| 关于重力学反问题的几个判定准则─—在某些特定约束下的场源问题 |
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| 引用本文： | 李斐.关于重力学反问题的几个判定准则─—在某些特定约束下的场源问题[J].地球物理学报,1998(1). |
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| 作者姓名： | 李斐 |
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| 作者单位： | 武汉测绘科技大学地球科学与测量工程学院!武汉，430070 |
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| 摘 要： | 从重力学反问题的基本理论出发，根据处理不适定问题的Tikhonov正则化原理，应用泛函分析概念，从理论上对如何将重力学反问题这一泛定的不适定问题在某些特定约束下转化成具有适定性的定解问题进行讨论．分别推演及刻画出重力场源密度在具有最小位能、最小L2模、最小H1，2模及最小“梯度模”等限定下的性质及表示式．对各种约束及对应的场源特性的数学、物理意义及合理性进行了分析．为重力学反问题研究提供理论判据．
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| 关 键 词： | 重力学反问题 场源特性 最小模 |
SOME CRITERIA ON GRAVITY INVERSION |
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| LI FEI.SOME CRITERIA ON GRAVITY INVERSION[J].Chinese Journal of Geophysics,1998(1). |
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| Authors: | LI FEI |
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| Abstract: | From basic theory of geophysics, a research on how to convert a improperly posed gravity inversion into a posed problem under some given restrictions is made according to Tikhonov Regularization. The restrictions include that corresponding to a given external gravity field, density distributions are with minimum potential energy,Aunt Li-norm, mini H1,2-norm, mini gradient-norm. The formulae of density under the restrictions above are derived cuL The geophysical significance of all the restrictions and their results are analysed and discussed in order to provide some needed uniqueness criteria for the gravity inversion. |
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| Keywords: | inverse gravimetric problem Character of density Minimum norm |
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