A Wavelet Transform based

application for seismic waves.

Analysis of the performance.

Telecommunication EngineeringThesis

Author: Pedro Cerón Colás

Fraunhofer IIS, Erlangen December 9th 2013

General outline of the presentation

Introduction

Method and Process

Simulation of the algorithm

Conclusions

Overview of the problem

Geophysicsfield

ComplexContinuous

Wavelet Transform

Design of Matlabalgorithms

But… Where can we apply the

Wavelet Transform?

Bio

Sound

Proccesing

_QRS Complex, “Biomedical Signal

Processing”, Sorno & Laguna.

_Circular buffer 3rd FIR filter. “Sound digital

processing”, Rocchesso.

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

General Outline of the

presentation

Introduction

Method and Process

Simulation of the algorithm

Conclusions

Method and process

Conversionof the

signals

Preprocessing: Correction

Multiresolutionfilter (WT)

Processingstep:

Filtering

SurphaseWavesBody Waves

Polarization

analysis

• Data format? SAC or Mseed

• Compressed Info?

STEIM1, STEIM2

• Not compressed Info?

ASCII, float, integer…

Onsetdetection

Matlab

.mat

D

A

T

A

B

A

S

E

S

Seismic formats: SAC and MiniSEED

Word Type NAMES o o o o

0 F DELTA DEPMIN DEPMAX SCALE ODELTA

5 F B E O AINTERNAL

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 GCARCINTERNAL

55 FINTERNAL

DEPMEN

CMPAZ CMPINCXMINIMUM

60 FXMAXIMUM

YMINIMUM

YMAXIMUM

UNUSED UNUSED

65 F UNUSED UNUSED UNUSED UNUSED UNUSED

70 I NZYEAR NZJDAY NZHOUR NZMIN NZSEC

75 I NZMSEC NVHDR NORID NEVID NPTS

80 IINTERNAL

NWFID NXSIZE NYSIZE UNUSED

85 I IFTYPE IDEP IZTYPE UNUSED IINST

90 I ISTREG IEVREG IEVTYP IQUAL ISYNTH

95 IIMAGTYP

IMAGSRC

UNUSED UNUSED UNUSED

100 I UNUSED UNUSED UNUSED UNUSED UNUSED

105 L LEVEN LPSPOL LOVROK LCALDA UNUSED

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 KUSER2KCMPNM

152 K KNETWK KDATRD KINST

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.

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.

Response for channel correction

•

.PAZ

.RESPONSE

Multiresolution filtering using the Wavelet

Transform

Mathematical toolAmplitude

Phase

Inst. Freq.

Multiresolution filter: www.sciencedirect.com, nov.

2013.Plot of a .cwt matrix in Matlab.

Freq?

Input

(Div.)

Prepocessing stage: Filtering

• 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.

Computations are done directly to

the .cwt matrixHow?

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:

Fineradjustment

Lowfrequencyenvelope

High Frequencyenvelope

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.

Surphase wave: Dispersion

What is the distinctive element that define

the Surphase Waves?Dispersion

How can be use the wavelet coefficients to

analyse this phenomenon?

.cwt

matrix

Polarization analysisA

rriv

altim

es

P wave onset

S wave onset

Surphase wave onset

Transformation of 3

axis into 2:

• Polarization of P, S, Love

and Rayleigh waves?

http://www.motionscript.com/mastering-expressions/random-

sphere.html, november 2013

General Outline of the

presentation

Introduction

Method and Process

Simulation of the algorithm

Conclusions

Time errors: First onsetInner

structure

problem

0

0.5

1

1.5

2

2.5

3

3.5

1 2 3 4 5 6 7 8 9 10 11 12

Low SNR

Time errors: Second onsetInner

structure

problem

0

0.5

1

1.5

2

2.5

3

3.5

4

1 2 3 4 5 6 7 8 9 10 11 12

Low SNR

General Outline of the

presentation

Introduction

Method and Process

Simulation of the algorithm

Conclusions

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 processingand 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 non-stationary signals where we don’t know (in advance) where are the frequency bands of interest.

FIR of how many coefficients and what are the frequenciesof the design?