科研之友
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摘要
A new method is proposed for continuation of the potential field from a measurement surface S to a horizontal plane P which lies below S. Given the potential field on S and relative elevation between S and P, we want to determine the potential field on P. According to the integral formula of upward continuation from P to S, an integral equation is established which is determined by the potential field on S, the potential field on P and the relative elevation, and it is a Fredholm integral equation of the first kind. The integral formula is changed from space domain to wave number domain by the inverse Fourier transform formula, and is further changed into a series by the Taylor expansion of the exponential function. Solution of the integral equation is gained by successive approximation iteration. That is, observation values of potential field on S are used as an initial guess of potential field on P, and theoretical values of potential field on S are calculated by the series, and the values of potential field on P is corrected by the difference between the observation values and the theoretical values, and multiple iterations are made until the termination criterion is satisfied. Wave number domain iteration method is also given for solving the integral equation. Theoretical examples show that the rms error between the reduction anomaly and the theoretical anomaly is 0. 0008 mGal for the gravity model, and is 0.0019 nT for the magnetic model, and the reduction time is 975 s for a grid of 2048X2048 points by a notebook computer of which main frequency is 2. 26 GHz. A field magnetic example demonstrates the validity of the approach.
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