| In this paper, we examine an efficient, practical method to calculate approximate, finite-frequency waveforms for the early signals from a point source in 3-D acoustic media with smoothly varying velocity and constant density. In analogy to the use of Feynman path integrals in quantum physics, we obtain an approximate waveform solution for the scalar wave equation by a Monte Carlo summation of elementary signals over a representative sample of all possible paths between a source and observation point. The elementary signal is formed from the convolution of the source time function with a time derivative of the Green's function for the homogeneous problem. For each path, this elementary signal is summed into a time series at a travel time obtained from an... |
