MOD 3.2 3D reflection tomography designed for complex structures

International audienceS u m m a r y A 3D reflection tomography that can determine correct subsurface velocity structures is of strategic importance for an effective use of 3D prestack depth migration. We have developed a robust and fast 3D reflection tomography that is designed to handle complex models. We use a B-spline representation for interface geometries and for the lateral velocity distribution within a layer and we restrict the vertical velocity variation to have a constant gradient. We solve the ray tracing problem by use of a bending method with a circular ray approximation within layers. For the inversion we use a regularized formulation of reflection tomography which penalizes the roughness of the model. The optimization is based on a quadratic programming formulation and constraints on the model are treated by the augmented Lagrangian technique. We show results of ray tracing and inversion on a rather complex synthetic model. Introduction Ehinger and Lailly, 1995, have shown the interest of reflection tomography for computing velocity models adequate for the seismic imaging of complex geologic structures. In 2D, reflection tomography has proved its effectiveness in this context (Jacobs et al., 1995). In 3D, Guiziou et al., 199 1, have developed a ray tracing based on a straight line ray approximation within a layer and an inversion of poststack data. But it suffers of a non derivability of its traveltime formula due to the Gocad interface representation. We describe a 3D tomography that handles models with the necessary derivability and allows inversion of more complex kinematics by the use of a more accurate traveltime calculation. Model description We choose a blocky model representation of the subsurface, each layer being associated with a geological macrosequence. A velocity law has to be associated with each layer (Figure 1). The form of the velocity law is = y) + where is the lateral velocity distribution (described by cubic B-spline functions) and k is the vertical velocity gradient. Using blocky models can lead to difficulties associated with the possible non-definition of the forward problem (situations where there is no ray joining a source to a receiver) and more generally to all kind of difficulties involved in discontinuous kinematics. The blocky model representation allows velocity discontinuities as they exist in the earth and thus to straightforwardly integrate a priori information on velocities (see Lailly and Sinoquet, 1996, for a general discussion on blocky versus smooth model s for seismic imaging of complex geologic structures). We use a cubic B-spline representation for interface geometries. This Fig