The document presents a wavelet transform based application for analyzing seismic waves. It discusses analyzing the performance of an algorithm for seismic signal processing using continuous wavelet transforms. The algorithm is simulated and tested on seismic data with conclusions drawn regarding the results. Key steps of the algorithm include preprocessing the data, applying a multiresolution wavelet filter, detecting signal onsets, and analyzing body and surface wave dispersion and polarization.

1. A Wavelet Transform based
application for seismic waves.
Analysis of the performance.
Telecommunication Engineering Thesis
Author: Pedro Cerón Colás
Fraunhofer IIS, Erlangen December 9th 2013

2. General outline of the presentation
Introduction
Method and
Process
Simulation of
the algorithm
Conclusions

3. Overview of the problem
Geophysics
field
Design of Matlab
algorithms
Complex
Continuous
Wavelet
Transform
Bio
_QRS Complex, “Biomedical Signal
Processing”, Sorno & Laguna.
_Circular buffer 3rd FIR filter. “Sound digital
processing”, Rocchesso.
Sound
Procces
ing
But… Where can we apply the
Wavelet Transform?

4. Some geophysical issues
•
3 components:
EW, NS, Z (transverse)
•
Body Waves (P and S
waves) and Surphase
Waves (Rayleigh and
Love).
•
Seismic Spectrum:
0.001-10hz [1].
•
Frequency
characterization:
Spectrum overlaping of
Body and Surphase
Waves .
Image taken from Dr. José Ignacio Badal Nicolás (Faculty
of Geologics, Zaragoza University). Shared resource.
[1] “Fundamentals of Geophysics” Agustín Udías & Julio
Mezcua. Chap.13

5. General Outline of the
presentation
Introduction
Method and
Process
Simulation of
the algorithm
Conclusions

6. Method and process
D
A
T
A
B
A
S
E
S
Conversion
of the
signals
•
•
•
Preprocessing:
Correction
Data format? SAC or Mseed
Compressed Info?
STEIM1, STEIM2
Not compressed Info?
ASCII, float, integer…
Processing
step:
Filtering
Multiresolution
filter (WT)
Matlab
.mat
Onset
detection
Body Waves
Surphase
Waves
Polarization
analysis

7. Seismic formats: SAC and MiniSEED
Word
Type
NAMES
o
0
F
DELTA
DEPMIN DEPMAX SCALE
ODELTA
5
F
B
E
O
A
INTERN
AL
10
F
T0
T1
T2
T3
T4
15
F
T5
T6
T7
T8
T9
20
F
F
RESP0
RESP1
RESP2
RESP3
25
F
RESP4
RESP5
RESP6
RESP7
RESP8
30
F
RESP9
STLA
STLO
STEL
STDP
35
F
EVLA
EVLO
EVEL
EVDP
MAG
40
F
USER0
USER1
USER2
USER3
USER4
45
F
USER5
USER6
USER7
USER8
USER9
50
F
DIST
AZ
BAZ
GCARC
INTERN
AL
55
F
INTERN
AL
DEPME
N
CMPAZ
CMPINC
XMINIM
UM
60
F
XMAXIM YMINIM YMAXIM
UNUSED UNUSED
UM
UM
UM
65
F
UNUSED UNUSED UNUSED UNUSED UNUSED
70
I
NZYEAR
NZHOUR NZMIN
NZSEC
75
I
NZMSEC NVHDR
NORID
NEVID
NPTS
80
I
INTERN
AL
NWFID
NXSIZE
NYSIZE
UNUSED
85
I
IFTYPE
IDEP
IZTYPE
UNUSED IINST
90
I
ISTREG
IEVREG
IEVTYP
IQUAL
95
I
IMAGTY
P
IMAGSR
UNUSED UNUSED UNUSED
C
100
I
UNUSED UNUSED UNUSED UNUSED UNUSED
105
L
LEVEN
LPSPOL
110
K
KSTNM
KEVNM*
116
K
KHOLE
KO
KA
122
K
KT0
KT1
KT2
128
K
KT3
KT4
KT5
134
K
KT6
KT7
KT8
140
K
KT9
KF
KUSER0
146
K
KUSER1
KUSER2
KCMPN
M
152
K
KNETWK KDATRD KINST
NZJDAY
o
o
LOVROK LCALDA
o
ISYNTH
UNUSED
Algorithms to decode the
information.
Tables taken from:
http://www.iris.edu/software/sac/manual/file_format.html, november 2013.
SEED manual v.2.4, B appendix.

8. Compressional techniques: STEIM 1 and
STEIM 2
STEIM 2:More number of
possibilities (8) with dnib.
Algorithms to decompress the
information.
Tables taken from:
SEED reference manual (version 2.4). B appendix. November 2013.

9. Response for channel correction
•
.PAZ
.RESPONSE

10. Multiresolution filtering using the Wavelet
Transform
Amplitude
Mathematical tool
Phase
Inst. Freq.
Freq?
Input
(Div.)
Multiresolution filter: www.sciencedirect.com, nov.
2013.
Plot of a .cwt matrix in Matlab.

11. Prepocessing stage: Filtering
How?
Computations are done directly to
the .cwt matrix
• Band pass filtering.
• Once we have seen in the .cwt plot where we can locate
the parts of the signal with higher energetic
contributions, we can remove the unnecesary bands
(coefficients).
• Remove DC level and high frequency seismic noise.

12. Onset detector (body waves)
What’s the concept?
Body Waves tend to be at higher frequencies in the
octaves (higher divisions) than Surface waves.
Energetic Criteria:
Mk1
Mk2
Variability Criteria:
Finer
adjustment
Low
frequency
envelope
High
Frequency
envelope

13. Onset detector (surphase waves)
What’s the
concept?
Surphase Waves tend to be at lower
frequencies every octaves
Derivative
Derivative + envolope
We can roughly locate
where it’s located the
onset of the Surphase
waves.

14. Surphase wave: Dispersion
What is the distinctive element that define
the Surphase Waves?
How can be use the wavelet coefficients to
analyse this phenomenon?
.cwt
matrix
Dispersion

15. Arrival times
Polarization analysis
P wave onset
S wave onset
Surphase wave
onset
Transformation of 3
axis into 2:
http://www.motionscript.com/mastering-expressions/randomsphere.html, november 2013
•
Polarization of P, S, Love
and Rayleigh waves?

16. General Outline of the
presentation
Introduction
Method and
Process
Simulation of
the algorithm
Conclusions

17. Time errors: First onset
Inner
structure
problem
3.5
3
2.5
Low SNR
2
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
10
11
12

18. Time errors: Second onset
Inner
structure
problem
4
3.5
Low SNR
3
2.5
2
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
10
11
12

19. General Outline of the
presentation
Introduction
Method and
Process
Simulation of
the algorithm
Conclusions

20. Conclusions
• Algoritms easy to apply (engineering principles:
energy, variability, derivatives…)
• Very satisfactory results.
• Automatic algorithm: Input (signal).
• Outputs are specially interesting in terms of the signal processing
and geophysic field: Time-Frequency analysis, onsets, analysis of
the dispersion phenomena, polarization.
• Formats (SAC and Miniseed) and compressional techniques.
• The multiresolution analysis is specially appropiate for the nonstationary signals where we don’t know (in advance) where are
the frequency bands of interest.
FIR of how many coefficients and what are the frequencies
of the design?