presentation in the franhoufer iis about my thesis: a wavelet transform based application for...
TRANSCRIPT
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.
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?