A fast algorithm for depth migration by the Gaussian beam summation method

Abstract

Depth migration by the Gaussian beam summation method has no limitation on the seismic acquisition configuration. In the past, this migration method applied the steepest descent approximation to reduce the dimension of the integrals over the ray parameters at the cost of a precision loss. However, the simplified formula was still in the frequency domain, thereby impairing the computational efficiency. We present a new fast algorithm which can increase the computational efficiency without losing precision. To develop the fast algorithm, we change the order of the integrals and treat the two innermost integrals as a couple of two-dimensional continuous functions with respect to the real and imaginary parts of the total traveltime. A couple of lookup tables corresponding to the values of the two innermost integrals are constructed at the sampling points. The results of the two innermost integrals at a certain imaging point can be obtained through interpolation in the two constructed lookup tables. Both the numerical analysis and examples validate the precision and efficiency of the fast algorithm. With the advantage of handling rugged topography, we apply the fast algorithm to the 2D Canadian Foothills velocity model.