Abstract
In computational mathematics, the iterative method is a mathematical procedure. This method uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. The iterative method is widely used to solve complex problems in engineering. In this paper, the iterative method is applied to inverse the subsurface interface with the gravity anomaly. First, the classical Parker-Oldenburg interface inversion formula was introduced and analogized to the downward continuation formula. Then, combined with the regular-integral downward continuation method, the iterative inversion formula of the gravity interface is derived. The iterative mode of the improved method suppresses high-frequency signals effectively. At the same time, there is no need to perform forward calculations in the iterative process. The model test shows that the proposed method can accurately calculate the depth of the interface. Finally, the proposed interface inversion method is applied to the Qinghai-Tibet Plateau, and the calculated Moho interface provides some geophysical data support for the geological interpretation of the area in the future.
Highlights
MethodParker-Oldenburg interface inversion and steps: Using formula (5), we obtained residual value of Δh are calculated according to step 2 and step 3, respectively
By analogy with the downward continuation formula (13), the regular-integral downward continuation method is suitable for the Parker-Oldenburg interface inversion method. e following gravity inversion formula is obtained:
The reliability of the inversion interface is proven by model tests
Summary
Parker-Oldenburg interface inversion and steps: Using formula (5), we obtained residual value of Δh are calculated according to step 2 and step 3, respectively. Zeng et al [22] proposed the wavenumber domain regular-integral iterative method for downward continuation. By analogy with the downward continuation formula (13), the regular-integral downward continuation method is suitable for the Parker-Oldenburg interface inversion method. For the selection of regular parameters, we use the L curve method. Is paper mainly uses the L curve criterion method to select Tikhonov regularization parameters. E basic idea of cross-checking is as follows: if any point yi of the measurement data is removed, the selected regular parameter should be able to predict the change caused by the removed item. ′ represents the derivation of α. rough the parametric expression of the L curve, that is, the exact expression of functions u(α) and v(α), the maximum curvature function can be directly calculated, and the corresponding regularization parameters can be obtained
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