| 起伏地形上的位场转换 |
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| 引用本文： | 李世雄,叶雅梅,林其彭.起伏地形上的位场转换[J].地球物理学报,1983,26(6):574-587. |
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| 作者姓名： | 李世雄 叶雅梅 林其彭 |
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| 作者单位： | 安徽大学数学系 |
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| 摘 要： | 根据起伏地形上观测的异常场分量（沿任一方向的分量）换算出垂直与水平分量,本文提供了二维情况下的转换方法。其算法是:（1）通过共形映照,将w平面上的地形曲线L的上部映照为z平面的上半平面,将曲线L映照成z平面上的实轴。（2）求解边界为实轴的Hilbert边值问题。 通过理论模型的计算,验证了该方法的正确性。
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| 关 键 词： | 位场转换 起伏地形 共形映照 实轴 积分方程 误差 Hilbert边值问题 z平面 单连通区域 上半平面 |
| 收稿时间： | 1982-07-07 |
TRANSFERENCE OF POTENTIAL FIELD ON UNEVEN SURFACE |
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| LI SHI-XIONG YE YA-MEI LIN QI-PBNG.TRANSFERENCE OF POTENTIAL FIELD ON UNEVEN SURFACE[J].Chinese Journal of Geophysics,1983,26(6):574-587. |
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| Authors: | LI SHI-XIONG YE YA-MEI LIN QI-PBNG |
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| Institution: | Department of Mathematics, Anhui Unversity |
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| Abstract: | In geophysics only the component of the magnetic field along a definite direction is generally measured by the magnetometer. If we can calculate all the three components of the magnetic field from observed data, then the ability of inference can be greatly improved. When the data are obtained on a plane, the above problem has been solved. But when the data are obtained on an uneven surface, this problem remains yet unsolved. In this paper, we have solved this problem in two dimensional cases.Let u （ω） =u （ξ, η） be the potential of the magnetic field and I = （a, b） be a definite direction. We can calculate the value of = f（τ） on a given curve L, i.e.（where τ is an arbitrary point on the curve L）. The problem is to find the value of （?）u/（?）ξ, （?）u/（?）η on the curve L.Using the method of conformal mapping, we can transfer this problem to Hilbert's boundary value problem on the real line, i.e. to find an analytic functionwhich satisfies the boundary condition on the real line.It is known that the solution of Hilbert problem is2]whereThe numerical solution of the conformal mapping problem is reduced to a Fredholm integral equation of the second kind. A method of " smoothing by Spline functions" is used to smooth the given data. The influnce of the error in the observed data has also been discussed. Model examples are presented here to show that this method is accurate and reliable. |
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