In this paper, we theoretically discuss about regularization on logarithm bidirectional deconvolution proposed by Claerbout et al. (2011). We hope model fitting helps reduce the unwelcome strong precursors and noise in the bidirectional deconvolution results. INTRODUCTION Bidirectional deconvolution is an ill-posed and highly non-linear problem with many unexpected traps-local minima. When we t...

When conjugate gradient (CG) methods are applied to a problem like velocity transform in 2-D, the principal artifact faced is the half-integration waveform (Claerbout, 1993, 1995). Logically, the best filter to suppress a half-integration waveform is the half-derivative filter. In practice, filters like the half-derivative filter have been reported as causing CG residuals to diverge (Lumley, 19...

In real-world extraction of signal from data we are not given the needed signal prediction-error filter (PEF). Claerbout has taken S, the PEF of the signal, to be that of the data, S ≈ D. Spitz takes it to be S ≈ D/N . Where noises are highly predictable in time or space, Spitz gets significantly better results. Theoretically, a reason is that the essential character of a PEF is contained where...

Prediction-error filters (PEFs) may be used to interpolate missing data, either to increase the sampling of data that are regularly-sampled (Spitz, 1991), as well as to interpolate larger gaps in data (Claerbout, 1992, 1999). In addition to using multi-dimensional PEFs, non-stationary PEFs (Crawley et al., 1998) have been used to interpolate regularly-sampled data (Crawley, 2000). Non-stationar...

VLBI observations at 5 GHz have revealed that supernova 1979C, in the galaxy M100 in the Virgo cluster, has shell structure. The shell is approximately circular with the 50% contour deviating from a circle by an rms of no more than 8% of the radius. The brightness distribution along the ridge may vary. The position of the center of the shell is at R.A.=12 h 22 m 58. s 66758 and decl.=15 • 47 ′ ...

The main motivation in writing this paper is to better understand why the subtraction method attenuates the noise better than the filtering approach (Guitton and Claerbout, 2003). This is difficult to answer since both methods, although having their roots in the inversion theory framework, follow two different philosophies. The subtraction method models simultaneously the noise and the signal c...

L1-norm is better than L2-norm at dealing with noisy data and yielding blocky models, features crucial in many geophysical applications. In this report, we develop a hybrid-norm solver proposed by Claerbout (2009) to perform L1 regressions. The solver is tested on a 1-D field RMS velocity inversion, a 2-D regularized Kirchhoff migration inversion and a 2-D velocity analysis problem. The results...