The use of P wave amplitude data in a joint inversion with travel times for upper mantle velocity structure

A joint inversion of P wave travel time and amplitude data is performed to test whether the amplitudes can be used to increase the resolution of inversions using travel times alone. Geometrical spreading amplitudes depend on the curvature of the slowness field and may thus help to resolve sharp gradients. Travel times and amplitudes of short-period P waves observed at the Washington Regional Seismograph Network are jointly inverted for upper mantle velocity structure below the array. The processing of the observed P wave amplitudes is discussed in detail, and it is shown that it is important to correct the raw data for station statics, as these dominate the observed amplitude signal. A robust averaging procedure is used to identify and remove outliers from the data set, which is comprised of 8697 travel time and 4255 amplitude measurements. The travel time data alone are used to obtain a reference model for the amplitude data and in this way the nonlinear behavior of the amplitude equations is minimized. The results show that the amplitude data induce small, short-scale slowness perturbations to the starting model, producing an amplitude misfit reduction to an arbitrary degree, depending on the regularization. Inversions with synthetic data are performed to explain this result. An idealized model of a subducting slab is used to generate synthetic data sets. The model resulting from a joint inversion produces an amplitude misfit reduction of 77%, while the travel time misfit is unaffected. In agreement with the results for the real data sets, this is achieved by making small adjustments throughout the model, which do not alter the overall slowness variations. The amplitude data therefore do not improve the resolution of the sharp gradients present in the synthetic slab model. These results can be explained by both the strong sensitivity of geometrical spreading amplitude to slowness perturbations along the ray path and to the distribution of the amplitude data set, which is not complete enough to induce more than incoherent changes to the starting model. The strong sensitivity is due to the combination of long teleseismic ray paths and small-scale (about 30 km) slowness variations allowed by the model parameterization. With the present amplitude data set the curvature is changed on the scale of the node spacing in the model, whereas the overall slowness variations on a scale length of several times the node spacing are unaffected. The regularization has little effect on these small-scale changes, as these changes increase the total model roughness by only 1%. It is concluded that with the amplitude data set available, amplitudes do not improve the resolving power of travel time inversions for upper mantle velocity structure. This is due to the number of data required to both decrease the observed variance in the raw amplitudes to the variance in travel time data and to obtain a good coverage of the model. The application of P wave amplitude data as a validation tool is suggested for models obtained with, for example, travel time inversion. Applications to both synthetic and observed data sets are shown. Anelastic damping is ignored in the inversions. Using linear relations between velocity, temperature, and Q, it is shown that the effect of anelastic attenuation is of the order of 10–15% of that of geometrical spreading through the upper mantle.