Automatic Arc Distortion Correction of Seismograms Using the Low-Rank Matrix Recovery Method

Abstract

This letter presents a method of correcting the arc distortion of historical seismogram waveforms recorded by pen and paper drum-type seismographs. The proposed method employs the low-rank matrix recovery method to estimate deformation parameters and to correct geometrically distorted seismic waveforms. A seismogram is inherently regular and symmetrical, which motivates us to explore its textural properties. Given that rank is a natural measure of the regularity of textures and images, an undistorted seismogram texture is assumed to have a lower rank than its distorted versions. Thus, the proposed algorithm aims to find parameters that make the rank of the seismogram texture to the minimum. Compared with traditional methods, the proposed method can automatically estimate the parameters of recording devices and works efficiently and robustly.