Effects of observational errors on the resolution of surface waves at intermediate distances

Abstract

In this paper a simple procedure is shown that permits the estimation of resolution for a given set of data having specified measurement errors. For estimation of the resolution obtainable with a given set of data, it is not sufficient to combine the partial derivatives of the observed quantities with respect to the parameters at depth; since the resolution is severely limited by the errors of measurement, these errors must also be considered. The determination of shear velocity for the crust and upper mantle from surface‐wave observations is considered as an example. The relative effectiveness of various combinations of modes for the determination of shear velocity is discussed.

Attenuation of Love and Rayleigh waves across the Atlantic.

“…Inversion theory (BACKUS and GILBERT, 1967, 1968, 1970 in its stochastic form (DER et al, 1970;JORDAN and FRANKLIN, 1971) applied to the Rayleigh-wave attenuation data yields an average internal friction model of shear waves for this ocean.…”

Propagation Path Effects for Rayleigh and Love Waves (Surface Wave Studies of the Bering Sea and Alaska Area)

“…was also found that Love-wave dispersion contributes less information about earth structure than Rayleigh-wave dispersion (Der et al, 1970;Braile and Keller, 1975). Since, in general, the maxima of the Rayleigh-wave partial-derivative curves are larger and narrower than those of the corresponding Love-wave curves, Rayleigh waves give better resolution than SLove waves.…”

“…(ii) It is well known that group and phase velocity observations provide basically the same information about the earth model (Der, et al, 1970;Wiggins, 1972). Pilant and Knopoff (1970) Preliminary inspection of data showed that the quality of Love-wave data was inferior to that of Rayleigh-wave data.…”

“…Since it was found that the velocity differences of North and Dziewonski are smoothly varying quantities with period, their values were interpolated or extrapolated as necessary in the present study. Der et al (1970) used the uncertainty principle of Bendat (1958) in assessing the uncertainties in their group velocity data obtained by the multiple filter analysis technique. Judging that the multiple filter analysis gives an accuracy greater than that from the uncertainty principle, !V they took one-fifth of the error estimated from the uncertainty principle as their error of measurements.…”

Simultaneous Inversion of Receiver Functions, Multi-Mode Dispersion, and Travel-Time Tomography for Lithospheric Structure Beneath the Middle East and North Africa

“…Dispersion measurements equalize the weighting and have been used to estimate earth structure for more than four decades (e.g. Haskell, 1954, Brune, 1969Der, et al, 1970;Braile and Keller, 1975). Observed dispersion can be used to constrain portions of the subsurface structure along the propagation path but substantial trade-off in the details of the lower crust and upper mantle are difficult to control without additional information.…”