Traveltime tomography and prestack depth migration for vertical seismic profiling of an angle-domain walkaway on a complex surface

Abstract

Walkaway VSP cannot obtain accurate velocity field, as it asymmetrically reflects ray path and provides uneven coverage to underground target, thereby presenting issues related to imaging quality. In this study, we propose combining traveltime tomography and prestack depth migration for VSP of an angle-domain walkaway, in a bid to establish accurate two-dimensional and three-dimensional (3D) velocity models. First, residual curvature was defined to update velocity, and an accurate velocity field was established. To establish a high-precision velocity model, we deduced the relationship between the residual depth and traveltime of common imaging gathers (CIGs) in walkaway VSP. Solving renewal velocity using the least squares method, a four-parameter tomographic inversion equation was derived comprising formation dip angle, incidence angle, residual depth, and sensitivity matrix. In the angle domain, the reflected wave was divided into up- and down-transmitted waves and their traveltimes were calculated. The systematic cumulative method was employed in prestack depth migration of a complex surface. Through prestack depth migration, the offset-domain CIGs were obtained, and dip angle was established by defining the stack section horizon. Runge—Kutta ray tracing was employed to calculate the ray path from the reflection point to the detection point, to determine the incident angle, and to subsequently calculate the ray path from the reflection point to the irregular surface. The offset-domain residual depths were mapped to the angle domain, and a new tomographic equation was established and solved. Application in the double complex area of the Tarim Basin showed the four-parameter tomographic inversion equation derived in this paper to be both correct and practical and that the migration algorithm was able to adapt to the complex surface.