Expectation-maximization framework-based image-domain least-squares migration

Abstract

High-resolution and high-fidelity seismic inversion imaging is one of the core issues of lithologic reservoir exploration. As a linearization subproblem of full-waveform inversion, least-squares migration (LSM) can obtain inversion results with more reliable amplitude, better resolution, and fewer artifacts that can be solved in either the data domain or image domain. For data-domain LSM, the calculation of the data-domain iteration can be very computationally intensive. In practical situations, the convexity of the cost function of LSM could be poor, resulting in slow or even nonconvergence iteration, so the ideal inversion imaging results cannot be reached. The image-domain LSM (ID-LSM) follows the logic of image deblurring, which realizes the effects of LSM in another way. The key problem of ID-LSM is to calculate a reliable Hessian matrix that can be effectively replaced by a set of point-spread functions (PSFs). Affected by the unknown source wavelet, the accuracy of the background velocity, and the accuracy of the forward/migration operator, the calculation results of the Hessian/PSF cannot be accurate. We first illustrate the impact of incorrect Hessian/PSF on ID-LSM through numerical experiments. To eliminate the influence of the inaccuracy of PSF, we develop the ID-LSM problem as a high-dimensional image deconvolution problem. An alternate update strategy of PSF and imaging results is given under the framework of the expectation-maximization algorithm by additionally introducing prior information about PSF and the inversion result. Numerical examples of synthetic data and field data verify that our method significantly improves image quality.