Inverting SPAC curves

by eshabani » Fri Sep 21, 2007 2:02 pm

some problems:

1) in dispersion curves in the file resulting from "run_01 run_02 run_03

run_04 run_05" there is no good matching between misfit curves and the

theoretical curve resulting from assuming fundumental Rayleigh mode.

2) When I choose several Rayleigh modes, how the different modes are

distinguished and should i do "resampl" too?

3) the ground profiles are not displayed.

by admin » Fri Sep 21, 2007 3:55 pm

Hi Elham,

1) Are you running inversion of spac curves? Did you select them with spac2disp before? The

cause might be that your parameterization is too restrictive?

It would be helpful to be able to attach images (for instance showing your Vs profiles) to this

discussion. I'll try to add a modification to this forum to be able to attach files and especially

images.

2) When choosing several modes for the same curve, the misfit is computed with the theoretical

mode offering the best fit. In fact the misfit is the squared sum of normalized slowness

differences calculated for each individual samples of th curve. In this case, for "mode guess", for

each sample the best fitting theoretical mode is chosen. At first, one may expect that a lot

oscillations can occur from one mode to the other, from one sample to the next. With experience,

we just observed that it is not the case (probably due to the "rigid" shapes of dispersion curves).

The parameterization and the processing are the exactly the same as for a single mode inversion.

To view the results, the only difference is that you have to select more than one mode to plot (in

dispersion curve viewer), the number of modes you enter in the target specification. I would

suggest not to start with more than 2 modes (fundamental Rayleigh and first higher mode).

3) Several points might be checked:

1. What is your minimum misfit?

2. How many models are generated (see in status window)?

3. Make sure that the maximum misfit to plot is greater than the minimum misfit.

4. Look into the log of your runs to get the path to the report files generated during

inversion. Check that these files really exist.

5. You can finally check their contents with gpdcreport

by admin » Thu Oct 25, 2007 8:19 am

When I open your dinver file, I can see that the target is a spac target for which 5 rings are

defined. For 2 of the 5 rings, the curve is missing. There are two curves (3 in fact, 2 are the

same) for the fundamental mode for the first two rings. Is it correct? Do you have the same

situation? Or is it due to incompatibilities between the release you have installed and mine (the

most recent one)? I don't think so, I unpacked the .dinver file to look at its XML content and I

match exactly what I get in dinver.

So before continuing with the inversion, you should clarify the target definition. One cannot

invert two distinct curves for the same mode and the same ring without generating high misfits.

There must be only one curve per mode and per ring!

Another aspect is that your spac curve range is rather restricted: from 1.14 to 1.94 Hz only. In

most of the rings the curve is flat which is not the part of the curve that contains much

information about the soil structure. One expect at least to get the decrease of this curve, when it

drops towards -0.4 and in some case when you can see some lobes. These curves have been

selected with spac2disp where the original curves were computed over a wide range from 0.1 to

20 Hz. I have e few question that should be addressed:

1. Is it necessary to compute them on a so wide range when only frequencies from 1Hz are

used? It also results in a poor sampling of the curve in the range if interest.

2. What's the quality of the original spac curves? Can you clearly identify a dispersion curve

for the grid?

3. Did you try all other methods, FK, HRFK?

4. How many stations do you have in your array?

5. How many station couples do you have in each ring?

Just to check, I cleaned your target and run a simple inversion (simplifying also the

parameterization to a sediment layer over a bed-rock). As expected, a wide range of possible

models may explain your spac curves. There's also a supplementary problem that the curve

affected to the ring of 35 m has a strange shape compared the other rings. In usual situation, if

the frequency range remains the same, and if the aperture decrease the spac curve must increase

toward 1. In your case it is exactly the contrary. Can you check that it is correctly the curve from

a 35 m aperture ring?

Note: your parameterization was ok, but it is better to start with something really simple (often

too simple) like a sediment layer over a half-space, eventually with a gradient in the sediments.

spac curves

by eshabani » Thu Oct 25, 2007 11:33 am

Thanks Marc

I load the spac target files for 3 arrays, for all I have 7 rings and there is one curve for each ring

in Autocorrelation target curve window,but when I save the dinver file and reopen it in

Autocorrelation target curve window some curves are empty and some have 2 or 3 curves

overlay as you saw in the last dinver file I sent you.

In spite of using a simple parameterization, a sediment layer over a bed-rock, the Minimum

misfit will be more than 1. Also attached are two files of the spac curves and selected rings for

each array.

I have found the Kmin and Kmax for each Array through Build_Array. As you see the reliable

parts of the curves are too small.

May be the array dimentions are not suitable? Do you have any suggestion for array setting for

not repeating the above problems?

by admin » Thu Oct 25, 2007 12:21 pm

In fact, looking at spac2disp snapshots, your original spac curves are quite nice. From the shape

of the dispersion curve that can be outlined, which looks almost flat, I suspect that the interesting

and dispersive part is at lower frequencies, below 1.5 Hz. Do you have an idea of the H/V peak

frequency for the area?

Kmin and Kmax determined using build_array are suitable for FK processing. For HRFK, it can

often be extended a bit. For SPAC there is no quantitative measurement of the limits. The

resolution limit may be 2 or 3 times below the kmin observed for FK. Currently, from the visual

inspection of the dispersion plot in spac2disp you can define the limits for spac. Don't be too

restrictive. I think that in your case you can extend the range of validity up to 4 or 5 Hz

(especially for smallest array). At low frequency, I think that you selected the correct limit.

One question that's not clear in my mind: are you recording all three arrays at the same time? If

not, why did you set up only three stations for the small array?

Finally, your post suggests that there's a mismatch in saving target curves in dinver. Right?

Which version are you using? I also wander if it would be possible to include all target files from

the three arrays into spac2disp... it might be better than analyzing them separately. I'm looking

how to do it. Can you send me the three target files? So that I try here.

We cannot go to the inversion part before setting the spac curves correctly. Let's first solve the

first part...

by eshabani » Thu Oct 25, 2007 2:09 pm

Thanks for your answers.

Yes all three arrays have been recorded at the same time, which is not nessessary to.

I use sesarray-win-2.0.0-snapshot-20070918.

Attached are 3 spac target files.

by admin » Thu Oct 25, 2007 2:20 pm

I've just modified spac2disp to be able to load various .target files at the same time and performs

a selection over all rings.

I was able to reproduce the mixing problem in Dinver. I fix it and I keep you informed when the

new release is available (today evening).

If all your stations were recorded at the same time, why don't you try to process all arrays

together? For spac it may improve the azimuth coverage and for FK techniques it will enlarge the

valid wavenumber range.

Have you got some 3 component stations? What does the H/V curve look like?

by admin » Thu Oct 25, 2007 5:23 pm

I analyzed the three arrays at the same time (possible only with the next release):

Code: Select all spac2disp ARRAY_A.target SPAC_B.target SPAC_C.target

I discovered that your spac curves are not sampled the same way. To process them in spac2disp,

you must have the same sampling (option of the processing). In this case, I cut and resampled the

curve between 0.5 and 20 Hz, with 50 samples in log (using Dinver, now export of target is

working properly, next release).

A single target file is saved from Dinver and in spac2disp, all rings match a single dispersion

curve between 1.5 and 3.5 Hz, except the first two rings measured on the smallest array. I

suspect that the reduced number of station pairs (3) for this array leads to slightly biased results. I

discarded those two rings after loading the selected target in Dinver.

When you load the target file into dinver, the empty rings are still there. Don't forget to remove

those two rings. I used a very simple model for the inversion and got finally very good misfits.

All rings are well fitted except the last one. The frequency band is not different from other rings

so the misfit cannot be improved by adding more degrees of freedom. This probably due to

particular ground configurations or noise structure viewed by the larger ring.

It would probably help understanding this structure if you have H/V ratio. The depth of

investigation is difficult to estimate because the dispersion is almost flat. From the wavelength

criteria, I would say that we have information down to 100-150 m (1/3 of lambda). The

maximum depth was fixed to 100 m so all information below is not valid.

What can be learned from this inversion probably that you need lower frequency information (to

be confirmed by H/V results).

by eshabani » Fri Oct 26, 2007 10:53 am

Thanks alot Marc

I tried to process all arrays together, in this case the small array has a much more wider

frequency range.

In dinver using a simple model in parametrization the Min Misfit will be no less than 0.9. I test

different Poisson's ratios and also add sublayes but I see no differece.

Attached is the dinver file.

by admin » Fri Oct 26, 2007 12:36 pm

I checked your target with spac2disp and in fact the selection is probably too large. The first two

rings have a dispersion curve far from the one from all other rings (local structures close to

surface not viewed by larger wavelengths?). Your high misfit comes from the fact that it is no

possible to find a single dispersion curve explaining all autocorrelation curves. When you run the

inversion with all 7 rings the solution found falls inside the distribution of models shown in the

figure above. Still, a small contrast is visible (from 350 to 500 m/s).

The only way to decrease the misfit is to discard some points or entire rings from the inversion.

But at the end it won't change drastically the Vs profiles. I think that the best to do now is to

process H/V in the area and decide whether you need larger arrays or not.