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This thesis reports on studies that have been carried out to better image the crustal and upper mantle shear velocity structure around the Gulf of California, Mexico. The Gulf of California forms a part of the plate boundary between the Pacific and North-American plates, where transform motion in the North converts into oceanic spreading in the South. Although currently oblique extension occurs within the gulf, in the past subduction of the oceanic Farallon plate took place along a trench west of what is currently the Baja California Peninsula. Around 12 Ma subduction and spreading ceased and the remaining parts of the Farallon plate were captured by the Pacific plate. After this the Gulf of California started to develop and around 5 Ma the Pacific-North America plate boundary shifted to its present location within the gulf. The study is subdivided into three parts. In the first part we use a spectral-element code to model seismic wave propagation and the adjoint technique to calculate finite-frequency sensitivity kernels for two-station surface wave measurements. We found a dominant sensitivity in the interstation region, close to what is assumed in the two-station method. However, we also show that anomalous structures even far from the assumed propagation path can significantly affect the measurements. To improve regional tomographic inversions using the two-station method, sensitivity kernels should therefore be taken into account. At the regional scale we are interested in this requires high computational costs, which are difficult to reach in practice. In the second part, instead of improving the lateral resolution using the method described above, we improve the vertical resolution by 1-D joint inversions of surface wave and receiver function data recorded by NARS-Baja stations. We use a Neighbourhood Algorithm to obtain shear velocity models beneath the stations. We are able to find sediment and crustal thicknesses below the stations in the area. In the upper mantle we find indications for the presence of subducted plate remnants below the middle and southern parts of the Baja California Peninsula and we identify the top as a sharp interface. The absence of plate remnants below the northern part explains why the middle and southern parts of the Baja California Peninsula move faster to the Northwest with respect to the North-American plate than the northern part. In the third part we investigate the effects of dipping crustal layers on the receiver functions. We find that azimuthal differences is the receiver function data can be explained by a westward dipping Moho below the Baja California Peninsula, and a dipping mid-crustal layer throughout the entire area. For detailed crustal imaging of the Baja California area using receiver functions more complex modelling than a 1-D inversion is recommended.