Analysis on Convergence of Iteration Method for Potential Fields Downward Continuation and Research on Robust Downward Continuation Method

Hui, Zhang; Chen, Longwei; Ren, Zhigang; Wu, Meiping; Luo, Siqiang; Xu, Shuiqing

doi:10.1002/cjg2.1371

Cited by 15 publications

(6 citation statements)

References 6 publications

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“…The blue blocks in the middle column are the core of the entire algorithm, illustrating the intermediate calculations of the iteration and the equations used in the algorithm. In addition, the convergence verification of the upward continuation in the algorithm has been deduced in previous studies (Luo & Wu, 2016; X. N. Zeng et al., 2013; H. Zhang et al., 2009).…”

Section: Methodsmentioning

confidence: 69%

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Moho Inversion by Gravity Anomalies in the South China Sea: Updates and Improved Iteration of the Parker‐Oldenburg Algorithm

Rao,

Yu,

Chen

et al. 2023

Earth and Space Science

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The Moho is the interface between crust and mantle, and accurate location of the Moho is important for both resource exploration and deep earth condition and structural change investigations. The theory of the traditional Parker‐Oldenburg (P‐O) method is quite simple and it is widely applied in the frequency domain of Moho depth inversion. However, Moho fluctuation simulations using the P‐O method are not reliable because of the lack of field geographic data constraints during the inversion process and the excessively smoothing of data details caused by using filters to correct the source data signals. To solve those problems, we propose an improved iteration P‐O method with a variable density contrast model, the iterative process is constrained by geological data in the inversion parameters, and the variable depth of the gravity interface is iterated using an equivalent form of upward continuation in the Fourier domain, which is more stable and convergent than downward continuation term in original P‐O method. Synthetic experiments indicate that improved method has the better consistency among the simulations than original method, and our improved method has the smallest root mean square (RMS) of 0.59 km. In a real case, we employed the improved method to invert for the Moho depth of the South China Sea (SCS), and the RMS between our Moho depth model and the seismological data is the smallest value of 2.27 km. The synthetic experiments and application of the model to the SCS further prove that our method is practical and efficient.

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Section: Methodsmentioning

confidence: 69%

“…In addition, the convergence verification of the upward continuation in the algorithm has been deduced in previous studies (Luo & Wu, 2016;X. N. Zeng et al, 2013;H. Zhang et al, 2009).…”

Section: Convergence Assessment Of the Improved Algorithmmentioning

confidence: 81%

Moho Inversion by Gravity Anomalies in the South China Sea: Updates and Improved Iteration of the Parker‐Oldenburg Algorithm

Rao,

Yu,

Chen

et al. 2023

Earth and Space Science

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“…The results derived by the DC operator include more high-frequency characteristics and short wavelength anomaly components than the untransformed data because the result derived by the DC operator is closer to the anomalous sources than the untransformed data. However, the DC operator also significantly increases noise and results in an unstable continuation computation (Zhang et al, 2009;Zeng et al, 2011). Both problems can be attributed to the incorrect solution of the DC operator.…”

Section: Introductionmentioning

confidence: 99%

Stable downward continuation of the gravity potential field implemented using deep learning

Chen

et al. 2023

Front. Earth Sci.

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Downward continuation (DC) of the gravity potential field is an important approach used to understand and interpret the density structure and boundary of anomalous bodies. It is widely used to delineate and highlight local and shallow anomalous sources. However, it is well known that direct DC transformation in the frequency domain is unstable and easily affected by high-frequency noise. Recent deep learning applications have led to the development of image recognition and resolution enhancement using the convolutional neural network technique. A similar deep learning architecture is also suitable for training a model for the DC problem. In this study, to solve the problems in existing DC methods, we constructed a dedicated model called DC-Net for the DC problem. We fully trained the DC-Net model on 38,400 pairs of gravity anomaly data at different altitudes using a convolutional neural network. We conducted several experiments and implemented a real-world example. The results demonstrate the following. First, several validation data subset and test data prediction results indicate that the DC-Net model was sufficiently trained. Moreover, it performed better than the traditional strategy in refining the upscaling of low-resolution images. Second, we performed tests on test datasets with changing levels of noise and demonstrated that the DC-Net model is noise-resistant and robust. Finally, we used the proposed model in a real-world example, which demonstrates that the DC-Net model is suitable for solving the DC problem and delineating the detailed gravity anomaly feature near the field source. For real data processing, noise in the gravity anomaly should be reduced in advance. Additionally, we recommend noise quantification of the gravity anomaly before network training.

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“…The integral iterative method has a tremendous effect, achieving an extended depth of 20 times the point distance or even more significantly (Xu, 2006). Despite the excellent effect and strong convergence (Zhang et al, 2009), it also has problems such as noise amplification (Zeng et al, 2011b). The Fast Fourier Transform method (FFT) has the advantages of high computational efficiency and suitability for many quantity calculations.…”

Section: Introductionmentioning

confidence: 99%

High-precision downward continuation of the potential field based on the D-Unet network

et al. 2022

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Potential field data are of great significance to the study of geological characteristics. Downward continuation of the potential field converts potential field data from a high plane to a low plane. Since this method is mathematically an inverse problem solution, it is unstable. The Tikhonov regularization strategy is an effective means of the downward continuation of the potential field. However, achieving high-precision requirements in the stage of precise geophysical exploration is still challenging. Deep learning can effectively solve unstable problems with excellent nonlinear mapping capabilities. Inspired by this, for the downward continuation of the potential field, we propose a new neural network architecture for downward continuation named D-Unet. This study uses the potential field data of a high horizontal plane and the initial model as the network’s input, with the corresponding low-level data serving as the output for supervised learning. Moreover, we add noise to 10% of the data in the training dataset. Model testing shows that our D-Unet has higher accuracy, validity, and stability. In addition, adding noise to the training data can further improve the robustness of the model. Finally, we use the actual potential data of a particular place in northeast China to test our model and satisfactory results have been obtained.

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Analysis on Convergence of Iteration Method for Potential Fields Downward Continuation and Research on Robust Downward Continuation Method

Cited by 15 publications

References 6 publications

Moho Inversion by Gravity Anomalies in the South China Sea: Updates and Improved Iteration of the Parker‐Oldenburg Algorithm

Moho Inversion by Gravity Anomalies in the South China Sea: Updates and Improved Iteration of the Parker‐Oldenburg Algorithm

Stable downward continuation of the gravity potential field implemented using deep learning

High-precision downward continuation of the potential field based on the D-Unet network

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