Inversion of seismic arrival times with erratic noise using robust Tikhonov–TV regularization. Issue 2 (4th August 2017)

• Record Type: Journal Article
• Authors: Alrajawi, M.; Siahkoohi, H.R.; Gholami, A.
• Is Part Of: Geophysical journal international. Volume 211:Issue 2(2017:Nov.)
• Page Start: 831
• Page End: 842
• Publication Date: 2017-08-04
• Subjects: Downhole methods -- Inverse theory -- Tomography -- Seismic tomography; Geophysics -- Periodicals; 550
• DOI: 10.1093/gji/ggx340
• Languages: English
• ISSNs: 0956-540X

Abstract

Abstract: A variety of methods have been presented to invert arrival times of seismic waves for velocity distribution. In real world, the velocity distribution models are piecewise smooth and consist of blocky structures as well as smooth varying parts. In such cases, implementation of Tikhonov regularization alone will recover the smooth varying parts of the velocity model, while the total variation (TV) regularization only is capable of recovering the blocky varying parts of the velocity model. In previous studies, combination of Tikhonov and TV regularizations (hereafter called classic Tikhonov–TV regularization) was used as a remedy for solving such inverse problems. In this study, we propose a method to minimize a cost function which of both Tikhonov and TV regularizations. The method is capable of suppressing undesired effects of the erratic noises and recovering both blocky and smooth varying parts of the model. An iteratively reweighted least-squares technique is used as a fast and efficient algorithm for minimization of the cost function. To demonstrate the effectiveness of the method, it is tested on both synthetic and real vertical seismic profiling arrival times as well as on a synthetic and real cross well arrival times. The proposed robust Tikhonov–TV method estimates better velocity model as compared to the robust Tikhonov and robust TV regularization methods. According to the results, the proposed hybrid method efficiently eliminates the individual weaknesses of constituent regularization methods.