Low-rank matrix decomposition method for potential field data separation

Abstract

Separation of potential field data forms the basis of inversion and interpretation. The low-rank matrix theory is used for the separation of potential field data. A theoretical analysis led to the approximate equation that demonstrates the relation between the amplitudes of the wavenumber components of potential field data and the singular values of the trajectory matrix embedded from the potential field data matrix. Therefore, the low-rank feature of the trajectory matrix of regional field data and the sparse feature of the trajectory matrix of residual field data can be obtained based on the features of the power spectrum of the potential field data. Based on this, we have developed a low-rank matrix decomposition model for the separation of the trajectory matrix of the potential field data. Minimizing the rank of the trajectory matrix of the regional field data and the [Formula: see text]-norm of the trajectory matrix of the residual field data is a double-objective optimization task, and this optimization task can be solved by the inexact augmented Lagrange multiplier algorithm. The weighting parameter is robust and easy to set. Numerical experiment results indicate that our method is robust, and the separation errors of the method are smaller compared to the matched filtering and wavelet analysis methods. In addition, our method can be easily implemented and has clear geophysical significance. Finally, our method is applied on real data sets in the Daye area, Hubei Province, China. The separated gravity and magnetic fields coincide well with target geologic sources.

Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory

“…The impact of the choice of the parameters on the computational cost and the quality of the solutions is investigated. [32]. Experiments demonstrated that the results are consistent for a large subinterval.…”

“…r j e iφj e iuj m+ivj n , where (u j , v j ), r j , and φ j denote the 2D wavenumber, amplitude, and phase of the jth 2D component, respectively. It is also proved in [32] that rank(T) = J, and…”

“…A low-rank matrix decomposition algorithm for potential field separation (LRMD PFS), based on RPCA and singular spectrum analysis, is discussed in [32]. Singular spectrum analysis is a classical method using the trajectory matrix and the singular value decomposition (SVD) [22,3,24].…”

Can Targeted Source Information Be Extracted From Superimposed Magnetic Anomalies?

“…Zhu et al. (2020) derived a relation between the rank of ℋ( T ) and J , which is expressed as follows: $$$\text{rank}(\mathcal{H}(\boldsymbol{T}))=J.$$$ …”

“…Here, we use ℋ to denote the block Hankelization operator. Zhu et al (2020) derived a relation between the rank of ℋ(T) and J, which is expressed as follows:…”