Traveltime calculations from frequency-domain downward-continuation algorithms

Abstract

We present a new, fast 3D traveltime calculation algorithm that employs existing frequency-domain wave-equation downward-continuation software. By modifying such software to solve for a few complex (rather than real) frequencies, we are able to calculate not only the first arrival and the approximately most energetic traveltimes at each depth point but also their corresponding amplitudes. We compute traveltimes by either taking the logarithm of displacements obtained by the one-way wave equation at a frequency or calculating derivatives of displacements numerically. Amplitudes are estimated from absolute value of the displacement at a frequency. By using the one-way downgoing wave equation, we also circumvent generating traveltimes corresponding to near-surface upcoming head waves not often needed in migration. We compare the traveltimes computed by our algorithm with those obtained by picking the most energetic arrivals from finite-difference solutions of the one-way wave equation, and show that our traveltime calculation method yields traveltimes comparable to solutions of the one-way wave equation. We illustrate the accuracy of our traveltime algorithm by migrating the 2D IFP Marmousi and the 3D SEG/EAGE salt models.