Applications of traveltime modeling and imaging in cross-well seismology

Computation of seismic traveltimes has a wide variety of applications in cross-well seismology, including traveltime tomography, Kirchhoff migration and forward modeling of seismic wavefields. Unfortunately, the traditional raytracing methods have some restrictions and drawbacks, such as the inability to efficiently trace rays into shadow zones and to trace rays everywhere for models with large velocity contrasts. Moreover, the computation of ray traced traveltimes is very time consuming when an entire grid of traveltimes is needed. To overcome these problems, Chapters 1 and 2 present two new non-raytracing traveltime calculation methods for, respectively, isotropic and anisotropic media. Instead of solving for traveltimes by raytracing, they compute traveltimes by solving the appropriate eikonal equation on a finite-difference mesh (Chapter 1) or by propagating the first arrival wavefront according to Huygens' principle (Chapter 2).;The advantages of the eikonal finite-difference and the Huygens' principle methods include: (1) no iterative shooting or bending procedure for each traveltime calculation; (2) traveltimes throughout the model are calculated; (3) traveltimes in shadow zones are easily computed; and (4) efficient computation when traveltimes at all grid points are needed. The major disadvantage is that only the first-arrival time is calculated compared to the ray-tracing capability of calculating rays for a variety of events.;Chapters 3 and 4 present two applications that use these traveltime calculation methods, anisotropic traveltime tomography and Kirchhoff migration. Chapter 3 proposes a new method that separates the velocity distribution in an anisotropic medium into a rapidly varying isotropic background velocity and a slowly varying anisotropic parameter field. This ensures that the inverse problem is not too underdetermined and is therefore soluble by standard optimization methods in a least-squares sense. A key advantage of this method is that it makes no assumption about the type of anisotropy in the medium.;To image the fine details of the interwell geologic structure, Chapter 4 introduces a new migration procedure where constraints are used to alleviate the limited aperture problems in cross-well imaging. The migrated results suggest that constrained migration images reveal much more lithologic detail than do surface seismic images or standard Kirchhoff migration images.