Spectral Element Method andGPU Computing for Seismic Imaging

Chaiwoot BoonyasiriwatMay 1, 2010

Outline

1

• Introduction to Seismic Imaging• Spectral Element Method• GPU Computing and Computational Steering• Summary

Seismic Imaging

2

• Given a seismic data set )( trueobs A md

• Find a model that best describes the given data or minimizes the misfit function where

)(~ trialcalc A md 2

)()( mddm calcobsE

m?CSG

Common shot gather

Seismic Imaging

3

obsd

m?

• Use iterative gradient-based methods

Seismic Imaging in 3D

4

• Improve efficiency• Forward modeling: use better numerical methods• Improve convergence rate: preconditioning• Use many sources simultaneously

Forward Modeling

5

• Important component of seismic imaging methods)(md A

• Numerically solving a wave equation, e.g., acoustic wave equation

spvptt 22

• Numerical methods:• Finite difference• Spectral/pseudo-spectral• Finite element/spectral element

Outline

6

• Introduction to Seismic Imaging• Spectral Element Method• GPU Computing and Computational Steering• Summary

Finite Element Methods

7

8

FDM vs FEM

Finite Element Formulation

9

Acoustic wave equation),(),()(),( 22 tstpvtptt rrrr

rrr vsdpdvvvpdtt2 Weak form

n

iii tPtp

1

)()(),( rr Linear combination of basis functions

FKPPM tt

rM dM jiijij ][

rK dvK jiijij 2][

where

Matrix form

rdspvpv tt22 Weighted residual method

10

Geophysical Applications of FEM

• Global-scale• Exploration-scale

Outline

11

• Introduction to Seismic Imaging• Spectral Element Method• GPU Computing and Computational Steering• Summary

Seismic Imaging on GPUs

12

• High performance and large band-width• General-purpose computing on GPUs using CUDA• Advanced hardware (GPUs) + algorithm

(multisource imaging)• Computational steering: computation + visualization

13Courtesy of NVIDIA

1000

Peak

GFL

OP/

s 750

500

250

0

Performance of GPU vs CPU

Memory Bandwidth of GPU vs CPU

14Courtesy of NVIDIA

120

BandwidthGB/s

100

80

60

40

20

0

15

Conventional vs Multisource Method

Conventional RTM Image using 200 gathers

16

Multisource RTM Image using 20 supergathers

10x speedup

Conventional vs Multisource Method

Computational Steering

17

• Initial model• Line search method• Regularization• Iteration number• Perturb model

manually (steering)

User Interface

Iteration numberM

isfit

val

ue

True model

Tomogram 1

Tomogram 218

Summary

19

• Seismic imaging using spectral element methods• Global-scale waveform inversion using SEM• 3D seismic imaging on GPU cluster (CUDA+MPI)• Computational steering on GPU cluster