Ultralow-frequency amplitude variation with angle inversion of plane-wave primary reflection seismograms

Abstract

An amplitude variation with angle (AVA) inversion method is presented for estimating density and velocities of a stratified elastic medium from reflection seismograms in the intercept time-horizontal slowness domain. The elastic medium parameters are assumed to vary continuously with depth. The seismograms are Green’s function precritical incidence primary P-wave reflections of time length [Formula: see text], assumed to obey differential equations of a model for elastic primary P-wave backscattering, similar to seismograms representing the first term in the well-known Bremmer series/Wentzel–Kramers–Brillouin–Jeffreys iterative solution model. A relation is found between the plane-wave Green’s function seismograms at each horizontal slowness and the medium properties in time. The Green’s function seismograms after normal-moveout correction are directly inverted for the medium parameters as a function of zero-offset traveltime. It is documented theoretically and verified numerically that the signal at the fundamental frequency [Formula: see text] must be present in the seismograms for the AVA method to provide the parameter trends of the elastic medium, implying that ultralow frequencies <1 Hz for [Formula: see text] s must be generated and recorded. Noise in the seismograms at ultralow frequencies is not considered because the theoretical AVA model does not handle microseisms that would be measured in real data. The main mathematical findings are illustrated by using simple model seismograms.