Seismology for Dummies: Guesstimating nuke test yields

Kaushal · Post by **Kaushal** » 05 Jul 2002 22:00

This is very interesting to me, I had not known physical scientists to be so prey to their own biases

Why, are their chromosomes and cell structure different from the rest of us ordinary mortals. Having worked at LLNL , and observed all of the human emotions albeit couched in more polite lingo, i found nothing to distinguish physical scientists from the rest of humanity. Physics without spirituality (or character if you prefer) is no different from the rest of spiritually deprived humanity.

Kaushal

member_4218 · Post by **member_4218** » 05 Jul 2002 22:55

Originally posted by Kaushal:
The simple fact of the matter is that teleseismological methods of estimating yield are just not accurate enough within an order of magnitude, not least because these are empirical formulae based on a dash of physics and a dollop of statistics. This is not surprising since the tramsmission and attenuation of waves through various media is highly dependent on the properties of the media itself. The yields are exponentially dependent on a 'guestimated constant' - which says it all. Kaushal

Actually it is well accepted that the phenomenon of transmission and and attenuation of waves is independent of the media. This is akin to saying to that the force of gravity is qualitatively the same whether we are on the Earth or the Moon. The differences between the media are captured by the constant "a". So the real discussion is, should be, is there a way to know this constant for Pokhran.

It is also clear(from emprical observations) that the log-log plot between mb and yield is close to a straight line. So can regression analysis be used to compute the constant(which will be the slope of the line). If I understand correctly one of the statisticians on the forum(nanendu) has mentioned that "simple" regression analysis may not be applicable because of the errors may not be homoscedastic(sp?) which I think means that they may not be "identically and independently distributed(i.i.d)". The removal of this assumption complicates the math considerably.

Because the Americans and the Russians have carried out thousand of tests in Nevada and Kazakhstan they may have a pretty good idea of this constant for their local terrain. Is there a way to extrapolate this value to Pokhran and what will be the error?

A corollary is what is the quantitative relationship between "a" and the sub-surface. Is the sub-surface structure at Pokhran well studied and understood? Can this substructure be classified using remote sensing satellites.

IMO once more advances are made and the global CTBT system is in place then it will make it easier to compute accurate estimates of the yields. Till then the benefit of the doubt has to go to the Indian scientists especially since there have effectively been only three tests at Pokhran.

Kaushal · Post by **Kaushal** » 05 Jul 2002 23:01

sunil, Not questioning the basis for model building in the physical sciences. I am questioning models based on very little physics . If there is 0 physics or very little, and all statistics, that is one extreme. One can probably relate the mating habits of fireflies with positions of stars in the galaxy with a high degree of correlation but that tells us little about either. In this instance the accuracy of the models themselves is in question. There is a great deal of difference between teleological principles and models based on such principles ,applicable to a wide range of phenomena and a model applicable to just one phenomenon and that too when it is not very accurate.

But i digress, i do not believe we are disagreeing that these models are highly empirical and at the same time have no proven accuracy. Not worth more ink than they deserve.

Kaushal

Kaushal · Post by **Kaushal** » 05 Jul 2002 23:26

Actually it is well accepted that the phenomenon of transmission and and attenuation of waves is independent of the media. This is akin to saying to that the force of gravity is qualitatively the same whether we are on the Earth or the Moon.

Hmmm ... sigh . People assume the ignorance of others far too readily. I am not referring primarily to velocities of propagation(there are differences in velocity also which is dependent on physical properties of the media such as Youngs Modulus, poissons ratio, and density - this is not the velocity of light we are talking about, but more like the velocity of sound), but attenuation of amplitude and the resultant measurement. If this was independent of the media we should have no need for statistics every measurement would be identical dependent only on distance.

Kaushal

Calvin · Post by **Calvin** » 06 Jul 2002 00:05

Fear of fratricide. DId not want the second test to be damaged by the first test.

Sunil · Post by **Sunil** » 06 Jul 2002 00:17

Kaushal,

I think I see your point. I have deleted my previous post.

schawla:

> Actually it is well accepted that the phenomenon of transmission and and attenuation of waves is independent of the media.

Not quite sure what you are trying to say here. The propagation of a wave in a medium is a fairly complicated affair. You can `know' the Indian value for a constant at Pokharan upto a certain error based on the measurements, the indian value of the yields and the correct physics model.

Independently of this the way to accurately determine `a' is through close in seismic measurements of single events of known yeild.

> If I understand correctly one of the statisticians on the forum(nanendu) has mentioned that "simple" regression analysis may not be applicable because of the errors may not be homoscedastic(sp?) which I think means that they may not be "identically and independently distributed(i.i.d)". The removal of this assumption complicates the math considerably.

But Nabendu has not made such a sweeping statement. He said there was a model deviation observed in the data set that he reviewed, he made no claims of an extension to *all* data sets or even to all seismic detectors.

I do not know of any way to remote sense the properties of the ground. You have to put something into the ground and then create a disturbance deep within in.

However there were reports of measurements of a seismic nature at the time of the chinese nuclear tests by dropping some sort of probe from a U-2 spy plane but these reports are short on details, and the results of this `experiment' are not known.

member_4218 · Post by **member_4218** » 06 Jul 2002 02:10

Originally posted by Kaushal:

Hmmm ... sigh . People assume the ignorance of others far too readily.

Didn't intend to. My understanding is that the differences in media is captured in the constant "a". That is all. This is a conclusion arrived upon by the "experts".

The "dollop of statistics" required is regression analysis to calculate "a".

>sainis

BEGIN Nabendu comment[BOLD IS MY COMMENT]:

The standard regression models assume equality of error variances (Called `homoscadasticity) and independence of individual errors. But when model was fitted and residual analysis was done (to check the asuumptions of the model), it indicated
heteroscadascity i.e., error variances were unequal[READ NOT BELONGING TO IDENTICAL DISTRIBUTION]. In such a case you have to make a transformation of the variable(s), output and possibly input, and then fit a regression model with transformed data. The resultant is a completely different model.

If a model is homoscadastic then the error standard deviation (square-root of the variance) is called the model error. But when the model itself is heteroscadastic then the concept of `model error', the way we understand it, is meaningless.

End. Nabendu comment

I interpret this as that a transformation of mb and Yield is required before "classical" regression analysis is applied. This is because errors are not i.i.d. Since the relationship will be independent of the location where it is measured it may be safe to conjecture that similar transformation will be required for other data sets.

Sunil · Post by **Sunil** » 06 Jul 2002 02:33

Schawla,

I think you have missed these posts on the first page of this thread.

> Sunil Sainis

"am i correct to assume that you feel the current way of estimating error on seismograph measurements is (at the very least) incorrect? "

> Nabendu:

"Not totally. Every time we have a data set, we need to play with it. Some times, the conventional methods work, sometimes not. if not then go thru careful transformations of data (popular one is- `Box-Cox transformation') to see what makes the model assumptions valid. "

Now what he has said here applies to a particular seismograph's actual readings for a given event. We *do not* have access to this data for any of the seismic stations in question for the POK 1, 2 events.

As we have no data, the suggested model fitting cannot be attempted here, ergo any talk of this statistical model dependence of the error is entirely academic to the thrust of Shiv's post.

Shiv's post works on the assumption that readings of each seismograph are accurate to within the machine error. So long as the machine error is small and quantifiable, how it is obtained is irrelevant to the rest of the analysis. There is nothing to indicate that BARC uses a different calibration procedure on its seismographs than the international community.

After concluding the process of measurement, the application of a physics model begins. It is here that a key difference between the physical models used by BARC and Walter and Co. leads to different results. This is the thrust of Shiv's post.

saint · Post by **saint** » 06 Jul 2002 03:24

certain noteds from barc:

For these body wave magnitudes, the yield of May 11th explosions is bracketed in the range 40 to 70 kT (see Table 1 in Huggins3). <u>It may be noted that the International Data Centre (IDC) at Arlington, USA has classified our event as an earthquake </u>

====
Q: regarding two devices going off at nanosecond interval, wondering how and what positions/locations they were detonated. Were they placed to act on the waveforms against each others? plan.

Kaushal · Post by **Kaushal** » 06 Jul 2002 06:07

schawlaMy understanding is that the differences in media is captured in the constant "a". That is all. This is a conclusion arrived upon by the "experts".

But you say there are no dependencies on the media "Actually it is well accepted that the phenomenon of transmission and and attenuation of waves is independent of the media. This is akin to saying to that the force of gravity is qualitatively the same whether we are on the Earth or the Moon.

If the attenuation of the wave is independent of the media why do you need a constant "a", that expresses this dependence ?

Kaushal

Kaushal · Post by **Kaushal** » 06 Jul 2002 06:21

My comments on the model : The simplest mathematical relationship is a linear one between mb and the yield. Obviously that will not work since yields can increase an order of magnitude while mb (amplitude of the wave) does not. So, the next level up is an exponential relationship, which is really a linear relationship in disguise once you transform the variables to their logs. So that is the extent of the 'expert' knowledge here. And then you lump everything you dont know into one 'constant' , except that the constant is hardly a constant but varies for every conceivable situation.

So why did the Indians use this ? They already knew the answer and they need a rationale to give plausibility to their numbers without revealing their real source for their belief about the yields. Of course this is going to be challenged by the western powers. it would be surprising if they didnt. And so the game goes on, but in the meantime the man in the white house seems to be betting on the fact that the Indian claims are valid, otherwise why bother with travel advisories, if everybody believes these are firecrackers.

Kaushal

Calvin · Post by **Calvin** » 06 Jul 2002 07:58

Kaushal - its fairly well accepted that the travel advisory was a rather oblique attempt at diplomatic/economic coercion on the part of the americans. A rather successful attempt, one might add.

shiv · Post by **shiv** » 06 Jul 2002 08:39

Originally posted by Sai_NT:

Q: regarding two devices going off at nanosecond interval, wondering how and what positions/locations they were detonated. Were they placed to act on the waveforms against each others? plan.

Sai they were oriented in an east-west axis - as per the BRM paper - probably quoting a ref that I hae not bothered to check
http://www.bharat-rakshak.com/MONITOR/ISSUE3-6/ramana.html

The question of whether they were placed to deliberately interfere has been asked - and I think the overall consensus of answers is that they were placed and detonated simultaneously because there would be only a small window of opportunity to test before international pressure forced the abandonment of testing.

Maybe the people involved might not have minded testing the devices one at a time, but with having to test simultaneously they had to consider interference effects. From India's point of view, "interference" of one test device on another was a lot more serious and immediate. One nearby underground blast would crush the shafts (and devices) made for other tests unless all were set off simultaneously.

Kaushal · Post by **Kaushal** » 06 Jul 2002 09:13

Kaushal - its fairly well accepted that the travel advisory was a rather oblique attempt at diplomatic/economic coercion on the part of the americans. A rather successful attempt, one might add.

Hardly news to anybody in this part of the galaxy. But such coercion would be meaningless unless it was also accepted that India and Pakistan had credible nuclear weapons. It is cognitive dissonance to claim that the nukes are really firecrackers but oh btw one should evacuate a country of 1.6 million square miles. it is either one or the other.

As for being a successful attempt at coercion , i suppose that would be a valid point of view, depending on one's perspective. It does not seem to have coerced India into anything.

In any event this is not a central issue for this thread. The powers that be in GOTUS seem to have accepted that India has a credible nuclear weapon.

Kaushal

A_Gupta · Post by **A_Gupta** » 06 Jul 2002 17:17

Originally posted by schawla:

It is also clear(from emprical observations) that the log-log plot between mb and yield is close to a straight line.

You missed my earlier post, where the observations at Borovoye, Kazakhstan of the US Nevada test site, require not one but three straight lines, the particular straight line depends on the range of yield.

mb = 4.78 + 0.52 log Y for Y < 20 kilotons
mb = 4.13 + 1.07 log Y for 20 < Y < 150 kilotons
mb = 5.48 + 0.53 log Y for Y > 150 kilotons

(Reference to the original paper can be found in my earlier post.)

Calvin · Post by **Calvin** » 06 Jul 2002 18:39

Kaushal: The credibility of the nuclear deterrent had relevance, in the context of the travel advisory, ONLY in the minds of the hoi polloi - not the governments. I think there is a fairly obvious distinction between these two groups.

A_Gupta · Post by **A_Gupta** » 06 Jul 2002 19:20

Originally posted by Kaushal:
This is very interesting to me, I had not known physical scientists to be so prey to their own biases

Why, are their chromosomes and cell structure different from the rest of us ordinary mortals. Having worked at LLNL , and observed all of the human emotions albeit couched in more polite lingo, i found nothing to distinguish physical scientists from the rest of humanity. Physics without spirituality (or character if you prefer) is no different from the rest of spiritually deprived humanity.

Kaushal

Keeping one's biases out of one's work is part of the discipline of science; and in a field like physics, where there is an impartial arbiter, nature, it should be easier than elsewhere. Nature, after all, does not respect a temper tantrum.

Kaushal · Post by **Kaushal** » 06 Jul 2002 19:23

Kaushal: The credibility of the nuclear deterrent had relevance, in the context of the travel advisory, ONLY in the minds of the hoi polloi - not the governments. I think there is a fairly obvious distinction between these two groups.

Are you saying the the GOTUS (the state dept., defense or white house )has questioned the credibility of the Indian nuclear weapons. if so that is news to me. Can you share the relevant news items please ?

Kaushal

A_Gupta · Post by **A_Gupta** » 06 Jul 2002 19:42

Yet another paper :

http://coulomb.geol.uconn.edu/~cormier/DTRA99final.pdf

"Seismic Calibration for IMS stations in Eastern Asia"

Perhaps why India/Pakistan give different teleseismic results than other regions of the world may find its explanation in something like this stuff.

"Many of the IMS stations located in area 1 (figure 1) lie near some of the most significant lateral variations in crustal structure on earth, including a near doubling in crustal thickness associated with the Indian collision with Eurasia,..."

A_Gupta · Post by **A_Gupta** » 06 Jul 2002 21:27

Sunil Sainis :

I think the correct answer to Walter and Douglas is that the tele-seismic relationship :

mb = a + b Log Y

is an empirical one, and requires calibration. The yield estimate Y is very sensitive to the values of a and b; a and b are known to vary with test site. In the case where calibration has been done in detail, with a few hundred data points, not one, but three pairs of values of (a,b) are needed to achieve an acceptable piece-wise fit of the ranges 0 - 20 kilotons, 20-150 kilotons and above 150 kilotons (Borovoye/Nevada). Thus one cannot simply plug in generic values of a and b into the equation.

In the same example (Borovoye/Nevada), using additional information from the seismograph estimates are accurate to only within 20% (so a 10 kiloton blast will be measured as 8 - 12 kilotons). Finally, there is an empirically observed directional effect in the seismographs which renders suspect the usual procedure of averaging out worldwide mb values.

Therefore the teleseismic data is a very weak leg to stand on when claiming that Indian scientists who have local data are committing fraud. Yes, Sikka et. al. are also under the impression that teleseismology is fairly exact, and hence are taking pains to reconcile the data rather than dismissing the discrepancies as being within the limits set by the rather crude method of teleseismology. Rather than recognizing the weakness of your science, you see these attempts as further evidence of a cover-up.

------

Coming to physics, if the above is satisfactory, then hopefully physics is now decoupled from politics.

Waves carry energy. Wave interference can change the pattern of energy flow from being the simple sum because of interference. Interference, however, requires waves to be in lock-step. How nuclear blast energy is converted into seismic waves is a stochastic process and conditions for interference do not apply.

Another way to look at it is that if there is no dispersion and the two explosions are impulses, then what is recorded at a remote seismograph is two impulses with different arrival times. In effect, depending on where the seismograph is, you have one short but large amplitude earthquake or a smaller amplitude but prolonged earthquake. ( You can see my assumption very clearly here. Earthquakes vary in duration and amplitude, and the energy of the earthquake is dependent on both. I'm assuming that seismologists are smart enough to obtain a measure of energy of an earthquake from their seismographs that takes both into consideration. My claim is that the energy deposited at the seismograph has no interference effects.)

How can directional effects that were observed happen ? Geology of South Asia may be one possibility. Another is that the two blast shield each other (analogy : in a spray of bullets from two sources, bullets shot at each other collide and thus there are fewer bullets far away along the axis between the two sources than along perpendicular to the axis. This is a non-linear effect and involves ""interference"" at the source rather than at the distant point). (analogy 2 : shape charges produce a directional effect by local interaction, not interference at distant points).

The speed of sound in the earth is around 3 km/sec and in air a factor of 10 less. Set off simultaneously two firecrackers at 100 meters apart (1/10th the distance for 1/10th the wavelength). Firecrackers are small enough that they do not interact with each other at this distance in any nonlinear way. The interference theory such as it is, should still hold good, however...

vkrishna · Post by **vkrishna** » 08 Jul 2002 08:01

A_Gupta,
I dont understand what you mean by the statement that "how nuclear blast energy is converted into seismic waves is a stochastic process". If the blast is impulsive, how can it be stochastic-furthermore even if there is some randomness in the energy transfer, the timescale of it is surely small enough that this so called "stochastic nature" is irrelevant?

You recently gave a definition of incoherence-that of the phases in the spectral distributions having random correlations and thus averaging out. By this definition, I dont see how such an averaging can occur when there is a simultaneous explosion of two different bombs-I dont understand how such randomization can occur.

Kuttan · Post by **Kuttan** » 08 Jul 2002 08:28

Gee! I sure am glad I slept through all those hours and hours of Physics classes in the IIT - R*M*B*** who came in to lecture wearing his Convocation Gown and turban to look like CV Raman - Sw******* who tried to get us to believe that he knew (only) Russian and never gave partial credit - but only convinced us that he was cuckoo ... "Sussex" who didn't know diddly but bullied everyone .. "Nixon", who was dittout (but actually pretty harmless), and knew that we could see the same, and hence sweated at every question... and the horrid barracudas who probably flew in over traffic on their brooms - and whom I won't even name because I don't want to get nightmares...

Don't seem to have missed much - and the art of sleeping with eyes open has come in handy in many Meetings since.

Kuttan · Post by **Kuttan** » 08 Jul 2002 18:20

With above disclaimer regarding my knowledge of physics, let me try to understand what's going on here: Good thing this stuff was not on R*M*B's exam, or I would not even have got that "B" (in my days, "B" meant "barely passing" - above 50%

Anoop · Post by **Anoop** » 08 Jul 2002 20:22

Narayanan,

Just a minor nitpick with your excellent physical picture of why seismological measurements are subject to inaccuracies in measuring nuclear yields.

In one of the references mentioned in a related thread, the wave trains originating from earthquakes were distinguished from those originating from nuclear explosions - the former are transverse, the latter are longitudinal. I guess that apart from that, the general principles of interference and the natural occurrence of integral equations are still valid.

Cheers
Anoop

Kaushal · Post by **Kaushal** » 08 Jul 2002 20:34

Offered without comment

http://www.smu.edu/geology/CF%203397/CTBT_new_3_words.pdf

A_Gupta · Post by **A_Gupta** » 08 Jul 2002 20:50

http://quake.wr.usgs.gov/recent/spectrograms/Examples/teleseism.html

(Spectogram recorded from a distant earthquake)

These are not simple sinusoidal waves.

A_Gupta · Post by **A_Gupta** » 08 Jul 2002 21:02

http://www.saag.org/papers5/paper451.html

Kaushal · Post by **Kaushal** » 08 Jul 2002 21:13

It bears repeating for the umpteenth time, ad nauseum, that the yield estimates are based on 'close in' measurements and ONLY confirmed using seismological models. So, the primary source of information for the yields is available only to BARC, which IMO they will not release for quite a while. But if somebody is diligent enough they should find sufficient collateral information that should shed sufficient light on the radionuclide data,

Kaushal

Kuttan · Post by **Kuttan** » 08 Jul 2002 21:23

former are transverse, the latter are longitudinal.

Thanks! - But..

I have never understood the difference between a "transverse" and a "longitudinal" wave.

Is it "fair" to say that "transverse" = hula dancer, while "longitudinal" = belly dancer?

Unfortunately this analogy would be so distracting as to not permit extension to other concepts.

Kaushal · Post by **Kaushal** » 08 Jul 2002 21:35

These are not simple sinusoidal waves

Obviously not. But that is hardly moot. Any non-sinusoid can be representated as the sum(fourier series) or integral(fourier integral) of sinusoids. The energy content remains invariant under such a transformation (Parseval's theorem).

Kaushal

Anoop · Post by **Anoop** » 08 Jul 2002 21:38

Originally posted by narayanan:

Is it "fair" to say that "transverse" = hula dancer, while "longitudinal" = belly dancer?

Unfortunately this analogy would be so distracting as to not permit extension to other concepts.[/QB]

. Since you've given ample reason to move away from distracting analogies, let's just be drab and 'scientific' about it.

As I understand it, the displacement of a material particle in a transverse wave is in the direction perpendicular to the direction of propagation of the wave - like water particles on the surface roughly bobbing up and down but the wave moving horizontally. In the longitudinal wave, the particles move in the same direction as the wave - like a spring whose one end is fixed to a wall and the other pulled out and released.

I hope I haven't officiously answered a rhetorical question!

Cheers
Anoop

Umrao · Post by **Umrao** » 08 Jul 2002 21:48

quote:
--------------------------------------------------
Originally posted by narayanan:

Is it "fair" to say that "transverse" = hula dancer, while "longitudinal" = belly dancer?

Unfortunately this analogy would be so distracting as to not permit extension to other concepts.[/QB]
--------------------------------------------------

Sorry those are exclusively mechanical in nature and are due to linkages and cam motion. At most they may set off sympathetic vibrations in the audience.

Sunil · Post by **Sunil** » 08 Jul 2002 22:01

A_Gupta,

> the relationship is an empirical one, and requires calibration.

The natural sciences are full of empirical relationships, and hence we have error terms. Any physical phenomena can be characterized upto an error.

One can plug in `generic' values for slowly varying quantities into any equation. However the results of such a calculation are `correct'(i.e. physical upto an error) if and only if we know what the likely (order of magnitude) deviation from the value is like at the particular site and that error is appropriately propagated.

This is *not* the case with Wallace and Co. They have simply poured values at random into the equations without propagating their errors.

The above is imo basic physics not politics.

> How nuclear blast energy is converted into seismic waves is a stochastic process and conditions for interference do not apply.

Why do you ignore the issue of timescale. I have stated before that the `stochastic' stuff happens *once* of the order of nanoseconds and the waves have a period of a second or so.

> Another way to look at it is that if there is no dispersion and the two explosions are impulses, then what is recorded at a remote seismograph is two impulses with different arrival times. ***** ( You can see my assumption very clearly here. Earthquakes vary in duration and amplitude, and the energy of the earthquake is dependent on both. I'm assuming that seismologists are smart enough to obtain a measure of energy of an earthquake from their seismographs that takes both into consideration. My claim is that the energy deposited at the seismograph has no interference effects.)

Arun, this little explanation adds absolutely nothing to the physics discussion. This does not motivate the claim of lack of interference in seismic measurements in any way.

An earthquake is *completely* different from an underground nuclear explosion. The duration of the source disturbance is not nanoseconds it is order of a second.

> How can directional effects that were observed happen ? Geology of South Asia may be one possibility.

There are directional effects due to the inhomogenous nature of seismic media. This changes the path length to various seismic stations. Once this is taken into consideration, the simple two slit picture breaks down and a more complicated treatment has to be applied to determine the magnitude of the interference effects. Kaushal's comment about fourier transforms should be seen in this light.

> Another is that the two blast shield each other (analogy : in a spray of bullets from two sources, bullets shot at each other collide and thus there are fewer bullets far away along the axis between the two sources than along perpendicular to the axis. This is a non-linear effect and involves ""interference"" at the source rather than at the distant point).

This would apply to the pattern of explosive fragments of the nuclear weapon. If you went around looking for the fragments of the bomb yes you would obtain the "interference at source" phenomena that you speak about.

But.. IIRC we are not talking about the motion of the bomb projectiles. We are talking about the motion of the earth 1000s of kilometers away.
The fragments have nothing to do with the formation of the seimic waves. The cavities formed by the blasts are much smaller than the inter-device distance.

This is not analogous to the shaped charge where a single body of explosive exists.

> The speed of sound in the earth is around 3 km/sec and in air a factor of 10 less. Set off simultaneously two firecrackers at 100 meters apart (1/10th the distance for 1/10th the wavelength). Firecrackers are small enough that they do not interact with each other at this distance in any nonlinear way. The interference theory such as it is, should still hold good, however...

I do not follow this part, please explain what this part is about.

A_Gupta · Post by **A_Gupta** » 08 Jul 2002 22:36

Kaushal :

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

Sunil Sainis:

This is *not* the case with Wallace and Co. They have simply poured values at random into the equations without propagating their errors.

I am not sure what the "without propagating their errors" corresponds to; but yes, they have simply poured values at random into the equations.

mb = A + B log Y, where mb is the body wave magnitude and Y is the Yield has two parameters that need to be fitted, A and B. We have only two data points, 1974 and 1998, to obtain A and B.

And again, as with Borovoye/Nevada test site, calibrated with a few hundred nuclear tests and not just two, the above relationship separates into three distinct sets of (A,B) depending on the yield Y.

So, yes, Wallace & co are putting random numbers into the relationship.

The above is imo basic physics not politics.

When a physical scientist does things like Wallace & co, it is no longer physics but politics.

> How nuclear blast energy is converted into seismic waves is a stochastic process and conditions for interference do not apply.

Why do you ignore the issue of timescale. I have stated before that the `stochastic' stuff happens *once* of the order of nanoseconds and the waves have a period of a second or so.

I think the blast energy couples to seismic waves over a rather large radius and not just in a few meters (which is what nano-seconds imply).

(different arrival times explanation)

Arun, this little explanation adds absolutely nothing to the physics discussion. This does not motivate the claim of lack of interference in seismic measurements in any way.

The difference in arrival time of the two impulses from the two explosions is of the order of a few hundred milliseconds. I believe modern seismographs have a better time resolution. Then the two impulses do not interfere.

[much snipped]
I agree, I have no idea how big the shock waves are at 500 meters midway between the blasts, and whether at this point, the shock waves are in the non-linear regime, which is what would be required for source effects. The library available to me, unfortunately, does not have any of the books that I would need to look this up.

> The speed of sound in the earth is around 3 km/sec and in air a factor of 10 less. Set off simultaneously two firecrackers at 100 meters apart (1/10th the distance for 1/10th the wavelength). Firecrackers are small enough that they do not interact with each other at this distance in any nonlinear way. The interference theory such as it is, should still hold good, however...

I do not follow this part, please explain what this part is about

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.

Kuttan · Post by **Kuttan** » 08 Jul 2002 22:57

Thanks for the explanation of transerve vs. longitudinal. I read somewhere that particle motion in ocean surface waves actually goes in circles, which seems to be a combination of the two

The other thing I've never understood is the relation between these kinds of waves. Somewhere in the distant past I seem to have read about transverse surface waves caused by sound propagation inside media. Is the propagation still a "transverse" type deep inside the solid medium, or only at the surface?

Jumraoji:

This is why I took up sleeping in Physics class. I could understand neither the questions nor the answers, but had the sense of being a mouse trying to hide during an artillery duel between Al Qaeda and Pakistan Army. I'll try tossing a grenade and then hide again:

Sunilji:

The time scale of the initial radiation blast front of a nuclear explosion may be nanoseconds (or is it microseconds for the actual pressure wave?) but do you actually see anything on the nano-scale even on a sensor placed, say, 10 m from the source? Remember that light travels only 1 foot in one nanosecond even in vacuum.. much slower in any madrassa..

Also, once the nuke cavity is formed, there must be a lot of other waves radiating out from successive monopole-type oscllations of the medium. The basic source is monopole - how does this get translated into shear / bending -type waves (transverse waves) as the energy radiates through the Earth?

A_Gupta · Post by **A_Gupta** » 08 Jul 2002 23:05

Getting back to politics :

http://www.fas.org/news/india/1999/991011-india-nuke11.htm

Had India faked the explosive tests? Were they flops? Or had small blasts eluded the eavesdroppers? And if they had, what did that mean for a global ban on nuclear blasts in which compliance was to be assiduously verified? All of these questions inevitably have a bearing on the increasingly strident debate in the Senate to ratify the test ban treaty where President Clinton has staked the prestige of his administration.
.....
The equation here is fairly straightforward. If the May 13 pair of Indian tests had indeed failed, it reinforced the arguments of the pro-test ban group who can say with conviction, the world's monitoring system, were foolproof.

On the other hand, if the tests were a success as claimed by New Delhi, those who argue that the international monitoring network were deeply flawed, would have concrete evidence.

...

As to how Indian scientists react to these innuendoes and allegations that the May 13 tests may have failed will be watched closely here in Washington.

saint · Post by **saint** » 08 Jul 2002 23:27

Shiv:

Thanks for the reply. Is there another way to interfere in the wave propagation. E.g: multiple walls arround the test site filled/packed with some sort of material (rubber!? or coil springs waste fillings) that takes the shock. I am a novice thinker in N-terms.

Sunil · Post by **Sunil** » 09 Jul 2002 00:29

A_Gupta,

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

I don't think I see how this claim works.

> I am not sure what the "without propagating their errors" corresponds to; but yes, they have simply poured values at random into the equations.

There is a way to propagate errors in measurements in a calculation, it is usually taught in a first year undergraduate lab.

Wallace and Co. have not done this. Their motivations for doing so aside, the fact that they haven't done it stands.

> I think the blast energy couples to seismic waves over a rather large radius and not just in a few meters (which is what nano-seconds imply).

The cavity measurements place the radius to be less than a 100 meters. This expansion take place over a a few hundred nanoseconds.

The seismic disturbances we observe are ~ 1 -10 Hz.

> The difference in arrival time of the two impulses from the two explosions is of the order of a few hundred milliseconds. I believe modern seismographs have a better time resolution. Then the two impulses do not interfere.

The explosions are simultaneous and in the *same* location so unless there is a faultline that runs between the sources, there is no reason to have one impluse arrive a few hundred milliseconds before the other at any given seismograph. On the timescale of the explosions the 100 milliseconds is a really large time.

> I agree, I have no idea how big the shock waves are at 500 meters midway between the blasts, and whether at this point, the shock waves are in the non-linear regime, which is what would be required for source effects. The library available to me, unfortunately, does not have any of the books that I would need to look this up.

I feel the shockwaves are greatly attenuated otherwise we wouldn't get the formation of the cavity, the earth would just continously rip apart. (This imo is also what Narayanan said).

> 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.

Neither have I.

Narayanan,

> Sunilji:

> The time scale of the initial radiation blast front of a nuclear explosion may be nanoseconds (or is it microseconds for the actual pressure wave?) but do you actually see anything on the nano-scale even on a sensor placed, say, 10 m from the source? Remember that light travels only 1 foot in one nanosecond even in vacuum.. much slower in any madrassa..

The pressure wave will form ~1 microsecond after the blast.

I don't think the seismic detector will `see' anything on that timescale. Any seismic detector embedded within 10mts of the device will be destroyed.

> Also, once the nuke cavity is formed, there must be a lot of other waves radiating out from successive monopole-type oscllations of the medium. The basic source is monopole - how does this get translated into shear / bending -type waves (transverse waves) as the energy radiates through the Earth?

I will have to read up before I attempt to answer this.

Anoop · Post by **Anoop** » 09 Jul 2002 00:59

Originally posted by narayanan:
I read somewhere that particle motion in ocean surface waves actually goes in circles, which seems to be a combination of the two

Is the propagation still a "transverse" type deep inside the solid medium, or only at the surface?

Actually, yes, the particle motion on wave surface is circular. I oversimplified the situation to illustrate the idea and covered my bases by throwing in the word 'roughly'

.

As to the second question, I think it should be longitudinal deep inside the medium - the idea being that molecules oscillate around their mean fixed positions and transfer energy to their neighours through collisions. The wave then propagates much further than the mean individual displacement of molecules, but in the same direction. Actually, I didn't know about transverse waves caused by sound propogation. Guessing wildly, it might be caused by the difference in density between the two medium at the surface, though I cannot explain why.

ramana · Post by **ramana** » 09 Jul 2002 01:00

The explosions were conducted 1km apart and timed with .25 sec delay.
The initial effects of the explosion are not detectable outside except for the cavity formation (by satellite pictures etc.) The seismic waves are of 1 hz to 10 Hz as Sunil says. Only the 1 Hz waves travel over teleseismic distanes (>2000km) All other waves(Lg phase, Rayleigh etc) attentuate and are detected only locally- The Current Science has two articles on this. See refs 13, 15 & 16 in the BRM paper.

Sunder has given a very good description of the intereference issue in BRM.( The Indian Nuclear tests - Summary paper )

Read the refs in the BRM article. Especially 30 & 31 for basic info on how the waves travel. Ref 23 describes how the cavity is formed and gives numerical curve fit to actual cavity and known yield.

Right now there is an exchange of articles between Dougal and Sikka in the Current Science. The matter as it stands is that Douglas et al think it is 40kt and the BARC says its the full value- 55kt. Douglas pooh poohs the interference issue and says that the yield is all over the place from 106kt(extreme value) to 12 kt(Wallace). Sundar has shown that from these two values the actual yields can be deduced by some math. The stuff is being reviewed for quite a few months. So its a matter of time for it to be settled.

The problem is when RC felt that simultaneous tests will ensure shaft integrity and confuse the observers he didint know how accurate it would turn out to be.