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Stephen P. Huestis 《Geophysical Journal International》1981,65(1):165-170
Summary. The formalism of Huestis for placing bounds on subsurface temperatures is generalized to the case of heat flow measurements on a surface which is neither flat nor isothermal. The strip extending between the surface and the depth of interest is imbedded in a larger flat strip extending to a horizontal level everywhere above the topography. Using linear programming, heat sources within and temperatures on the boundary of this simpler region are found such that the heat flow data and temperatures on the Earth's surface are fit, heat production constraints are met, and the extremal bound is achieved. 相似文献
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Stephen P. Huestis 《Geophysical Journal International》1982,69(1):253-263
Summary. For linear geophysical inverse problems, the exercise of finding a greatest lower bound on the uniform norms of positive solutions fitting N data, is shown to have a geometrical counterpart in the N- dimensional space of N -tuples of real numbers. By application of the Fenchel Duality Theorem, we demonstrate that the problem is equivalent to the discovery of a particular hyperplane tangent to a convex set in this space. As examples in the case of two data, the new formulation is applied to the problems of recovering density information from planetary mass and moment of inertia, and from two vertical gravity anomalies. 相似文献
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Stephen P. Huestis 《Geophysical Journal International》1984,78(1):119-137
Summary. We demonstrate a method of performing linear programming optimizations of functionals of subsurface temperature, when thermal conductivity is a known piecewise-constant function. Data comprise heat flow measurements on the flat isothermal surface of this structure, within which heat transfer is by steady-state conduction. Two-dimensionality is assumed. The approach involves establishing constraints which demand the continuity of temperature and the normal component of heat flow across all internal boundaries. These unknown functions are expanded as truncated Fourier series whose coefficients become unknowns of the linear programming solution vector; linear relations are established between these coefficients which guarantee harmonicity of temperature in each region of uniform conductivity, as well as the continuity requirements. Variations of the formalism are detailed for three simple types of geometry. As an example the method is applied to a heat flow data set from Sass, Killeen & Mustonen over the Quirke Lake Syncline of Ontario, Canada. 相似文献
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Summary. Using the techniques of linear and quadratic programming, it can be shown that the isostatic response function for the continental United States, computed by Lewis & Dorman (1970), is incompatible with any local compensation model that involves only negative density contrasts beneath topographic loads. We interpret the need for positive densities as indicating that compensation is regional rather than local. The regional compensation model that we investigate treats the outer shell of the Earth as a thin elastic plate, floating on the surface of a liquid. The response of such a model can be inverted to yield the absolute density gradient in the plate, provided the flexural rigidity of the plate and the density contrast between mantle and topography are specified.
If only positive density gradients are allowed, such a regional model fits the United States response data provided the flexural rigidity of the plate lies between 1021 and 1022 N m. The fit of the model is insensitive to the mantle/ load density contrast, but certain bounds on the density structure can be established if the model is assumed correct. In particular, the maximum density increase within the plate at depths greater than 34 kin must not exceed 470 kg m−3 ; this can be regarded as an upper bound on the density contrast at the Mohorovicic discontinuity.
The permitted values of the flexural rigidity correspond to plate thicknesses in the range 5–10 km, yet deformations at depths greater than 20 km are indicated by other geophysical data. We conclude that the plate cannot be perfectly elastic; its effective elastic moduli must be much smaller than the seismically determined values. Estimates of the stress-differences produced in the earth by topographic loads, that use the elastic plate model, together with seismically determined elastic parameters, will be too large by a factor of four or more. 相似文献
If only positive density gradients are allowed, such a regional model fits the United States response data provided the flexural rigidity of the plate lies between 10
The permitted values of the flexural rigidity correspond to plate thicknesses in the range 5–10 km, yet deformations at depths greater than 20 km are indicated by other geophysical data. We conclude that the plate cannot be perfectly elastic; its effective elastic moduli must be much smaller than the seismically determined values. Estimates of the stress-differences produced in the earth by topographic loads, that use the elastic plate model, together with seismically determined elastic parameters, will be too large by a factor of four or more. 相似文献
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Upward and downward continuation as inverse problems 总被引：2，自引：0，他引：2
Summary . The formalism of Backus & Gilbert is applied to the problems of upward and downward continuation of harmonic functions. We first treat downward continuation of a two-dimensional field to a level surface everywhere below the observation locations; the calculation of resolving widths and solution estimates is a straightforward application of Backus—Gilbert theory. The extension to the downward continuation of a three-dimensional field uses a delta criterion giving resolving areas rather than widths. A feature not encountered in conventional Backus—Gilbert problems is the requirement of an additional constraint to guarantee the existence of the resolution integrals. Finally, we consider upward continuation of a two-dimensional field to a level above all observations. We find that solution estimates must be weighted averages of the field not only on this level, but also on a line passing between the observations and sources. Weighting on the lower line may be traded off against resolution on the upper level. 相似文献
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