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Wiggins, R. A.

Publications and source records attributed to Wiggins, R. A..

6 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Range of earth structure nonuniqueness implied by body wave observations.

The Herglotz-Wiechert integral for the direct inversion of ray parameter versus distance curves can be manipulated to find the envelope of all possible models consistent with geometrical body wave observations (travel time and ray parameter versus distance). Such an extremal inversion approach has been used to find the uncertainty bounds for the velocity structure in the mantle and core. It is found, for example, that there is an uncertainty of plus or minus 40 km in the radius of the inner core boundary, plus or minus 18 km at the core-mantle boundary, and plus or minus 35 km at the 435-km transition zone. The velocity uncertainty is about plus or minus 0.08 km/sec for P and S waves in the lower mantle and about plus or minus 0.20 km/sec in the core. Experiments with various combinations of ray types in the core indicate that rather crude observations of SKKS-SKS travel times confine the range of possible models far more dramatically than do the most precise estimates of PmKP travel times. Comparisons of results from extremal inversion and linearized perturbation inversions indicate that body wave behavior is too strongly nonlinear for linearized schemes to be effective for predicting uncertainty.

Wiggins, R. A.↗
NASA NTRS1972

Monte Carlo inversion of seismic data

The analytic solution to the linear inverse problem provides estimates of the uncertainty of the solution in terms of standard deviations of corrections to a particular solution, resolution of parameter adjustments, and information distribution among the observations. It is shown that Monte Carlo inversion, when properly executed, can provide all the same kinds of information for nonlinear problems. Proper execution requires a relatively uniform sampling of all possible models. The expense of performing Monte Carlo inversion generally requires strategies to improve the probability of finding passing models. Such strategies can lead to a very strong bias in the distribution of models examined unless great care is taken in their application.

Wiggins, R. A.↗
NASA NTRS1972

The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.

The discrete general linear inverse problem reduces to a set of m equations in n unknowns. There is generally no unique solution, but we can find k linear combinations of parameters for which restraints are determined. The parameter combinations are given by the eigenvectors of the coefficient matrix. The number k is determined by the ratio of the standard deviations of the observations to the allowable standard deviations in the resulting solution. Various linear combinations of the eigenvectors can be used to determine parameter resolution and information distribution among the observations. Thus we can determine where information comes from among the observations and exactly how it constraints the set of possible models. The application of such analyses to surface-wave and free-oscillation observations indicates that (1) phase, group, and amplitude observations for any particular mode provide basically the same type of information about the model; (2) observations of overtones can enhance the resolution considerably; and (3) the degree of resolution has generally been overestimated for many model determinations made from surface waves.

Wiggins, R. A.↗