FREQUENCY-DEPENDENT TRAVELTIME TOMOGRAPHY FOR 2D AND 3D NEAR-SURFACE SEISMIC REFRACTION DATA

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In near-surface studies there is a strong likelihood for the assumptions of ray (infinite-frequency) theory to be violated given typical seismic wavelengths and the length scale of heterogeneities. By taking the finite frequency of real seismic data into account when inverting traveltimes, a more accurate estimation of velocity is theoretically possible. The finite-frequency theory developed for global seismology is not applicable to near-surface data because there is typically no reference model capable of yielding a reliable delay time when cross-correlating real and model-derived synthetic waveforms. A new methodology for picked traveltime data called frequency-dependent traveltime tomography (FDTT) is presented. It uses a wavelength-dependent pre-smoothing of the velocity model to calculate frequency-dependent traveltimes, a direct consequence of which is “fat” wave paths and sensitivity kernels. Applications of FDTT to several real datasets will be presented, including 2D and 3D P-wave data from a groundwater contamination site at the Hill Air Force Base, Utah, and 2D P- and SH-wave data recorded over a known tunnel structure on the campus at Rice University. In each case a minimum-structure, smoothest model is estimated using regularization to address the issue of model non-uniqueness. For the same RMS traveltime misfit, the FDTT models contain more velocity structure with better resolution than the equivalent ray-theory-derived models. In addition, given the width of the wave paths/frequency-dependent sensitivity kernels, it is possible to perform traveltime tomography without regularization and thereby allow the data alone to determine the final model structure. The results presented demonstrate the following benefits of FDTT over ray theory methods: (1) more accurate velocity estimation, (2) less need for regularization, and (3) better starting models for the highly nonlinear problem of full waveform inversion. The main benefits of FDTT over ray theory are due to the use of frequency-dependent traveltimes, not the fat wave paths/sensitivity kernels.