Multiscale Waveform Tomography C. Boonyasiriwat, P. Valasek, P. Routh, B. Macy, W. Cao, and G. T. Schuster * ConocoPhillips * **

Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 1 GoalGoal

Goal 2

Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 3 Goal and MotivationGoal and Motivation

? Introduction 4

Introduction: Traveltime Tomography 5

Introduction 6

Introduction: Waveform Tomography 7

8

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

Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 10 GoalGoal

Why Acoustic? Waveform inversion is also expensive.Waveform inversion is also expensive. Previous research shows acoustics is adequate.Previous research shows acoustics is adequate. 11 Elastic wave equation is expensive.Elastic wave equation is expensive. Use acoustics and mute unpredicted wavefields.Use acoustics and mute unpredicted wavefields.

Theory of Waveform Tomography An acoustic wave equation: The waveform misfit function is 12

Theory of Waveform Tomography The waveform residual is defined by The steepest descent method can be used to minimize the misfit function: 13

Theory of Waveform Tomography The gradient is calculated by where 14

Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 15 GoalGoal

Why Use Multiscale? Low Frequency High Frequency Coarse Scale Fine Scale Image from Bunks et al. (1995) Model parameter (m) Misfit function ( f ) 16

Our Multiscale Approach Use a Wiener filter for low-pass filtering the data.Use a Wiener filter for low-pass filtering the data. Combine Early-arrival Waveform Tomography (Sheng et al., 2006) and a time-domain multiscale approach (Bunks et al., 1995).Combine Early-arrival Waveform Tomography (Sheng et al., 2006) and a time-domain multiscale approach (Bunks et al., 1995). 17 Use a window function to mute all energy except early arrivals.Use a window function to mute all energy except early arrivals. Use multiscale V-cycles.Use multiscale V-cycles.

Why a Wiener Filter? 18 Original Wavelet Target Wavelet Wavelet: Hamming WindowWavelet: Wiener Filter

High Frequency Fine Grid Low Frequency Coarse Grid Multiscale V-Cycle 19

Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 20 GoalGoal

Synthetic SSP Data Results SEG Salt ModelSEG Salt Model Layered Model with ScatterersLayered Model with Scatterers Mapleton ModelMapleton Model 21

Layered Model with Scatterers 22

Initial Velocity Model 23

TRT Tomogram Gradient 24

EWT Tomogram using 15-Hz Data Gradient 25

MWT Tomogram using 2.5-Hz Data Gradient 26

MWT Tomogram using 5-Hz Data 2.5-Hz 27

MWT Tomogram using 10-Hz Data 5 Hz 28

MWT Tomogram using 15-Hz Data 10 Hz 29

Layered Model with Scatterers 30

Comparison of Misfit Function 15 Hz 10 Hz 5 Hz 2.5 Hz 15 Hz 31

SEG Salt Velocity Model 32

TRT Tomogram Gradient 33

MWT Tomogram (2.5,5 Hz) TRT 34

SEG Salt Velocity Model 35

Mapleton Model 36

TRT Tomogram 37

MWT Tomogram (30, 50, 70 HZ) 38

Mapleton Model 39

Marine Data Results 40

Marine Data 515 Shots 480 Hydrophones 12.5 m dt = 2 ms T max = 10 s 41

Low-pass Filtering 42

Reconstructed Velocity 43

Observed Data vs Predicted Data 44

Waveform Residual vs Iteration Number 45 1 s 2 s 5 Hz 10 Hz 5 Hz 10 Hz 5 Hz

Common Image Gather 46 5 Hz 10 Hz

Outline IntroductionIntroduction ResultsResults Multiscale Waveform TomographyMultiscale Waveform Tomography ConclusionsConclusions Theory of Acoustic Waveform TomographyTheory of Acoustic Waveform Tomography 47 GoalGoal

Conclusions MWT partly overcomes the local minima problem.MWT partly overcomes the local minima problem. MWT provides more accurate and highly resolved than TRT and EWT.MWT provides more accurate and highly resolved than TRT and EWT. MWT is much more expensive than TRT.MWT is much more expensive than TRT. 48 Accuracy is more important than the cost.Accuracy is more important than the cost. MWT provides very accurate tomograms for synthetic data and shows encouraging results for the marine data.MWT provides very accurate tomograms for synthetic data and shows encouraging results for the marine data.

Future Work Apply MWT to land data.Apply MWT to land data. 49 Use wider-window data and finally use all the data to obtain more accurate velocity distributions.Use wider-window data and finally use all the data to obtain more accurate velocity distributions. Take into account the source radiation pattern.Take into account the source radiation pattern.

Acknowledgment We are grateful for the support from the sponsors of UTAM consortium.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.Chaiwoot personally thanks ConocoPhillips for an internship and also appreciates the help from Seismic Technology Group at ConocoPhillips. 50