Minimum‐phase decon of band‐limited data

1982 ◽  
Author(s):  
J. M. Fourmann
Keyword(s):  
Minimum Phase ◽  
Limited Data ◽  
Band Limited

Robust wavelet estimation and blind deconvolution of noisy surface seismics

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. V37-V46 ◽  
Author(s):  
Mirko van der Baan ◽  
Dinh-Tuan Pham
Keyword(s):  
Blind Deconvolution ◽  
General Purpose ◽  
Sufficient Accuracy ◽  
Wiener Filtering ◽  
Challenging Problem ◽  
Limited Data ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Principal Frequency ◽  
Band Limited

Robust blind deconvolution is a challenging problem, particularly if the bandwidth of the seismic wavelet is narrow to very narrow; that is, if the wavelet bandwidth is similar to its principal frequency. The main problem is to estimate the phase of the wavelet with sufficient accuracy. The mutual information rate is a general-purpose criterion to measure whiteness using statistics of all orders. We modified this criterion to measure robustly the amplitude and phase spectrum of the wavelet in the presence of noise. No minimum phase assumptions were made. After wavelet estimation, we obtained an optimal deconvolution output using Wiener filtering. The new procedure performs well, even for very band-limited data; and it produces frequency-dependent phase estimates.

Feasibility of approximate broadband estimation of acoustic impedance profile from first principles and band-limited reflection data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. R57-R74 ◽  
Author(s):  
Santi Kumar Ghosh ◽  
Animesh Mandal
Keyword(s):  
First Principles ◽  
Acoustic Impedance ◽  
Linear Equations ◽  
Synthetic Data ◽  
Reflection Coefficients ◽  
Limited Data ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Impedance Profile ◽  
Band Limited

Because seismic reflection data are band limited, acoustic impedance profiles derived from them are nonunique. The conventional inversion methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by imposing mathematical constraints such as sparsity of the reflection coefficients. By making a nominal assumption of an earth model locally consisting of a stack of homogeneous and horizontal layers, we have formulated a set of linear equations in which the reflection coefficients are the unknowns and the recursively integrated seismic trace constitute the data. Drawing only on first principles, the Zoeppritz equation in this case, the approach makes a frontal assault on the problem of reconstructing reflection coefficients from band-limited data. The local layer-cake assumption and the strategy of seeking a singular value decomposition solution of the linear equations counter the nonuniqueness, provided that the objective is to reconstruct a smooth version of the impedance profile that includes only its crude structures. Tests on synthetic data generated from elementary models and from measured logs of acoustic impedance demonstrated the efficacy of the method, even when a significant amount of noise was added to the data. The emergence of consistent estimates of impedance, approximating the original impedance, from synthetic data generated for several frequency bands has inspired our confidence in the method. The other attractive outputs of the method are as follows: (1) an accurate estimate of the impedance mean, (2) an accurate reconstruction of the direct-current (DC) frequency of the reflectivity, and (3) an acceptable reconstruction of the broad outline of the original impedance profile. These outputs can serve as constraints for either more refined inversions or geologic interpretations. Beginning from the restriction of band-limited data, we have devised a method that neither requires a starting input model nor imposes mathematical constraints on the earth reflectivity and still yielded significant and relevant geologic information.

Minimum entropy deconvolution with frequency‐domain constraints

Geophysics ◽  
1994 ◽  
Vol 59 (6) ◽  
pp. 938-945 ◽  
Author(s):  
Mauricio D. Sacchi ◽  
Danilo R. Velis ◽  
Alberto H. Comínguez
Keyword(s):  
Linear Programming ◽  
Field Data ◽  
Fourier Transforms ◽  
Computational Cost ◽  
Linear Operators ◽  
Minimum Entropy ◽  
Limited Data ◽  
Band Limited ◽  
Entropy Criterion ◽  
Domain Constraints

A method for reconstructing the reflectivity spectrum using the minimum entropy criterion is presented. The algorithm (FMED) described is compared with the classical minimum entropy deconvolution (MED) as well as with the linear programming (LP) and autoregressive (AR) approaches. The MED is performed by maximizing an entropy norm with respect to the coefficients of a linear operator that deconvolves the seismic trace. By comparison, the approach presented here maximizes the norm with respect to the missing frequencies of the reflectivity series spectrum. This procedure reduces to a nonlinear algorithm that is able to carry out the deconvolution of band‐limited data, avoiding the inherent limitations of linear operators. The proposed method is illustrated under a variety of synthetic examples. Field data are also used to test the algorithm. The results show that the proposed method is an effective way to process band‐limited data. The FMED and the LP arise from similar conceptions. Both methods seek an extremum of a particular norm subjected to frequency constraints. In the LP approach, the linear programming problem is solved using an adaptation of the simplex method, which is a very expensive procedure. The FMED uses only two fast Fourier transforms (FFTs) per iteration; hence, the computational cost of the inversion is reduced.

scholarly journals Band limited data reconstruction in modulated polarimeters

2011 ◽  
Vol 19 (16) ◽  
pp. 14976 ◽  
Author(s):  
Charles F. LaCasse ◽  
Russell A. Chipman ◽  
J. Scott Tyo
Keyword(s):  
Data Reconstruction ◽  
Limited Data ◽  
Band Limited

Homomorphic deconvolution

Geophysics ◽  
1983 ◽  
Vol 48 (7) ◽  
pp. 1014-1016 ◽  
Author(s):  
D. J. Jin ◽  
J. R. Rogers
Keyword(s):  
Reflection Coefficient ◽  
Additive Noise ◽  
Critical Role ◽  
Minimum Phase ◽  
Integration Algorithm ◽  
The Public ◽  
Band Limited ◽  
Frequency Transformations ◽  
Analytical Expressions ◽  
Phase Reflection

The advantages of homomorphic deconvolution are that it does not require the assumptions of minimum‐phase wavelet and of a white random reflection coefficient series. Disadvantages of the method which have been recognized in the public domain are difficulties in unwrapping the phase, in dealing with band‐limited signals, and in handling mixed‐phase reflection coefficient series. These difficulties may be respectively overcome by using an “adaptive numerical integration algorithm” (Tribolet, 1977), frequency transformations (Tribolet, 1979), and exponential weighting of the signal (Tribolet, 1979). There seems to have been some understanding in the literature and among exploration researchers that additive noise would affect the performance of homomorphic deconvolution. However, to the best of our knowledge there have not appeared in the literature any analytical expressions or experiments conclusively showing how additive noise affects homomorphic deconvolution. Analytic and experimental analyses demonstrated that additive noise plays a critical role in homomorphic deconvolution such that homomorphic deconvolution is unreliable whenever the spectral amplitudes of the signal are very small over certain frequency bands and even a small amount of noise is present. This unreliability of the method overshadows its advantages.

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