Representation of a velocity model with implicitly embedded interface information

Accurately representing a velocity model for complex media still faces many challenges. The key issue involves the description of discontinuity surface with complicated shapes, such as pinch-out layers, salt domes with overhangs, and faulted interfaces. In this paper, a novel method for representing complex models is proposed. Each velocity discontinuity is described as an iso-value surface of a signed distance function, similar to an implicitly embedded interface. The implicit representation can construct the surfaces with non-manifold characteristics or multi-valued properties, e.g., fractured interfaces or mushroom models. For the velocity field within blocks, an approach involving the multiple copies of the computational mesh is used to bind a mesh to a block. This approach can faithfully describe the velocity distribution close to the block boundary without increasing the complexity of the computational mesh. A new data structure, termed stratigraphic binary tree, is also proposed to define the topological relationships between model elements (interfaces and blocks) and to efficiently manage the model data. A number of examples for different applications are given to evaluate the feasibility of the proposed representation scheme. The velocity model represented by the proposed method can serve as a good candidate for general ray-based forward and inverse applications.