Open AccessThree‐dimensional waveform sensitivity kernels
Author(s) -
Marquering Henk,
Nolet Guust,
Dahlen F.A.
Publication year - 1998
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.1998.00426.x
Subject(s) - sensitivity (control systems) , smoothness , waveform , inversion (geology) , earth structure , seismic wave , wave propagation , geophysics , geology , mathematical analysis , geometry , algorithm , physics , mathematics , seismology , optics , electronic engineering , engineering , quantum mechanics , voltage , tectonics
The sensitivity of intermediate‐period (∼10–100 s) seismic waveforms to the lateral heterogeneity of the Earth is computed using an efficient technique based upon surface‐wave mode coupling. This formulation yields a general, fully fledged 3‐D relationship between data and model without imposing smoothness constraints on the lateral heterogeneity. The calculations are based upon the Born approximation, which yields a linear relation between data and model. The linear relation ensures fast forward calculations and makes the formulation suitable for inversion schemes; however, higher‐order effects such as wave‐front healing are neglected. By including up to 20 surface‐wave modes, we obtain Fréchet, or sensitivity, kernels for waveforms in the time frame that starts at the S arrival and which includes direct and surface‐reflected body waves. These 3‐D sensitivity kernels provide new insights into seismic‐wave propagation, and suggest that there may be stringent limitations on the validity of ray‐theoretical interpretations. Even recently developed 2‐D formulations, which ignore structure out of the source–receiver plane, differ substantially from our 3‐D treatment. We infer that smoothness constraints on heterogeneity, required to justify the use of ray techniques, are unlikely to hold in realistic earth models. This puts the use of ray‐theoretical techniques into question for the interpretation of intermediate‐period seismic data. The computed 3‐D sensitivity kernels display a number of phenomena that are counter‐intuitive from a ray‐geometrical point of view: (1) body waves exhibit significant sensitivity to structure up to 500 km away from the source–receiver minor arc; (2) significant near‐surface sensitivity above the two turning points of the SS wave is observed; (3) the later part of the SS wave packet is most sensitive to structure away from the source–receiver path; (4) the sensitivity of the higher‐frequency part of the fundamental surface‐wave mode is wider than for its faster, lower‐frequency part; (5) delayed body waves may considerably influence fundamental Rayleigh and Love waveforms. The strong sensitivity of waveforms to crustal structure due to fundamental‐mode‐to‐body‐wave scattering precludes the use of phase‐velocity filters to model body‐wave arrivals. Results from the 3‐D formulation suggest that the use of 2‐D and 1‐D techniques for the interpretation of intermediate‐period waveforms should seriously be reconsidered.