I demonstrate the utility and benefits of a combined use of frequency-dependent traveltime tomography (FDTT) and full waveform inversion (FWI) to estimate the near-surface seismic velocity that contains wavelength- and sub-wavelength-scale features. FDTT is fundamentally different from conventional ray-theory infinite-frequency traveltime tomography (IFTT) methods in the calculation of a frequency-dependent traveltime using wavelength-dependent velocity smoothing (WDVS). I justify the use of WDVS in FDTT for calculating a frequency-dependent traveltime by using forward modeling examples to show its frequency-dependent behaviors that are consistent with finite-frequency wave propagation. Compared to the conventional infinite-frequency traveltimes calculated based on ray-theory, the frequency-dependent traveltimes calculated using WDVS can better match that from synthetic seismographs.

In the combined workflow of FDTT and FWI, FDTT provides a long-wavelength background seismic velocity model as the starting model, and then FWI introduces wavelength- and sub-wavelength-scale features that allow for direct geologic interpretation of the velocity models as is usually carried out in conventional imaging using seismic reflection data. I apply this workflow to seismic data generated by a near-surface realistic synthetic velocity model representing a geologic setting consisting of unconsolidated sediment overlying faulted bedrock, successfully imaging the key model features, a thin low-velocity layer in the sediments, a steep bedrock offset and a steeply dipping low-velocity fault zone. These structures are all at the wavelength-scale that are weakly presented by conventional ray-theory methods. I then apply this workflow to 2D P- and SH-waves collected in 2011 at Rice campus with a known target consisting of a buried tunnel with concrete walls and a void space inside. FDTT inverted the P- and SH-wave picked traveltimes at 250 Hz to provide long-wavelength background velocity models as the starting models for FWI. FWI inverted 18-54 Hz P-wave data and 16-50 Hz SH-wave data to produce velocity models with sub-wavelength- and wavelength-scale features. The P- and SH-wave models image the top part of the tunnel at the correct location at a depth of 1.6 m as a high-velocity anomaly. The P-wave models also image the air in the void space of the tunnel as a low-velocity anomaly. As a comparison, in both the realistic synthetic test and real data applications, conventional IFTT is also applied in a combined workflow with FWI. The comparisons of the inverted models show that both IFTT and FDTT models can serve as adequate starting models for FWI, but FDTT is favored over IFTT because: 1) The FDTT models better recover the magnitude of the velocity anomalies, and 2) The FDTT model serves as a better starting model for FWI, which results in a more accurate FWI velocity estimation with better recovery of the magnitude and location of the key features, particularly in the absence of usable low frequency data.