Monochromatic wave equation reflection traveltime inversion

Abstract

Wave equation reflection traveltime inversion (WRTI) is a fundamental method for interrogating the deep subsurface macrovelocity model. The time-domain WRTI calculates the gradient through the crosscorrelation of the source background and receiver scattered wavefields and the crosscorrelation of the source scattered and receiver background wavefields. During the backward propagation of the adjoint source, access to the source background and scattered snapshots of the entire propagation time is required. Because the source and receiver wavefields are extrapolated in opposite temporal directions, these source background and scattered wavefields are either stored in memory or reconstructed by additional wavefield extrapolation. This leads to a heavy memory burden and/or high computational cost. To address these challenges, we develop a new frequency-domain WRTI that is based on a monofrequency. By using the wavenumber coverage and gradient analyses, we prove that the monochromatic WRTI can produce comparable wavenumbers with time-domain and multifrequency-based WRTI. Our method directly stores monochromatic wavefields in memory because only one frequency is used for the gradient calculation. Therefore, our method significantly outperforms the conventional time-domain implementation in terms of memory requirement and computational cost. The accuracy of the monochromatic WRTI method is validated by gradient and result comparisons of several models with different complexities. Finally, we determine the effectiveness of our method by applying it to offshore streamer data.