The Calculation of High-Order Vertical Derivative in Gravity Field by Tikhonov Regularization Iterative Method

Wei Du and Yangyang Zhang

Mathematical Problems in Engineering, 2021, vol. 2021, 1-13

Abstract:

In mathematics, statistics, and computer science, particularly in the fields of machine learning and inverse problems, regularization is a process of introducing additional information in order to solve an ill-posed problem or to prevent overfitting. The Tikhonov regularization method is widely used to solve complex problems in engineering. The vertical derivative of gravity can highlight the local anomalies and separate the horizontal superimposed abnormal bodies. The higher the order of the vertical derivative is, the stronger the resolution is. However, it is generally considered that the conversion of the high-order vertical derivative is unstable. In this paper, based on Tikhonov regularization for solving the high-order vertical derivatives of gravity field and combining with the iterative method for successive approximation, the Tikhonov regularization method for calculating the vertical high-order derivative in gravity field is proposed. The recurrence formula of Tikhonov regularization iterative method is obtained. Through the analysis of the filtering characteristics of this method, the high-order vertical derivative of gravity field calculated by this method is stable. Model tests and practical data processing also show that the method is of important theoretical significance and practical value.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2021/8818552.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2021/8818552.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:8818552

DOI: 10.1155/2021/8818552

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().