J. Claerbout, J. Black's Basic Earth Imaging PDF
By J. Claerbout, J. Black
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Subroutine stack0( adj, add, slow, t0,dt, x0,dx, nt,nx, stack, gather) integer ix, adj, add, nt,nx real x, slow(nt), t0,dt, x0,dx, stack(nt), gather(nt,nx) call adjnull( adj, add, stack,nt, gather,nt*nx) do ix= 1, nx { x = x0 + dx * (ix-1) call nmo0( adj, 1, slow, x, t0,dt, nt, stack, gather(1,ix)) } return; end Let S′ denote NMO, and let the stack be defined by invoking stack0() with the adj=1 argument. Then S is the modeling operation defined by invoking stack0() with the adj=0 argument. 2 illustrates both.
This weight made a big difference in the resolution of the stacks but I cannot explain whether this weighting function is the best possible one, or what systematic procedure leads √ to the best weighting function in general. To understand this better, notice that (τ/t)(1/ t) can be factored into two weights, τ and t −3/2 . One weight could be applied before NMO and the other after. That would also be more efficient than weighting inside NMO, as does nmo1(). Additionally, it is likely that these weighting functions should take into account data truncation at the cable’s end.
5: A common midpoint gather from the Gulf of Mexico before (left) and after (right) linear moveout at water velocity. Later I hope to estimate velocity with depth in shallow strata. Press button for movie over midpoint. 5001 + (tau-tau0)/dt if( 0 < iu && iu <= nt) if( adj == 0 ) data(it,ix) = data(it,ix) + modl(iu,ix) else modl(iu,ix) = modl(iu,ix) + data(it,ix) }} return; end Nearest neighbor rounding is crude but ordinarily very reliable. 5=3/2. 499999) and the fractional part should be exactly 1/2 but numerical rounding pushes it randomly in either direction.
Basic Earth Imaging by J. Claerbout, J. Black
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