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Isostatic response of the earth's crust derived by inverse isostasy

机译：反等静性推导的地壳等静响应

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Postulate that the density anomaly is proportional to the earth's radius vector so that it is linearly related to the topography by a convolution of the topography and an isotropic kernel function. Accordingly, one can prove that the attraction of the compensating masses is also a convolution of the topography and an isotropic isostatic response function. Such an isostatic response function can be determined by deconvo-lution. The paper gives the derivation of such a deconvolution by means of spherical harmonics. A practical determination of the isotropic isostatic response function needs the harmonic analysis of both the topography and the attraction of the compensating masses. Applying the principle of inverse isostasy, by which we aim to achieve zero isostatic anomalies, then the attraction of the compensating masses equals the Bouguer anomalies with an opposite sign. The harmonic analysis of the Bouguer anomalies is thus a combination of the harmonic analysis of the topographic potential and the already existed global reference models. A practical application has been carried out using EGM96 and GPM98CR geopotential earth models as well as TUG87 and TBASE digital height models. The results show that the estimated isotropic isostatic response functions behave similarly as that given by the exact bending curve of the earth's crust represented by the Kelvin function kei x. This shows that the isostatic response of the earth's crust computed by direct isostasy using the most realistic isostatic model (modified Vening Meinesz isostatic model with Kelvin function kei x as the exact bending curve) matches the isostatic response of the earth's crust derived by inverse isostasy.
机译：假设密度异常与地球的半径矢量成正比，因此它通过地形和各向同性核函数的卷积与地形线性相关。因此，可以证明补偿质量的吸引力也是形貌和各向同性等静响应函数的卷积。这种等静响应功能可以通过反卷积确定。本文通过球谐函数给出了这种反卷积的推导。实际确定各向同性静力响应函数需要对形貌和补偿质量的吸引力进行谐波分析。应用反等静原理，我们旨在达到零等静距异常，那么补偿质量的吸引力等于具有相反符号的布格异常。因此，布格异常的谐波分析是对地形势的谐波分析和已经存在的全局参考模型的组合。使用EGM96和GPM98CR地势地球模型以及TUG87和TBASE数字高度模型已经进行了实际应用。结果表明，估计的各向同性等静响应函数的行为与开尔文函数kei x表示的地壳精确弯曲曲线给出的行为类似。这表明，使用最现实的等静模型（采用开尔文函数kei x作为精确弯曲曲线的修正的Vening Meinesz等静模型）通过直接等静力计算的地壳等静响应与反等静论导出的地壳等静响应相匹配。

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