Surface wave sensitivity: mode summation versus adjoint SEM

We compare finite-frequency phase and amplitude sensitivity kernels calculated based on frequency-domain surface wave mode summation and a time-domain adjoint method. The adjoint calculations involve a forward wavefield generated by an earthquake and an adjoint wavefield generated at a seismic receiver. We determine adjoint sources corresponding to frequency-dependent phase and amplitude measurements made using a multitaper technique, which may be applied to any single-taper measurement, including box car windowing. We calculate phase and amplitude sensitivity kernels using an adjoint method based on wave propagation simulations using a spectral element method (SEM). Sensitivity kernels calculated using the adjoint SEM are in good agreement with kernels calculated based on mode summation. In general, the adjoint SEM is more computationally expensive than mode summation in global studies. The advantage of the adjoint SEM lies in the calculation of sensitivity kernels in 3-D earth models. We compare surface wave sensitivity kernels computed in 1-D and 3-D reference earth models and show that (1) lateral wave speed heterogeneities may affect the geometry and amplitude of surface wave sensitivity; (2) sensitivity kernels of long-period surface waves calculated in 1-D model PREM and 3-D models S20RTS+CRUST2.0 and FFSW1+CRUST2.0 do not show significant differences, indicating that the use of a 1-D reference model is adequate in global inversions of long-period surface waves (periods of 50 s and longer); and (3) the differences become significant for short-period Love waves when mode coupling is sensitive to large differences in reference crustal structure. Finally, we show that sensitivity kernels in anelastic earth models may be calculated in purely elastic earth models provided physical dispersion is properly accounted for.