Pseudoelastic PP and PSSP modeling in stratified media

Abstract

Many modeling techniques have been developed to find the acoustic and elastic responses of a stack of plane layers to a plane spectral wave. For an elastic medium bounded above by an acoustic half-space, the acoustic wave propagator matrix modeling method can be modified to model pseudoelastic PP arrivals and PSSP arrivals. PP arrivals propagate as pure longitudinal (P) waves in the layers, whereas PSSP arrivals propagate as shear (S) waves in the elastic part of the model. A simple modification of the pseudoelastic PP response modeling scheme allows modeling of primary P reflections. A primary reflection event involves just one reflection in the plane stratified model and thus excludes internal multiples. The propagator modeling scheme is formulated in the frequency-horizontal slowness domain. By applying inverse Fourier transforms over the frequency and horizontal wavenumbers, where the wavenumber is the horizontal slowness divided by the frequency, modeled seismograms are computed and displayed in the time-space domain. By applying an inverse Fourier transform over the frequency for selected horizontal slowness components, the computed seismograms can be shown in the intercept time-horizontal slowness ([Formula: see text]) domain. When the source wavelet is unity for frequencies of interest, the [Formula: see text] domain seismograms become plane-wave Green’s function seismograms. The [Formula: see text]-traces of the Green’s function primary P-wave seismograms accumulate with increasing time band-limited step functions weighted by reflection strengths.