Ocean-bottom Seismic Interferometry in Coupled Acoustic-Elastic Media

Green’s function expressions for seismic interferometry in acoustic and elastic media have been extensively studied and applied across a wide range of applications, including surface-wave tomography and generating virtual shot gathers. However, analogous expressions for coupled acoustic-elastic media systems remain absent, despite their importance for analysing cross-correlation wavefields from ocean-bottom nodal and seismometer recordings and other seismic problems in marine settings. To address this issue, we derive convolution- and correlation-type reciprocity relations for physically coupled acoustic-elastic media by combining Rayleigh’s and Rayleigh-Betti reciprocity theorems, incorporating the constitutive equations governing coupling at the acoustic-elastic interface, and applying time-reversal invariance principles for an arbitrary 3-D inhomogeneous, lossless medium. The derived relationships show that the acoustic and elastic Green’s functions between any two observation points in the medium can be expressed as integrals of cross-correlations of wavefield observations at those locations, generated by sources distributed over an arbitrarily shaped closed surface enclosing the two observation points. When the Earth’s free surface coincides with the enclosing surface, integral evaluation is required only over the remaining portion of the closed surface. If the sources are mutually uncorrelated ambient sources, the Green's function representation simplifies to a direct cross-correlation of wavefield observations at the two points, generated by a specific ambient source distribution on the closed surface. However, in practical scenarios, the ideal source distribution necessary to retrieve Green’s functions is rarely realized, for example, due to non-uniform illumination. To address these challenges, we represent the ambient cross-correlations as self-consistent observations and introduce a cross-correlation modelling methodology that accounts for practical limitations in source distribution for coupled acoustic-elastic media scenarios. We illustrate the theory by modelling ambient cross-correlation wavefields for a deep-water scenario.