P-wave first arrival time data from earthquakes and surface seismic data have been used to map the crustal velocity structure in southern California. The combined data result in a dense and highly non-uniform ray-path distribution in the study area. Moho depths obtained from previous published studies have been used in the tomographic inversions to improve the lower crust portion of new models, where is relatively poorly sampled by local earthquakes. A new deformable-layer tomography (DLT) approach, different from the conventional cell tomography, is applied. The tomographic images can contain both real structures and artifacts, while tomographic velocity models have been extensively used in understanding the nature of the Earth's interior structure. In this study, I have investigated and demonstrated how to apply the new DLT method to represent velocity structure in layers, as well as using resolution tests to identify effects from artifacts mapped in the models. First, a large amount of data is collected and analyzed in the study area, which includes: (1) Compiling and sorting local earthquake P-wave first arrivals from 1980 to 2000; (2) Collecting and processing an additional data set from the Los Angeles Region Seismic Experiment (LARSE) survey that complements the ray coverage in the upper crust; and (3) Compiling Moho depths from other independent studies to constrain the lower crust of the velocity model, where has relative poor ray coverage from first arrival times. Secondly, velocity models with different model parameters and Moho constraints have been derived and their resolution has been assessed; the preferred models are validated by restoration resolution tests. The new DLT is able to derive the layered velocity structure by directly inverting the depth perturbations of velocity discontinuities. Both velocity and discontinuities can be determined in our models.

P-wave tomographic images are along two 320-km-long profiles that transverse in approximately the dip directions of the major structures in the earthquake-prone areas in southern California. The effect of Moho geometry on the tomographic inversion has been investigated with and without additional surface seismic LARSE data. Incorporating Moho depths as constraints in the inversions has reduced RMS travel time residuals in the relatively low ray coverage area, because ray paths and travel times can be computed more accurately with incorporating reliable Moho depth estimates as inversion constraints. First arrivals from LARSE lines have significantly improved the resolution of tomographic solutions at shallow depths. The resulting models clearly image the velocity contrast in the upper crust near the basin boundaries with high velocity gradient zones, which correspond to the surface features closely along the profiles. The artifacts in travel time tomography are mainly associated with poor ray coverage and size of model elements. Developing 3D deformable-layer tomography is very challenging. Combining a large set of well resolved 2D models into a 3D model is worthwhile for further research.