3D traveltime computation for quasi-P-wave in orthorhombic media using dynamic programming

Abstract

A fractured area, such as a fault area, usually induces orthorhombic anisotropy. Ignoring orthorhombic anisotropy may degrade the subsurface image by creating a well mistie and blurring the image. Traveltime computation is essential for many processing techniques, such as depth imaging and tomography. Solving the ray-tracing system and eikonal equation are two popular methods for traveltime computation in isotropic media. However, because the ray-tracing system becomes complex and the eikonal equation becomes highly nonlinear, their applications in orthorhombic media become complex. We have developed an alternative 3D traveltime computation method in orthorhombic media based on dynamic programming. To avoid solving the complex ray-tracing system and nonlinear eikonal equation, it adopts an explicitly expressed group velocity from the moveout approximation to describe the propagation of the wavepath and computes the traveltime by Fermat’s principle. Similar to depth extrapolation, it computes the traveltime from one depth to the next depth and does not suffer from a shadow zone. Besides, three strategies of traveltime computation are proposed to deal with different geologic scenarios. Because classic dynamic programming (i.e., the first strategy) computes all possible wavepaths (i.e., 24 wavepaths) across one spatial location, it may be computationally intensive. Based on the idea of wavefield decomposition (e.g., upgoing and downgoing), the second and third strategies simplify the traveltime computation and reduce the computational cost. Numerical examples on the vertical and tilted orthorhombic models indicate that the traveltime contour obtained by our method matches well with the wavefront extrapolated from the wave equation. Our method can be applied in depth imaging and tomography.