Research On Tilt Correction Of Seismic Waveform And Tracking In The Digitization Of Seismograms

This paper focuses on the problems of correcting the tilted scanned seismograms and automatic tracking during the process of digitizing analog seismograms. To solve the problem of tilt correction this paper proposes two methods based on sparse representation and low-rank matrix recovery technique. The first method seeks a pair of optimal affine transfor-mations using a pair of continuous seismograms so that the tilted seismogram is aligned with the standard one. Because the rank measures correlation of the matrix, the lower rank is, the more correlative its column or row is. The tilted seismogram is assumed to be corrected if the rank of the matrix of the vectorized and transformed seismograms reaches its minimum. Therefore, the tilt correction problem is considered as the optimization problem of matrix rank minimization. The second method for tilt correction seeks a Euclidean transformation in order to implement the correction. Since rank is a natural measure for regularity and sym-metry of images, by extracting the low-rank texture from seismograms, this method can cor-rect it based on the waveform and its direction in the texture. The tilted seismogram is as-sumed to be corrected if the rank of the extracted texture reaches its minimum. Therefore, the tilt correction problem can also be considered as the optimization problem of matrix rank minimization. Thanks to the recent breakthrough in convex optimization, Accelerated Proxi-mal Gradient (APG) and Augmented Lagrange Multiplier (ALM) are applied to solve these optimization problems for their fast convergence. This paper verifies the efficiency of the proposed methods with extensive experiments. Compared with traditional geometrical meth-ods, our methods work efficiently and conveniently as well as exclude disturbance such as thermal noises, illumination variation, marks and stains. For the problem of automatic track-ing, this paper focuses on filling in the texture at the intermittent. This paper matches up with the incomplete texture with the one searched in our data base of seismograms. Then our algo-rithm iteratively computes the optimal texture for the case with low-rank matrix recovery technique without any manual filling-ins.