ps, ssp, pspi, ffd

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PS, SSP, PSPI, FFD. KM. SSP. PSPI. FFD. z. 2. 2. k = k 1 – k. ~ k (1 – k + ..). x. x. z. k. 2. k. 2. 2. k. z. k. x. ik(x). z. P(x,z, w ) = P(x,0 , w ) e. PS, SSP, PSPI, FFD. 2. 2. 2. k = k 1 – k. k. k. - PowerPoint PPT Presentation

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  • 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.*