Frequency-Dependent Traveltime Tomography For Controlled-Source, Near-Surface Seismic Data

About 10 years ago finite-frequency traveltime tomography (FFTT) was developed in global seismology. By taking frequency into account, a more accurate estimation of velocity anomalies is theoretically possible. However, the results are not always clear when dealing with real data because of the inherit model non-uniqueness of the inverse problem, and hence the need to use regularization to seek the minimum-structure model. The theory of FFTT is generally not applicable to controlled-source data because there is no reference model known in advance capable of yielding waveforms that are close enough to the recorded seismograms to yield a meaningful delay time. A new approach designed specifically for controlled-source data called frequency-dependent traveltime tomography (FDTT) is presented. It uses wavelength-dependent velocity smoothing as part of a wavefront tracking scheme to calculate frequency-dependent traveltimes, as opposed to delay times, and the appropriate sensitivity kernels. The most important application of FDTT is in near-surface studies since there is a strong potential for ray theory to be invalid given typical seismic wavelengths and the length scale of heterogeneities in the near surface. Applications of FDTT to synthetic data and real data from a groundwater contamination site are presented in which the minimum-structure model is estimated using smoothing regularization. These models contain better resolved velocity anomalies than the equivalent infinite-frequency-derived models. In addition, given the typical width of the sensitivity kernels in near-surface studies, it is possible to perform stable traveltime tomography without regularization and thereby allow the data alone to determine the final model structure. For the equivalent fit to the data, these models contain more structure than the minimum-structure models.