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Multiscale Waveform Tomography. C. Boonyasiriwat, P. Valasek * , P. Routh * , B. Macy * , W. Cao, and G. T. Schuster * ConocoPhillips. Outline. Goal. Introduction. Theory of Acoustic Waveform Tomography. Multiscale Waveform Tomography. Results. Conclusions. 1. Goal. 2. Outline.

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multiscale waveform tomography
Multiscale Waveform Tomography

C. Boonyasiriwat, P. Valasek*, P. Routh*, B. Macy*,

W. Cao, and G. T. Schuster

* ConocoPhillips

outline
Outline
  • Goal
  • Introduction
  • Theory of Acoustic Waveform Tomography
  • Multiscale Waveform Tomography
  • Results
  • Conclusions

1

outline1
Outline
  • Goal and Motivation
  • Introduction
  • Theory of Acoustic Waveform Tomography
  • Multiscale Waveform Tomography
  • Results
  • Conclusions

3

introduction waveform tomography2
Introduction: Waveform Tomography
  • No high frequency approximation
  • Frequency domain: Pratt et al. (1998), etc.
  • Time domain: Zhou et al. (1995), Sheng et al. (2006), etc.
  • Pratt and Brenders (2004) and Sheng (2006) used early-arrival wavefields.
  • Bunks et al. (1995) and Pratt et al. (1998) used multiscale approaches.

10

outline2
Outline
  • Goal
  • Introduction
  • Theory of Acoustic Waveform Tomography
  • Multiscale Waveform Tomography
  • Results
  • Conclusions

11

why acoustic
Why Acoustic?
  • Elastic wave equation is expensive.
  • Waveform inversion is also expensive.
  • Previous research shows acoustics is adequate.
  • Use acoustics and mute unpredicted wavefields

12

theory of waveform tomography
Theory of Waveform Tomography

The waveform misfit function is

An acoustic wave equation:

13

theory of waveform tomography1
Theory of Waveform Tomography

The steepest descend method is used to minimize the misfit function:

The waveform residual is defined by

14

theory of waveform tomography2
Theory of Waveform Tomography

where

The gradient is calculated by

15

outline3
Outline
  • Goal
  • Introduction
  • Theory of Acoustic Waveform Tomography
  • Multiscale Waveform Tomography
  • Results
  • Conclusions

16

why using multiscale
Why using Multiscale?

Misfit function ( f )

Model parameter (m)

Low Frequency

Coarse Scale

High Frequency

Fine Scale

Image from Bunk et al. (1995)

17

our multiscale approach
Our Multiscale Approach
  • Combine Early-arrival Waveform Tomography (Sheng et al., 2006) and a time-domain multiscale approach (Bunk et al., 1995)
  • Use a Wiener filter for low-pass filtering.
  • Use an early-arrival window function to mute all energy except early arrivals.
  • Use multiscale V-cycles.

18

multiscale v cycle
Multiscale V-Cycle

High Frequency Fine Grid

Low Frequency Coarse Grid

19

why a wiener filter
Why a Wiener Filter?

Target Wavelet

Original Wavelet

Wavelet: Hamming Window

Wavelet: Wiener Filter

20

outline4
Outline
  • Goal
  • Introduction
  • Theory of Acoustic Waveform Tomography
  • Multiscale Waveform Tomography
  • Results
  • Conclusions

21

synthetic ssp data results
Synthetic SSP Data Results
  • Three-Layer Model
  • Layered Model with Scatters
  • SEG Salt Model
  • Zhu’s Model
  • Mapleton Model

22

trt tomogram
TRT Tomogram

Gradient

25

ewt tomogram
EWT Tomogram

Gradient

26

trt tomogram1
TRT Tomogram

Gradient

32

comparison of misfit function
Comparison of Misfit Function

15 Hz

15 Hz

5 Hz

10 Hz

2.5 Hz

38

trt tomogram2
TRT Tomogram

Gradient

40

trt tomogram3
TRT Tomogram

Gradient

44

marine data
Marine Data

480 Hydrophones

515 Shots

12.5 m

dt = 2 ms

Tmax = 10 s

52

outline5
Outline
  • Goal
  • Introduction
  • Theory of Acoustic Waveform Tomography
  • Multiscale Waveform Tomography
  • Results
  • Conclusions

58

conclusions
Conclusions
  • MWT partly overcomes the local minima problem.
  • MWT provides more accurate and highly resolved than TRT and EWT.
  • MWT is much more expensive than TRT.
  • Accuracy is more important than the cost.
  • MWT provides very accurate tomograms for synthetic data and shows encouraging results for the marine data.

59

future work
Future Work
  • Use wider-window data and finally use all the data to obtain more accurate velocity distributions.
  • Apply MWT to land data.

60

acknowledgment
Acknowledgment
  • We are grateful for the support from the sponsors of UTAM consortium.
  • Chaiwoot personally thanks ConocoPhillips for an internship and also appreciates the help from Seismic Technology Group at ConocoPhillips.

61

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