Reflection tomography: How to cope with multiple arrivals?

Triplications and other multiple arrivals are a major obstacle to the use of reflection tomography for the determination of the velocity model in the process of imaging complex geologic structures. A new formulation of traveltime inversion is proposed to overcome this difficulty. It relies on the choice of a parametric representation of the traveltime versus receiver location curves: the parameter we have chosen for this representation is the "ray parameter" at source location, a quantity directly accessible from seismic data. The associated forward problem is a ray shooting for sparse take off angles. The least squares formulation of the inverse problem consists in minimizing an objective function that measures the traveltime mismatch as well as the emergence point mismatch for the ray parameters observed in the dataset. For the solution, we have proposed a dedicated algorithm: use of a gradient type method (Quasi-Newton), the gradient being computed by the adjoint state technique, which is essential to avoid very expensive computations. It is also interesting to note that no two point ray tracing is required in our method.