1. TECHNICAL UNIVERSITY OF CRETE
DEPARTMENT OF MINERAL RESOURCES ENGINEERING
APPLIED GEOPHYSICS LAB
73 100 CHANIA
TEL: (+30-28210) 37670 - Fax: (+30-28210) 69554 – e-mail: gkritik@mred.tuc.gr
USERS’ MANUAL FOR kriSIS v1.04
Open Source Matlab™ Algorithms for Analysis of Surface Waves
Programmed by g. kritikakis
Manual v. 1.1
July 2010

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USERS’ MANUAL FOR kriSIS v1.04
kriSIS OPEN SOURCE ALGORITHMS HAVE BEEN TESTED IN MATLAB™ 6.5
RUNNING ON WINDOWS XP sp2 AND ARE DISTRIBUTED FOR FREE "AS IS",
WITHOUT WARRANTIES AS TO PERFORMANCE OR MERCHANTABILITY OR
ANY OTHER WARRANTIES WHETHER EXPRESSED OR IMPLIED. NO
WARRANTY OF FITNESS FOR A PARTICULAR PURPOSE IS OFFERED.
Consult the installation guide before running kriSIS v1.04.
Run the command “kriSIS_auto” on the command window to launch the
application. For further documentation press “help kriSIS_auto“ on the
command window. The MASW data processing is competed to 5 steps:
1. The first step includes reading SGY seismic files or importing a dispersion
curve.
To proceed with the first step, press “Continue”. To terminate the process
press “Cancel”.
IMPORTANT: The byte of binary SGY data must be 32-Bit Floating Point
ordered as “Most Significant Byte First”. To create SGY file from a Matlab
array use the command DATA2SGY(data,dt,offset).

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Dispersion curves can be imported either by an *.RDC file (from previously
processed data) or just a (stored as *.mat file) 3-column ([frequency phase
velocity dispersion curve error]) MATLAB table. IMPORTANT: The selection
of this kind of date bypasses the steps 2 and 3.
2. The second step includes the transformation of seismic data from Time-
Distance domain to Frequency-Phase velocity domain where the dispersion
curves will be shown among the local energy maxima.
To proceed with the second step, press “Continue”. To terminate the
process, press “Cancel”. To return to the previous step press “Back”.

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The kriSIS uses the available from file headers information to set up “Shot
Geometry” parameters. IMPORTANT: All that matters is the relative position
of the seismic source compare to the geophones. It is also correct, for
example, to insert as Source Coordinate 0.00, and first Receiver Coordinate
7.5, instead of –7.5 and 0.0, respectively.
If the geophones were placed in irregular intervals along seismic line, the user
can edit geophone offsets individually by pressing the “Get from Headers
/ Set Irregular Group Intervals” button.
If you set on (default option) the “Normalize amplitudes of original
(t,x) data” radio button, the amplitudes of seismic traces will be
normalized (before the wavefield transformation) to revert the seismic energy
loss due to geometrical spreading.

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Phase velocity – Frequency domain window is selected by setting the
minimum and maximum values of phase velocity and frequency as well as
their increment. Normally, the default values are adequate to image the
dispersion curve of the most seismic records. The user can refine the window
afterwards using the “Back” option.
3. The third step includes the selection of fundamental and higher mode
dispersion curves from the local energy maxima.
To proceed with the third step, press “Continue”. To terminate the
process, press “Cancel”. To return to the previous step press “Back”.

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There is an option to import dispersion curves (DCs) from adjacent seismic
records as a guide DCs for easier selection. Dispersion curves can be
imported either by an *.RDC file (from previously processed data) or just a
(stored as *.mat file) 3-column ([frequency phase velocity dispersion curve
error]) MATLAB table.
Fundamental DC selection is performed by surrounding the white crosses
(which correspond to the local maxima along frequency) using a polygon.
LEFT mouse key sets a point of the polygon on the image, DELETE button
deletes previously set points and RIGHT mouse key is used to terminate the
selection. IMPORTANT: Usually the fundamental dispersion curve is
appeared at lower frequencies and phase velocities than higher modes. Make
sure that the first DC you select corresponds to the fundamental one.

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In MATLAB 6.5, the selected crosses are automatically highlighted with
magenta squares and an estimation of the DC standard deviation is calculated
(bounds). DC standard deviation is calculated along each frequency by the
determination of the difference between the phase velocity, which corresponds
to selected DC point and the phase velocity of a point with energy equal to
63% of the corresponding energy of selected DC point. IMPORTANT: In
MATLAB 7.5 (R2007b) the polygon selection must be verified by pressing
RIGHT mouse button and selecting the option “Create Mask”

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Afterwards, kriSIS prompts a window to request if the user intends to select
the next higher mode. IMPORTANT: You cannot neglect the selection of a
higher mode in order to proceed with the selection of the next one. Thus,
higher modes must be selected sequentially.
Higher mode selection is repeated (up to 9 modes including fundamental)
unless the user terminates DC selection by pressing “NO” button.

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4. The forth step includes the selection of initial model, inversion parameters
and convergence criteria.
To proceed with the forth step, press “Continue”. To terminate the
process, press “Cancel”. To return to the previous step press “Back”.
MODEL PARAMETERS
kriSIS_auto creates automatically an initial model parameters based on the
values of fundamental dispersion curve. In this case, the “No of Layers“ is
affected from the selection of DC to initial model transformation mode
(“Coarse“, “Medium“, “Fine“). IMPORTANT: Usually, only the low depth
layers are split when the user increases the level of layering (i.e. to Fine). The
default value is “Coarse“. The first layer is common to get greater thickness
than the second, third, etc.

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The user can modify the “No of Layers“ from 2 to 35, either by writing the
number in the box, or using the up and down arrows. In this case, the DC to
initial model transformation mode is turned automatically to “Variable“ layer
thickness and the model layers receive gradually increased thickness as the
depth increases.
Maximum investigation depth is correlated to the greatest observed
wavelength (λ=VR/f) with “λ / depth ratio”. This ratio can be modified
from 1 to 3. However, by pressing the “OR” button, the user can define the
maximum depth. In this case “λ / depth ratio” is deactivated.
IMPORTANT: Extreme values of depth (compared to the proposed) may lead
to erroneous solutions or unstable inversion.
The model layers can also be equal by pressing the “Equal” radio button.
Initial model can be imported by reading the best iteration from an
“ACDC_OUT.txt” export file of a previously processed record or DC file (see
saved files further down).
By pressing “Default”, the model parameters are set according to the
values: “Medium“ layering calculated from DC and “λ / depth ratio =
2.0”
All table elements are adjustable apart from depth (Z) values, which are
calculated from layers Thickness.
Either Vp, or Poisson’s ratio (ν) value of each layer must be fixed during the
inversion. Fixing value equal to 1 means that the model parameter of the
corresponding layer is free to change during the inversion. Fixing value equal
to 0 means the opposite. IMPORTANT: Any a-priory information can be
retained during the inversion by fixing the appropriate values. IMPORTANT:
Vp, ν and density (ρ) ARE NOT inverted. They just change values every
iteration according to the fixed values (Vp or ν) and the values of Vs.
Fixing all values of Vp, Poisson’s ratio or density can be done by selecting the
corresponding check box (“fix all Vp”, “fix all Pois”, “fix all ρ”).
The values of all Poisson’s ratios can also be edited by setting its value to the
“all Pois” box.

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Poisson’s ratio values is calculated from the Vs and Vp values according to
the formula:
1
15.0
2
2
−⎟
⎠
⎞
⎜
⎝
⎛
−⎟
⎠
⎞
⎜
⎝
⎛
⋅
=
Vs
Vp
Vs
Vp
ν , while density is calculated from:
ρ = 0.0002·Vp + 1.7 (g/cm3
)

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INVERSION PARAMETERS
The values of Jacobian matrix can be calculated numerically from Thomson-
Haskell method using Ridder’s discrete differentiation technique (“T – H”
selection) or estimated using “Quasi – Newton” techniques. The later
method is NOT recommended due to its unstable inversion behavior and the
insecure results that may produce.
Weighting DC data can be done by taking into consideration the “DC error”
bounds (see STEP 3), the values of Jacobian matrix (“Jacobian values”)
and/or the differences between the observed and the calculated dispersion
curves (“Robust Inversion”) in any combination of the three. The selection
of the later, corresponds to the minimization of the sum of absolute differences
between the observed and the calculated dispersion curves (Norm L1) using
the Iteratively Re-weighted Least Squares (IRLS) method.
Five types of constraints can be applied: (1) Smoothing, (2) Damping and (3)
Blocky (a modified smoothing constraint which MAY highlights sharp
boundaries), as well as the combination of (4) Smoothing and Damping or (5)
Damping and Blocky.
The default inversion parameters are: “T - H” Jacobian calculation, “Robust
inversion” weight and “Bloky” constraint.
CONVERGENCE CRITERIA
The selection of “Optimizing RMS” radio button optimizes the inversion
process by calculating the optimum Lagrangean multiplier in each iteration
using internal sub-iterations. This forces inversion to the reduction of RMS
error in each iteration and stops the process when no further RMS reduction
can be achieved. It should be deactivated only when the inversion stops at the
first few iterations and the RMS error remains high.
“Max Iteration” is the maximum number of iterations in case that the
following convergence criteria are not satisfied. It can be set up to 200. Its
default value, when “Optimizing RMS” is activated, is 30. 100 otherwise.
“Min % RMS Error” is the main (desired) stopping criterion. Inversion
process stops when the percentile root mean square error between the

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observed and the calculated dispersion curves is lower than the selected
value. Takes values from 0.1 to 99.9 %.
By pressing “AND” button the “Max Vs correction for RMS satisfied
(m/s)” box is activated and another stopping criterion is added to the
previous one (RMS). Namely, inversion process stops when the RMS error is
lower than its limit AND the maximum model correction (in m/s) is lower than
the selected value (default 1 m/s).
The last convergence criterion “Min Vs correction for RMS NOT
satisfied (m/s)” prevents the inversion to converge very slowly. The
process stops when the maximum model correction (in m/s) is lower than the
selected value (default 0.01 m/s).
Default values are shown on the figure above.
When the user presses “OK” button, kriSIS performs check to the imported model
parameters. Some warning messages may appear on the screen related to the
maximum depth of investigation and the correction of Vp or Poisson’s ratio
values.
By minimizing (not necessary) all prompted windows the user is able to observe
on the command window information about the inversion process (Iteration No,
RMS error, Damping, Smoothing and/or Blocky factors, and the maximum value
of model correction – DVs(max)).

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5. On the fifth step the user is able to observe the final inversion results and
save or discard them.
To save the inversion results, press “Save”. To discard the inversion result,
press “Clear”. To return to the previous step press “Back”.
IMPORTANT: The displayed inversion results concern the Vs profile, which gives
the smallest RMS error.

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By pressing “Back” button, the window of the 4th
step is appeared.
By pressing “Clear” button, the inversion results are discarded.
By pressing “Save” button, a dialog box is prompted where the user can
specify the directory and the filename for the inversion results to be saved. It
takes some time to save the inversion results because the forward problem
(dispersion curve calculation) is solved to calculate all possible dispersion
curves (fundamental and higher modes) of the final model, which appeared

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within the specified (on Step 2) frequency – phase velocity window. A warning
message may also appear when the dispersion curves is not possible to be
calculated for the complete frequency range.
The inversion results are saved in a folder named by the given filename and
placed in the specified location. These results consist of:
ACDC_IN.dat is a text file containing the observed DC, initial model
parameters, inversion parameters and convergence criteria.
ACDC_JAC.txt is a text file containing the Jacobian matrix of each
iteration.
ACDC_OUT.txt is a text file containing the inversion history (observed
and calculated DC, DC misfit and corresponding RMS error, intermediate
Vs profiles and their adjustments and Lagrangean multipliers).
ACDC_RES.txt is a text file containing the resolution and covariance
matrices for each iteration.
‘Filename’.RDC is a MATLAB file (struct array) containing information
about the observed DCs and the transformed seismic data in the
frequency – phase velocity damain.
‘Filename’.VSD is a MATLAB file (double array) containing information
about the final model.

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‘Filename’_1-TRACES.emf is a picture file (Enhanced Metafile)
displaying the seismic traces.

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‘Filename’_1-DC.emf is a picture file (Enhanced Metafile) displaying the
distribution of seismic energy in frequency – phase velocity domain, the
observed DC and the calculated ones (black dashed curves).
‘Filename’_3-RES-SNS-SGM.emf is a picture file (Enhanced Metafile)
displaying the values of Resolution matrix, the sensitivity (%) of each
model layer Vs value and the corresponding model bounds (standard
deviation of Vs values deduced from Covariance matrix).

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‘Filename’_4-RMS_DISTR.emf is a picture file (Enhanced Metafile)
displaying (a) the number of samples distributed to the RMS error (%)
levels, (b) the distribution of RMS error (%) vs the sample number and (c)
the contribution (%) of the RMS error vs the frequency range.

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‘Filename’_5-RMS.emf is a picture file (Enhanced Metafile) displaying the
RMS error vs iterations and the current Lagrangean multiplier.

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‘Filename’_6-RES.emf is a picture file (Enhanced Metafile), which
displays the calculated DC fit on the observed one and the corresponding
RMS error (%) as well as the initial and final Vs depth profile.
‘Filename’_OUT.xls is a tab delimited text file containing information
about the observed and calculated DC (of the best iteration), the initial
and final (best) model, the inversion parameters, convergence criteria
and RMS error for each iteration (see further down).
Either save or discard the inversion results, the processing can be repeated
(“Continue”) with the same or another data set (seismic record or DC).
Otherwise, the processing is terminated by pressing “Cancel”.

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Example of ‘Filename’_OUT.xls file
Filename : SS1_S
No of modes : 2
Fundamental : 50
No Freq DCobs DCcalc DC error
1 5 198 202.704 26
2 5.2 195 198.552 25
3 5.4 193 194.84 25
4 5.6 190 191.528 23
5 5.8 189 188.57 23
6 6 187 185.917 22
7 6.2 186 183.523 22
8 6.4 183 181.347 20
9 6.6 181 179.352 19
10 6.8 180 177.508 19
11 7 178 175.789 19
12 7.2 175 174.172 17
13 7.4 173 172.638 16
14 7.6 171 171.172 15
15 7.8 169 169.76 14
16 8 168 168.393 14
17 8.2 167 167.06 13
18 8.4 166 165.757 13
19 8.6 165 164.478 12
20 8.8 164 163.218 12
21 9 163 161.978 12
22 9.2 162 160.754 12
23 9.4 161 159.546 12
24 9.6 160 158.355 12
25 9.8 158 157.182 12
26 10 155 156.027 11
27 10.2 153 154.891 11
28 10.4 151 153.776 10
29 10.6 150 152.682 10
30 10.8 149 151.61 9
31 11 148 150.561 8
32 11.2 148 149.534 9
33 11.4 147 148.53 8
34 11.6 147 147.548 8
35 11.8 146 146.589 8
36 12 145 145.651 9
37 12.2 144 144.735 9
38 12.4 143 143.84 9
39 12.6 142 142.965 9
40 12.8 141 142.11 8
41 13 141 141.274 8
42 13.2 140 140.458 7
43 13.4 139 139.661 7
44 13.6 139 138.882 7
45 13.8 138 138.123 6
46 14 138 137.382 6
47 14.2 138 136.661 6

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48 14.4 137 135.958 6
49 14.6 136 135.276 6
50 14.8 134 134.614 4
Higher mode 1: 64
No Freq DCobs DCcalc DC error
1 8.2 280 270.38 34
2 8.4 274 268.108 32
3 8.6 269 265.722 31
4 8.8 264 263.229 30
5 9 259 260.639 29
6 9.2 254 257.967 28
7 9.4 250 255.23 27
8 9.6 247 252.449 26
9 9.8 245 249.647 26
10 10 244 246.85 25
11 10.2 243 244.082 25
12 10.4 241 241.369 23
13 10.6 240 238.733 23
14 10.8 238 236.194 21
15 11 236 233.768 20
16 11.2 234 231.464 19
17 11.4 231 229.29 17
18 11.6 229 227.248 17
19 11.8 227 225.336 16
20 12 225 223.551 16
21 12.2 222 221.887 15
22 12.4 221 220.336 15
23 12.6 219 218.892 14
24 12.8 218 217.544 14
25 13 217 216.285 14
26 13.2 216 215.107 14
27 13.4 216 214.001 14
28 13.6 216 212.96 13
29 13.8 215 211.977 13
30 14 214 211.044 12
31 14.2 212 210.155 12
32 14.4 210 209.304 11
33 14.6 209 208.484 11
34 14.8 208 207.691 11
35 15 207 206.92 11
36 15.2 206 206.164 11
37 15.4 205 205.42 11
38 15.6 205 204.682 11
39 15.8 204 203.947 11
40 16 204 203.21 10
41 16.2 203 202.468 10
42 16.4 202 201.716 10
43 16.6 201 200.953 10
44 16.8 201 200.175 9
45 17 200 199.382 9
46 17.2 199 198.571 9
47 17.4 198 197.744 10

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48 17.6 197 196.9 10
49 17.8 197 196.041 10
50 18 196 195.171 10
51 18.2 196 194.292 9
52 18.4 195 193.409 9
53 18.6 194 192.526 10
54 18.8 193 191.647 10
55 19 192 190.778 10
56 19.2 190 189.921 10
57 19.4 189 189.082 10
58 19.6 188 188.262 10
59 19.8 187 187.466 10
60 20 187 186.695 9
61 20.2 186 185.951 9
62 20.4 185 185.235 9
63 20.6 184 184.547 10
64 20.8 183 183.889 10
Iteration % RMS error
0 6.77E+01
1 3.21E+01
2 3.79E+00
3 2.50E+00
4 2.07E+00
5 1.46E+00
6 9.18E-01
Model layers: 20
Thickness (m) Depth (m) Poisson's ratio Density (gr/cm^3) Vp (m/s) Vs (m/s) σ (m/s)
0.10 0.10 0.4 1.742 210.600 85.977 14.784
0.20 0.30 0.4 1.742 210.624 85.987 11.032
0.30 0.60 0.4 1.755 277.084 113.119 10.920
0.39 0.99 0.4 1.766 330.973 135.119 11.971
0.49 1.48 0.4 1.778 387.615 158.243 10.429
0.59 2.07 0.4 1.774 372.472 152.061 7.441
0.69 2.76 0.4 1.751 255.332 104.239 5.613
0.79 3.55 0.4 1.756 281.628 114.974 5.915
0.89 4.44 0.4 1.798 490.542 200.263 6.445
0.99 5.43 0.4 1.802 512.002 209.024 5.706
1.09 6.52 0.4 1.777 384.379 156.922 6.415
1.18 7.70 0.4 1.773 364.195 148.682 5.424
1.28 8.98 0.4 1.798 487.806 199.146 7.663
1.38 10.36 0.4 1.812 558.420 227.974 7.433
1.48 11.84 0.4 1.813 565.881 231.020 6.861
1.58 13.42 0.4 1.804 521.254 212.801 7.078
1.68 15.10 0.4 1.791 454.589 185.585 7.039
1.78 16.88 0.4 1.785 422.615 172.532 6.529
1.88 18.76 0.4 1.802 508.073 207.420 7.600
0 18.76 0.4 1.847 735.202 300.145 2.895