An Amplitude And Traveltime Calculation Using A Higher-Order Parabolic Equation

Abstract

A higher-order parabolic equation is used to compute the traveltime (phase) and the amplitude in constant density acoustic media. This approach is in the frequency domain, thereby avoiding the high frequency approximation inherent in the Eikonal equation. Intrinsic attenuation can be naturally incorporated into the calculation. The error at large angles of propagation caused by the expansion of the square root operator can be virtually eliminated by adding more terms to the expansion. An efficient algorithm is obtained by applying the alternate direction method. Our results are in excellent agreement with the finite element approach for the range-dependent wedge-shaped benchmark problem. The amplitude and the phase are calculated for a syncline and the Marmousi models.