

Of course, finding this data, outside of a university department or govt lab., is probably not easy.

[A_Gupta]

Do you have the date of the Douglas Current Science article ?

And is this citation correct ?

Stewart, R. C. and Marshall, P. D. (1988). Seismic P-waves from Novaya Zemlya explosions : seeing double!

Geophysical Journal, 92, 335-338

Thanks !
-Arun

[Arun_S]

Originally posted by A_Gupta:
( The Indian tests were 0.25 seconds apart as per Ramana).

What Ramana meant is that the Shakti-1 & 2 test distance were 0.25 seconds apart (w.r.t sonicwave propogation in earth's rock crust, I think shock wave propogation speed may be slightly more).

IMHO Ramana rarely ever makes mistakes, if there is sign of mistake in his writing I usually read it few times over to understand what he is saying.

[ramana]

Thanks Arun for the ringing endorsement but even Homer nods. The triggering was simulataneous but there was delay due to physical separation of the test shafts. Here is the description: Indian Explosions of May 11, 1998 : An Analysis of Global Seismic Bodywave Magnitude Estimates
"The first three of these observations may be attributed to the modification of the body-waves due to the time delays introduced by the physical separation of the two large explosions of POK-2( their shafts were located 1km apart in east-west direction) which varied from 0.0s to about 0.125s. Thus, minimum time delay would be in the north and the south directions with respect to POK-2 while maximum delay would be in the east and west directions. With the help of synthetic seismograms it will be demonstrated in the next section that the resultant amplitude of two explosions reduces from a maximum true value to a minimum value as the delay is varied from 0.0s to 0.125s. "

From this ref the delay is about 0.0 ~ 0.125 secs and not .25sec as I wrote earlier.

[A_Gupta]

Remember, this thread is for dummies, it says so in the title, and therefore we do not have to be seismologists. The fun is to try to understand the physics and the politics.

Anyway, coming to Douglas, Marshall, etc., in Curr Science (http://www.iisc.ernet.in/~currsci/jul102001/72.pdf)

1. I find the title interesting

"The yields of the Indian Nuclear Tests of 1998 and their relevance to Test Ban verification"

The title ( and the text ) indicate to me that concern, of saving CTBT, is lurking here.

2. The authors have the interesting question :

Sikka et al. argue that many of the assumptions made by others in estimating the yield of 980511 are incorrect and that without the availability of 'close-in ground motion measurements, radiochemical methods, calibration events and hydrodynamic shock measurements' together with 'knowledge of the surroundings of the device' any estimates other than those by scientists involved in the test 'will be not just highly subjective but erroneous'. If Sikka et al. have so little confidence in such methods - and we agree that yields estimated by seismological methods are subject to large uncertainties - it is not clear why they have gone to such lengths to obtain so precise a seismological estimate of the yield.

It always takes two sides for an argument. I believe the Indian scientists, but believe they have made a mistake of tactics in trying to find teleseismic justification.

3. The authors make the argument that the 1998 tests would have been at a greater depth than 1974 (so as to contain radioactivity), and hence may have been in water saturated rock which produces more seismic motion for the same yield.
On the other hand, they seem to want their mb = a + b log Y relationship to hold as well, for a fixed a and b. Slightly contradictory, it seems.

4. Coming to vsunder's question : the authors write :

However, at long range, the maximum time-separation of the two signals is less than 0.1s, so the frequency for optimum destructive interference is > 5 Hz, well above the dominant frequency (1-2 Hz) of the P waves at most stations.

Some comments :

1. For the time separation of two signals sent simultaneously one kilometer apart to be less than 0.1 s, the speed of the signals must be greater than 10 km/sec. I think the BRM paper refers to 4 km/sec.

2. Presumably at the distant stations, all but the 1-2 Hz waves have attenuated into indetectability. So that is why Harsh Gupta, et. al.'s findings that POKII had most of its energy in the 5-7 Hz range may not falsify Douglas, etc. assertion. ( It does however, make the phenomenology of yield estimation seem even more inexact).

3. The point about 5 Hz waves needed for showing destructive interference is as follows : you need at least a half-period delay ( or three half-periods, or five-half periods, ...) to show destructive interference. For 0.1 second delay, i.e., half-period of 0.1 seconds, the frequency is 1/0.2 = 5 Hz. For a 1 Hz wave, 0.1 seconds corresponds to a phase difference of 36 degrees and the waves are still adding constructively. In the BRM paper

Code: Select all

A_cum**2 = A_1**2 + A_2**2 + 2 A_1 A_2 cos( phi ),

phi has to get to be more than Pi/2 for destructive interference, and the claim is that phi never gets to be more than Pi/5 for waves upto five hertz.

Of course, there still is more constructive interference versus less constructive interference (at 1 Hz, cos( phi ) goes from 1 to 0..

[Sunil]

A_Gupta,

> The point is that there is potentially plenty of data available to validate (or invalidate) interference of near simultaneous, close to each other, nuclear explosions.

I am sorry i fail to see how you conclude this from that table in your post.

As far as I can see the data simply lists a number of `shots' and their launch times, it tells us nothing about the variation in the seismic data at various IMT stations in the world. So how precisely do you conclude that this table that you have presented supports anything?

Mr. Gupta, I am a physicist by profession and will remain so for the foreseeable future. Maybe it is very obvious to you as to how exactly the seismic waves from two or more simultaneous nuclear explosions dephase wrt each other. However it is not equally obvious to me and I am completely lost with regards to your explanations.

Could you please be a little more concrete about the physics of the dephasing mechanism?

I have less interest in the politics of yield at the present time.

[A_Gupta]

Sunil Sainis :

In the very first post of this thread it was said :

Now all that is written above is just great for single shot nuke tests. Now what if some sneaky people set off two or more nuclear tests simultaneously? The seismologists of this world have next to zero experience of seismic signals from nuclear tests set off simultaneously. And that was what was done on May 11th at Pokhran.

I have provided references to multiple explosions in Novoya Zemlya and in Nevada; and in Nevada, there is data sufficient to see if the conditions (depth, distance and time separation) are comparable to POKII.

Now, perhaps seismologists have been ignoring nuclear explosions over a few decades until Pokhran II. That is certainly possible but not plausible. On the other hand propagation of waves from underground nuclear tests give seismologists another probe of the earth's interior, and therefore they have been paying attention for scientific reasons - if the needs of the military-industrial complex were not enough. Anyway, vsunder gave a reference to a 1988 paper "Seeing double" regarding explosions in Novoya Zemlya. Further evidence of whether seismologists have been paying attention or not will require a literature survey. If you have evidence that POKII is somehow unique, then please present it. I suppose it would be unfair to ask you to prove the negative, namely, that seismologists have ignored all these nuclear tests; because proving a negative is next to impossible.

As to how dephasing might occur, I do not have an answer to give you and that is why I'm started taking the BRM argument seriously. To decide the question, we have to go into detail how the low frequency seismic waves are produced. The claim to demonstrate or disprove is that UNTs produce low frequency waves in a defintie phase relationship.

Coming to the BRM argument, Douglas et. al. have presented an point hat has to be addressed. In terms of the BRM paper,

2 Pi d sin(theta)/lambda = phi

and phi= Pi/2 is the boundary between constructive and destructive interference.

Setting phi = Pi/2 and using lambda = c / f where c is the speed of sound and f is the frequency, the BRM paper arrives at :

sin(theta) = c / ( 4 d f )

d=1 km; BRM uses c = 4 km/sec.

The point is that the equation has a solution for theta only as long as the RHS is less than or equal to one, i.e, for a solution

f >= c/4d

For 1 Hz waves to destructively interfere somewhere, we need c <= 4 km/sec.

What is the appropriate value of c ?

[Kuttan]

Question from the Dummy Lobby:

1. For the time separation of two signals sent simultaneously one kilometer apart to be less than 0.1 s, the speed of the signals must be greater than 10 km/sec. I think the BRM paper refers to 4 km/sec.

Really? Or the observer could be standing (lying with ear to the ground, in this case) at a point equidistant from both sources (i.e., started midway between the sources and ran until he was tired)?????

Also, does the "optimum frequency for interference" change with the angle between the observer and the line joining the two points? Anyone thought about this claim? If this is not true, how does the time delay seen by the observer influence the measurements at a given frequency? From my dumminess, this Wallace claim appears to be bogus.

Note from ramana's quote that the delay is in the observation, NOT between the actual events.

[Sunil]

A_Gupta,

> I have provided references to multiple explosions in Novoya Zemlya and in Nevada; and in Nevada, there is data sufficient to see if the conditions (depth, distance and time separation) are comparable to POKII.

Is this what you were showing in the last table?because the distance of separation between devices was not clear in that table. Without that any claims of interference etc... are a little difficult to analyse.

Shiv's assertion is correct as a fraction of the number of underground nuclear tests, the mulitple shots are very small. Most people don't have a whole lot of experience in this.

Shiv never made an assertion saying that `no one' knew about double tests. He merely said, the number of people that do know about this is pretty low, and douglas and wallace if their writings are anything to go by don't seem like they know very much about this at all.

> On the other hand propagation of waves from underground nuclear tests give seismologists another probe of the earth's interior, and therefore they have been paying attention for scientific reasons - if the needs of the military-industrial complex were not enough. Anyway, vsunder gave a reference to a 1988 paper "Seeing double" regarding explosions in Novoya Zemlya. Further evidence of whether seismologists have been paying attention or not will require a literature survey.

Umm.. I don't think the seismology community is ever going to be allowed to conduct simultaneous underground nuclear blasts for `scientific purpose of understanding the earth's crust'.

> If you have evidence that POKII is somehow unique, then please present it. I suppose it would be unfair to ask you to prove the negative, namely, that seismologists have ignored all these nuclear tests; because proving a negative is next to impossible.

The POKII tests were the first simultaneous tests conducted in the Pokharan area. The fact that simultaneous tests were conducted elsewhere has little or no bearing on the POKII issue. The fact remains that when the POKII tests were conducted Wallace and Co came running out of the woodwork to analyse the test as a single event not multiple events. This speaks volumes for who is comfortable with what.

> As to how dephasing might occur, I do not have an answer to give you and that is why I'm started taking the BRM argument seriously. To decide the question, we have to go into detail how the low frequency seismic waves are produced. The claim to demonstrate or disprove is that UNTs produce low frequency waves in a defintie phase relationship.

Agreed and my question to you was how precisely does that little table up there prove this?

> Coming to the BRM argument, Douglas et. al. have presented an point hat has to be addressed. In terms of the BRM paper,

That 2Pi d Sin(Theta)/Lambda = Phi is *not* valid in the real physical world when dealing with the output of nuclear explosions.

That relationship holds *only* when there is a uniform (in theta) media in which the waves from the explosions travel. This not the case in reality. In reality the measurements are made by seismic stations that lie across different geological media from the site of the explosions. This path dependence can be accounted for and an interference pattern can be divined, but the treatment is much more complicated than the simple undergrad level two slit approach.

The BRM paper does not make firm quantitative assertions about the nature of the interference pattern from POKII. It merely suggests a likely scheme given certain assumptions on wave velocity.
Most importantly it drives home the point that there is an interference pattern and that such a pattern forces a theta dependent variation in seismic readings.

[Kuttan]

Jumraoji:

This is the other reason why I decided to take up sleeping in the IIT PLT (That's "Physics Lecture Theatre", not "Pakistan Laskhar-e-Toiba" though it might take an astute observer to tell the difference between the two )

Reason: Whenever I gathered up enough courage to blurt out a question, they just ignored me - on good days when they were too busy to laugh

[vkrishna]

narayanan,
as another dummy here, could you explain what you mean by the question about angle between the observer and the line joining the two points? if the observer is a point/symmetric one, i dont know how one defines the angle. additionally, it is true that if one is equidistant, one would not see any delays- in a simple interference, this would be the central maximum; the "delays" or path differences are what cause the interference as you know. additionally, if one has two frequencies very close to each other, one gets "beats" as you pointed out and I'm pretty sure that a lot of the gentlemen making claims about the low yields dont bother about such complicated effects.

A_Gupta,
The application of simple interference or even Bragg's laws are probably invalid here. A simple but somewhat more accurate model of the problem would be to consider the medium of propagation as consisting of layers of different "refractive" indices-and this would give very different path lengths from the path length for propagation in a single homogenous medium. This is precisely why one gets structural information about the earth's crust, because this structure determines the spatial dependence of the "refractive index" for propagation.

[Kuttan]

Dummydom Zindabad!

This is the quote which puzzled me:

However, at long range, the maximum time-separation of the two signals is less than 0.1s, so the frequency for optimum destructive interference is > 5 Hz, well above the dominant frequency (1-2 Hz) of the P waves at most stations.

OK, he's not saying that he things there is an azimuth-dependence of the frequency. But there are some problems with his statement:

1. The max. time separation between the signals should be the time it took for the signal from one explosion to travel to the location of the other. This would be a factor if the observer is located along the line connecting the two explosion sites. Per the data given above, the distance is about 1 km? So A-Gupta says: that implies a propagation speed of 1 km in 0.1 seconds, or 10km/sec. Actualy propagation speed was around 4-5km/sec. - which would make the max time delay 0.2 seconds.

But all this means is the following:

Lets say the propagation speed was, 5 km/s, and separation between sites was 1km. Then a guy standing far away, exactly east or exactly west of POK-2 would see nothing at a frequency of 2.5 cycles per second. Why? Because 180 degrees of phase difference at 2.5 cycles per second, takes exactly 0.2 seconds. So the wave with frequency of 2.5 cycles per second, starting from POK-2B, arrives at POK-2A with a phase that is 180 degrees apart from that at POK-2A - and cancels out a part equal to its own amplitude. The 2.5 cps wave starting from POK-2A and heading towards Dr. Wallace has an amplitude which is the difference between the amplitudes from POK-2B and -2A.

Incidentally, we now see that the "optimum frequency for destructive interference" is 2.5 cps, which of course would fit right within the range of the signal which does propagate. Let me post this and see if I messed up the distance between the sites.

(OK, I checked - 1km between sites is correct. So, my calculation shows that the claim of interference is perfectly right, it DOES occur in the range of the signal, and Douglas ( Thanks, ramana) is full of **** when he says that "the optimum frequency for destructive interference is well above the range of the data". Assuming that waves don't travel at 10km/s. Actually I thought the propagation speed was something like 1500 m/sec (1.5km/s).

At 4km /second, can I use moonquakes or nuclear blasts to accelerate vehicles off the Moon? 4.2km/s is escape velocity at the surface of the Moon, IIRC, and the soil composition is something like that of Kazakhstan / Rajasthan / Nevada / New Mexico.

Let me state here as disclaimer that I never check calculation beyond the point where the results agree with my conclusions.

[ramana]

N^3 is it Douglas you are referring to?

[A_Gupta]

Speed of sound in sandstone is said to be 2200-2900 meters per second. So I would tend to think Douglas is blowing smoke;

but looking around I see P-wave speeds said to be anywhere from 3 km/sec to 13.6 km/sec. For the first arriving P-waves at a distant seismograph, the path from the nuclear test site is probably almost straight down, and perhaps the slower surface speed is not appropriate for estimating the difference in arrival times.

This is going beyond dummy territory.

[Kuttan]

13.6 km/sec. ..straight down

Hello!! The diameter of Earth is only about 8000+ miles (4000 according to Delta Airlines when they compute frequent flyer miles) - so this P-wave might reach Prof. Douglas' kursi in Amreeki before his stupid sensors in Kazakhstan pick anything up along the surface and call him on his cell-phone.

[A_Gupta]

Originally posted by narayanan:

Really? Or the observer could be standing (lying with ear to the ground, in this case) at a point equidistant from both sources (i.e., started midway between the sources and ran until he was tired)?????
I don't like the term "optimum frequency for interference", because if interference is taking place, at least constructive interference is taking place.

The question is what is the difference between where the most constructive interference and the least constructive interference is taking place ?

For a 1 Hz wave with a maximum of 0.1 second delay (using Douglas's numbers) in the context of the BRM paper ( i.e., without all the real life complications) A_cumulative**2 ranges from 4 A**2 and 3.6 A**2; i.e., interference causes a 10% effect.
If both oscillators are in phase at the sources, then the phase difference of waves coming along two different paths to the observer is simply proportional to the difference in travel times along the two paths. In the BRM paper,
T = d sin(theta)/c is the difference in travel times from the two sources to a distant observer in the appropriate direction; and 2 Pi f T is the phase difference phi.

Yes, an intermediate post confused me. Always check the sources, is the moral of that story.

[A_Gupta]

Brief reply to Sunil Sainis :

Along with the table I did mention that 1 second of longitude difference meant around 25 meters east-west at that latitude. 1 second of latitude difference corresponds to around 31 meters north-south.

I'm not into fine parsing of statements from friendlies. Let's leave it at that.

I am aware that propagation of seismic waves is a complicated business; and continue to be amazed that phase relationships, required for interference, are maintained through all the complications. Supposedly some digitized seismographs for nuclear tests are available on the web, and if I can find some, I will compute me some cross-correlation functions.

[Sunil]

A_Gupta,

> latitude and longitude.

I'm sorry i missed that part.

The table still does not tell us anything about how the announced yeild was calculated and what seismic station/s were used to calculate it.

At best we can plot announced yeild as a function of distance between sources, relative depth of burial, and time between explosions.

I still fail to see how that really helps us decide on interference effects one way or another as we have no independent handle on the yeilds.

> find it surprising that there isn't dephasing.

Philosophically speaking as counter point one should consider the fact that inspite of what appear to be random fluctuations in the world we do observe coherence effects.

> digitized siesmographs and cross correlation functions

Ah... finally an approach to the problem i find reasonable, if and when you do get this done, please do email the results to me. Also if you do find digitized seismographs of POKII please mail the link to sunil_sainis@hotmail.com.

[bala]

I know that the two simultaneous explosions were of different
nuke strengths - i.e. one the so-called H-bomb and the other plain old vanilla
fission bomb. I would presume that the wave frequencies and propagation
speed are a function of the strength of the explosion (can someone affirm
or correct this hypothesis). Any interference of asymmetric waves would
be rather complex. A more accurate picture is obtained when measurements
from different sites across the globe are taken into consideration. This was
done and analyzed by a english seismologist and the results tally close to
the Indian version of 60KT.