Coefficient Matrix Properties of Downward Continuation for Potential Fields and Barzilai-Borwein Downward Continuation Method

ZHANG Zhihou; LIAO Xiaolong; YAO Yu; FAN Xiangtai; LU Runqi

doi:10.3969/j.issn.0258-2724.20190440

Volume 56 Issue 2

Apr. 2021

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Journal of Southwest Jiaotong University > 2021 > 56(2): 323-330, 362.

ZHANG Zhihou, LIAO Xiaolong, YAO Yu, FAN Xiangtai, LU Runqi. Coefficient Matrix Properties of Downward Continuation for Potential Fields and Barzilai-Borwein Downward Continuation Method[J]. Journal of Southwest Jiaotong University, 2021, 56(2): 323-330, 362. doi: 10.3969/j.issn.0258-2724.20190440

Citation:

ZHANG Zhihou, LIAO Xiaolong, YAO Yu, FAN Xiangtai, LU Runqi. Coefficient Matrix Properties of Downward Continuation for Potential Fields and Barzilai-Borwein Downward Continuation Method[J]. Journal of Southwest Jiaotong University, 2021, 56(2): 323-330, 362. doi: 10.3969/j.issn.0258-2724.20190440

Citation:

ZHANG Zhihou, LIAO Xiaolong, YAO Yu, FAN Xiangtai, LU Runqi. Coefficient Matrix Properties of Downward Continuation for Potential Fields and Barzilai-Borwein Downward Continuation Method[J]. Journal of Southwest Jiaotong University, 2021, 56(2): 323-330, 362. doi: 10.3969/j.issn.0258-2724.20190440

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Coefficient Matrix Properties of Downward Continuation for Potential Fields and Barzilai-Borwein Downward Continuation Method

doi: 10.3969/j.issn.0258-2724.20190440

Received Date: 25 Apr 2019
Rev Recd Date: 21 Mar 2020

Available Online: 13 Jan 2021

Publish Date: 15 Apr 2021

Abstract

Abstract

Downward continuation of potential fields can not only improve the reliability of geophysical data interpretation, but also plays an important role in navigation. In order to further enhance the calculation accuracy and speed of downward continuation, the Barzilai-Borwein (BB) downward continuation method is proposed. First, the coefficient matrix of downward continuation for potential fields is proved to be a symmetric block-Toeplitz-Toeplitz-block matrix (BTTB). Next, assuming that the coefficient matrix is positive definite, the BB method is used to solve the equations of downward continuation, and the iterative step is limited to ensure the convergence of the algorithm. Finally, the BB method is validated by noise-free data of the theoretical model and practical data, and compared with the integral iterative method. The results show that under the same convergence accuracy, in the case of the theoretical model, the calculation speed of BB method is more than 2 times that of integral iteration method. In the case of practical data, the average relative errors of BB method and integral iteration method are 6.1% and 7.7%, respectively.
- downward continuation,
- coefficient matrix,
- Barzilai-Borwein method,
- convergence

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References

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Coefficient Matrix Properties of Downward Continuation for Potential Fields and Barzilai-Borwein Downward Continuation Method

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Coefficient Matrix Properties of Downward Continuation for Potential Fields and Barzilai-Borwein Downward Continuation Method

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