2010
DOI: 10.1190/1.3459955
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Extended isochron rays in prestack depth (map) migration

Abstract: Many processes in seismic data analysis and seismic imaging can be identified with solution operators of evolution equations. These include data downward continuation and velocity continuation. We have addressed the question of whether isochrons defined by imaging operators can be identified with wavefronts of solutions to an evolution equation. Rays associated with this equation then would provide a natural way of implementing prestack map migration. Assuming absence of caustics, we have developed constructiv… Show more

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Cited by 19 publications
(20 citation statements)
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“…In the geometrical (high‐frequency) approximation, the function φ(x,k,t) appearing in equation should satisfy the appropriate eikonal equation, which is, in the case of prestack data, the double‐square‐root (DSR) equation (Duchkov and de Hoop ; Alkhalifah and Fomel ). For VTI media, it has the following form (Alkhalifah ; Duchkov and de Hoop ): pz=12vvr1vr2pr212vr2ηrpr2+12vvs1ps2vs212ps2vs2ηs,where pz=kzφ, ps=ksφ and pr=krφ. Ignoring the velocity variation between the source and receiver, which is a good approximation for small offsets, η=ηs=ηr, v=vs=vr and vv=vvs=vvr and thus, equation , after squaring quantities under the square roots has the following polynomial form: trueleft256vv4v8η4kr4ks4kz4128vv2v6η3kr2ks2kz2…”
Section: Theorymentioning
confidence: 99%
“…In the geometrical (high‐frequency) approximation, the function φ(x,k,t) appearing in equation should satisfy the appropriate eikonal equation, which is, in the case of prestack data, the double‐square‐root (DSR) equation (Duchkov and de Hoop ; Alkhalifah and Fomel ). For VTI media, it has the following form (Alkhalifah ; Duchkov and de Hoop ): pz=12vvr1vr2pr212vr2ηrpr2+12vvs1ps2vs212ps2vs2ηs,where pz=kzφ, ps=ksφ and pr=krφ. Ignoring the velocity variation between the source and receiver, which is a good approximation for small offsets, η=ηs=ηr, v=vs=vr and vv=vvs=vvr and thus, equation , after squaring quantities under the square roots has the following polynomial form: trueleft256vv4v8η4kr4ks4kz4128vv2v6η3kr2ks2kz2…”
Section: Theorymentioning
confidence: 99%
“…We follow the strategy from Duchkov and de Hoop (2010) and resolve the DSR equation explicitly with respect to k h :…”
Section: Sof Equation (Evolution In Subsurface Offset)mentioning
confidence: 99%
“…In (Duchkov and de Hoop, 2010) it was suggested to rewrite the DSR equation in alternative form such that function z(x, h,t) is computed while stepping in t that is two-way time (TWT):…”
Section: Twt Equation (Evolution In Two-way-time)mentioning
confidence: 99%
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“…Propagator. The typical case of a Fourier integral operator associated with a canonical graph is the parametrix for an evolution equation [14,15],…”
mentioning
confidence: 99%