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Establishing an effective offset‐dependent velocity model by ray tracing and its application in Kirchhoff time migration

Conventional Kirchhoff prestack time migration based on the hyperbolic moveout can cause ambiguity in laterally inhomogeneous media, because the root mean square velocity corresponds to a one‐dimensional model under the horizontal layer assumption; it does not include the lateral variations. The shot/receiver configuration with different offsets and azimuths should adopt different migration velocities as they contribute to a single image point. Therefore, we propose to use an offset‐vector to describe the lateral variations through an offset‐dependent velocity corresponding to the difference in offset from surface points to the image point. The offset‐vector is decomposed into orthogonal directions along the in‐line and cross‐line directions so that the single velocity can be expressed as a series of actual velocities. We use a simple Snell's law‐based ray tracing to calculate the travel time recorded at the image point and convert the travel time to an equivalent velocity corresponding to a pseudo‐straight ray. The double‐square‐root equation using such an equivalent velocity in the offset‐vector domain is non‐hyperbolic and asymmetrical, which improves the accuracy of the migration. Numerical examples using the Marmousi model and a wide azimuth field data show that the proposed method can achieve reasonable accuracy and significantly enhances the imaging of complex structures.