Topographic elastic least‐squares reverse time migration based on vector P‐ and S‐wave equations in the curvilinear coordinates

Abstract

ABSTRACTElastic least‐squares reverse time migration has been applied to multi‐component seismic data to obtain high‐quality images. However, the final images may suffer from artefacts caused by P‐ and S‐wave crosstalk and severe spurious diffractions caused by complex topographic surface conditions. To suppress these crosstalk artefacts and spurious diffractions, we have developed a topographic separated‐wavefield elastic least‐squares reverse time migration algorithm. In this method, we apply P‐ and S‐wave separated elastic velocity–stress wave equations in the curvilinear coordinates to derive demigration equations and gradient formulas with respect to P‐ and S‐velocity. For the implementation of topographic separated‐wavefield elastic least‐squares reverse time migration, the wavefields, gradient directions and step lengths are all calculated in the curvilinear coordinates. Numerical experiments conducted with the two‐component data synthetized by a three‐topographic‐layer with anomalies model and the Canadian Foothills model are considered to verify our method. The results reveal that compared with the conventional method, our method promises imaging results with higher resolution and has a faster residual convergence speed. Finally, we carry out numerical examples on noisy data, imperfect migration velocity and inaccurate surface elevation to analyse its sensitivity to noise, migration velocity and surface elevation error. The results prove that our method is less sensitive to noise compared with the conventional elastic least‐squares reverse time migration and needs good migration velocities as other least‐squares reverse time migration methods. In addition, when implementing the proposed method, an accurate surface elevation should be obtained by global positioning system to yield high‐quality images.