Surface Wave Caustics

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S U M M A R YA nymerically efficient implementation of J W K B theory is developed to calculate synthetic surface-wave seismograms on a smooth, laterally heterogeneous earth model. W e illustrate the method by applying it t o model SH12/WM13; the phase and amplitude anomalies of long-period, fundamental-mode Love and Rayleigh waves are compared with the corresponding results obtained using the great-circle approximation and first-order ray-perturbation theory, with the perturbations to the local eigenfunctions ignored. As expected, the most serious discrepancies between these two approximations and full JWKB theory occur for paths with large transverse phase-velocity gradients, which lead t o significant deviations away from the source-receiver great circle. The great-circle approximation consistently underestimates the phase of the first-arriving G1 Love and R1 Rayleigh waves, in accordance with Fermat's principle of least time. T h e global average Fermat bias is greater for Love than for Rayleigh waves; this may be partly responsible for the observed Love-Rayleigh discrepancy currently attributed t o upper mantle transverse isotropy.

Section: Phase and Amplitude Anomaliesmentioning

confidence: 99%

Section: Phase and Amplitude Anomaliesmentioning

confidence: 99%

JWKB surface-wave seismograms on a laterally heterogeneous earth

Wang

Dahlen

1994

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“…integral approximation used in the inversion are no longer valid. Lateral heterogeneity can stretch these caustics to shorter epicentral distances so that the measured angles cannot be modelled with great reliability (Wang, Dahlen & Tromp 1993).…”

Section: Inversion O F the Datamentioning

confidence: 99%

Global observation of off-great-circle propagation of Long-Period surface waves

Laske

1995

105

S U M M A R YIn the current generation of global dispersion maps of surface waves, the longwavelength structure seems to be very well determined. There is general agreement in the patterns of global phase velocity anomalies up to harmonic degree 1-6. However, the shorter-wavelength structure varies significantly between published maps, and it appears that this part of the models depends strongly on the inversion technique and on the data set of surface-wave dispersion (usually phase measurements). Polarization data depend on the lateral gradient of phase velocity and hence are more sensitive to shorter-wavelength structure than phase data; thus, including these data should enhance resolution. In this paper, I demonstrate that polarization data of long-period surface waves ( 2 80 s), as a function of frequency, can be reliably measured using a multitaper technique. The resulting off-great-circle arrival angles of the surface-wave packets are relatively easy to interpret within a ray-theoretical framework. Our data base of threecomponent recordings is now large enough to provide useful constraints on global dispersion maps, particularly on the shorter-wavelength parts. Apart from the phase velocity model itself, a possible misorientation of the horizontal components at each station is included in a non-linear inversion as an additional independent model parameter. This gives a significant improvement in the fit to the data. Misorientations of more than 3" are probable for at least four of the 37 stations investigated.

“…In this paper, we will develop criteria to assess the validity of surfacewave ray theory using these parameters based upon the Fresnel areas of the surface waves on the sphere, and examine the validity of surface-wave JWKB theory using accurate coupledmode seismograms as 'ground truth'. Rayleigh and Love waves propagating on the surface of a sphere exhibit strong focusing at both the epicentre and its antipode (Wang et al 1993) as a result of the spherical geometry, and this renders the validity criterion insensitive to the propagation distance, as we shall see.…”

Section: Introductionmentioning

confidence: 96%

Validity of surface-wave ray theory on a laterally heterogeneous earth

Wang

Dahlen²

1995

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A necessary and sufficient condition for the validity of surface-wave ray theory is S/ m << 1, where S is the root-mean-square degree of the phase-velocity perturbation 6c, and 1 is the degree of the equivalent mode ,,Sl or ,,T. This condition, which is independent of the number of orbits, is obtained by consideration of the Fresnel area along the surface-wave ray path between the source and receiver. We assess the accuracy of surface-wave ray theory by comparing the phase, arrival angle and amplitude anomalies obtained using the JWKB approximation with the corresponding quantities measured using 'ground-truth' synthetic coupled-mode seismograms on models of varying roughness. The JWKB results agree well with the coupled-mode results for model S12-WM13; on a contrived model with slightly rougher variations, however, the agreement deteriorates as the condition S/@ << 1 is less well satisfied. The misfit of the ray approximation, which is dependent upon the quantity S/@, can be attributed to diffraction and other finite-frequency effects within the Fresnel area along the ray path; these effects are ignored by the JWKB theory but are fully accounted for by the coupled-mode summation. The wavefront smoothing produced by this Fresnel-area averaging limits the resolution of surface-wave inversion studies based upon the JWKB approximation.