Joint inversion of direct waves, primaries, and multiples for vertical cable seismic data

Abstract

By anchoring vertical cable in seawater and receiving the data excited by the towing cable seismic source, the reflection data from subsurface structures with a high signal-to-noise ratio, wide frequency band, and wide azimuth angle can be obtained, thereby achieving high-quality imaging of the target area. However, due to drifting receivers driven by ocean currents and the nonuniform coverage caused by the vertical orientation of the receivers, the traditional imaging method cannot be directly used in the vertical cable seismic data. Furthermore, crosstalk between the primaries and multiples commonly contaminates the final imaging. A new inversion method, based on the Bayesian inference and the assumption that all errors are Gaussian distributed, is presented to address these problems. The direct waves are used to invert the source/receiver locations. The primary and multiple wavefields are accurately reconstructed based on the reconstructed direct wavefield, and the corresponding reflectivity updates are obtained. The model-domain Hessian matrices consisting of different data are approximated by their diagonal elements to mitigate the nonuniform coverage issue, and the related covariance matrices and data-domain Hessian matrices are defined and approximated, respectively, to alleviate the calculation problem. In addition, the zero-lag correlated wavefields in the gradient are consistent with the actual wavefield propagation process, e.g., a primary wave is generated when the direct wavefield encounters reflectivity, avoiding the crosstalk. Numerical examples for synthetic models and field data illustrate that our method can accurately recover the source/receiver locations and provide high-resolution balanced-amplitude imaging results without evident crosstalk.