Wave-equation Traveltime Inversion with Multi-Frequency Bands: Synthetic and Land Data Examples

A wave-equation traveltime inversion method with multifrequency bands is proposed to invert for the shallow or intermediate subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method searches for the velocity model that minimizes the squared sum of the traveltime residuals using source wavelets with progressively higher peak frequencies. Wave-equation traveltime inversion can partially avoid the cycle skipping problem by recovering the low-wavenumber parts of the velocitymodel. However, we also utilize the frequency information hidden in the traveltimes for obtaining a more highly resolved tomogram. Therefore, we employ different frequency bands when calculating the Fréchet derivatives so that tomograms with better resolution can be reconstructed. Results are validated by the zero offset gathers from the raw data associated with moderate geometrical irregularities. The improved wave-equation traveltime method is robust and merely needs a rough estimate of the startingmodel. Numerical tests on both the synthetic and field data sets validate the above claims.