ps, ssp, pspi, ffd

PS, SSP, PSPI, FFDSSPFFDKMPSPI

kkzxk = k 1 k z2k2x~ k (1 k + ..) 2xk22z

PS, SSP, PSPI, FFDkkxz

SSP Migration

FFD MigrationThin lens

Thin lensFFD Migration

FFD Migration

FFD Migration

other term

FFD MigrationPDE associated withother term

other termRearrange PDE

FFD MigrationSubstitute FD approximations into above

FFD MigrationSubstitute FD approximations into above

FFD MigrationThin lens

PS, SSP, PSPI, FFD

PS, SSP, PSPI, FFD

Summary

Course Summarym(x)= a(g,s,x) G(g|x)d(g|x)G(x|s)dgdsg,s,wG(g|x) = G(g|x) + G(g|x)d(g|x) = d(g|x) + d(x|g)G(g|x) = G(g|x)d(g|x) = d(g|x) FilterRTMAsymptotic GKM Phase Shift Beam 1-way GAsymptotic G+ Fresnel Zone

1980Multisource SeismicImagingvscopperVLIWSuperscalarRISC197019902010110010000010100010000AluminumYear202020001980CPU Speed vs Year

OUTLINE Theory I Theory II Numerical Results

RTM Problem & Possible Soln.Problem: RTM computationally costly

Solution: Multisource LSM RTM *Preconditioning speeds up by factor 2-3LSM reduces crosstalk5

Forward Model:Multisource Least Squares Migration TTTTTT

Multisource Least Squares Phase-encoded Migration mmigTTTTTT**Standard migrationIf = d(i-j)i jCrosstalk noise

Key Assumptiond(t) =Zero-mean white noise: =0; =0 + ~M1 SNR ~(k)(k)[ S(t) ]2~(k)M2[ S(t) ]2~M2M s

Multisource S/N Ratio# geophones/CSG L [d + d +.. ]1221 d +d T d , d 21 L [d + d + ]12T , . +.

Multisrc. Migration vs Standard Migration# iterationsIterative Multisrc. Migration vs Standard Migrationvsvs

SummaryTime StaticsTime+Amplitude StaticsQM Statics1. Multisource crosstalk term analyzed analytically2. Crosstalk decreases with increasing w, randomness, dimension, iteration #, and decreasing depth3. Crosstalk decrease can now be tuned4. Some detailed analysis and testing needed to refine predictions.TT

OUTLINE Theory I Theory II Numerical Results

0Z k(m)30X (km)16The Marmousi2 ModelThe area in the white box is used for S/N calculation.

0X (km)160Z k(m)30Z (km)30X (km)16Conventional Source: KM vs LSM (50 iterations)

0X (km)160Z k(m)30Z (km)30X (km)16200-source Supergather: KM vs LSM (300 its.)

S/N01Number of Iterations300S/N =7The S/N of MLSM image grows as the square root of the number of iterations.

Fast Multisource Least Squares Phase Shift.Multisource Waveform Inversion (Ge Zhan)Theory of Crosstalk Noise (Schuster)8Multisource Technology

The True Model use constant velocity model with c = 2.67 km/s center frequency of source wavelet f = 20 Hz

Multi-source PSLSM 645 receivers and 100 sources, equally spaced10 sets of sources, staggered; each set constitutes a supergather 50 iterations of steepest descent

Single-source PSLSM 645 receivers and 100 sources, equally spaced100 individual shots 50 iterations of steepest descent

Multi-Source Waveform Inversion Strategy(Ge Zhan) 144 shot gathers

3D SEG Overthrust Model(1089 CSGs)15 km3.5 km15 km

Numerical Results

OUTLINE Theory I Theory II Numerical Results

Multisource Least Squares Migration Time StaticsTime+Amplitude StaticsQM Statics36

SummaryTime StaticsTime+Amplitude StaticsQM Statics1. Multisource crosstalk term analyzed analytically2. Crosstalk decreases with increasing w, randomness, dimension, and decreasing depth3. Crosstalk decrease can now be tuned4. Some detailed analysis and testing needed to refine predictions.37

Forward Model:Multisource Least Squares Migration Standard migrationCrosstalk term Phase encodingKirchhoff kernel34

Multisource Least Squares Migration 35

Multisource Least Squares Migration Time StaticsTime+Amplitude StaticsQM Statics36

Crosstalk TermTime StaticsTime+Amplitude StaticsQM StaticsTT

SummaryTime StaticsTime+Amplitude StaticsQM Statics1. Multisource crosstalk term analyzed analytically2. Crosstalk decreases with increasing w, randomness, dimension, and decreasing depth3. Crosstalk decrease can now be tuned4. Some detailed analysis and testing needed to refine predictions.37

Multisource FWI Summary(We need faster migration algorithms & better velocity models)IO 1 vs 1/20Cost 1 vs 1/20 or betterResolution dx 1 vs 1Sig/MultsSig ? Stnd. FWI Multsrc. FWI

Key Assumption= + Zero-mean white noise: =0; =0i j+ ~ 2n ~ 2n2 ~1/n

Phase-Encoded Multisource Imaging

My talk is organized in the following way:

1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges.2. The second part is theory for a deblurring filter, which is an alternative method to LSM.3. In the third part, I will show a numerical result of a deblurring filter.

4. The fourth is the main part of my talk.Deblurred LSM (DLSM) is a fast LSM with a deblurring filter.I will explain how to use the filter in LSM algorithm.

5. Then I will show numerical results of the DLSM.6. Then I will conclude my presentation.

Each figure has a slide number is shown at the footer.

**Jerry, The multi-source and single-source approaches have used different strategies for the step length. Therefore direct comparison of their misfit error is not applicable. Sorry about that.*