Traveltime inversion for dipping layers, large moveouts, and arbitrary source and receiver positions

The seismic traveltime inversion algorithm presented here requires few limiting assumptions and is computationally efficient. The traveltime for a raypath in a layered earth (uniform or linearly varying sound speeds in each layer) can be written in closed form if the coordinates of the intersections between the raypath and the layer interfaces are known. The traveltime on an actual raypath is minimal with respect to neighboring paths. The raypath can thus be determined by equating the derivatives of the traveltimes with respect to the intersection coordinates to zero. This approach can be applied to the inverse problem, which seeks those layer parameter values which “best fit” the observed traveltimes from a CMP reflection gather. The result is a system of equations in which the intersection coordinates and layer parameters are independent variables, with the constraint that the traveltimes be minimal with respect to the coordinates. When this systemis linearized with a step‐size constraint, an efficient ...