Obtaining the Hessian from the force covariance matrix: Application to crystalline explosives PETN and RDX

2015 ◽  
Vol 142 (13) ◽  
pp. 134110 ◽  
Author(s):  
Andrey Pereverzev ◽  
Thomas D. Sewell
Keyword(s):  
Covariance Matrix ◽  
Matrix Application

Eigenstructure‐based coherence computations as an aid to 3-D structural and stratigraphic mapping

Geophysics ◽  
1999 ◽  
Vol 64 (5) ◽  
pp. 1468-1479 ◽  
Author(s):  
Adam Gersztenkorn ◽  
Kurt J. Marfurt
Keyword(s):  
Gulf Of Mexico ◽  
Covariance Matrix ◽  
Seismic Data ◽  
Cross Correlation ◽  
Uncorrelated Noise ◽  
Seismic Wavelet ◽  
Three Generations ◽  
Matrix Application ◽  
Geological Discontinuities

Coherence measures applied to 3-D seismic data volumes have proven to be an effective method for imaging geological discontinuities such as faults and stratigraphic features. By removing the seismic wavelet from the data, seismic coherence offers interpreters a different perspective, often exposing subtle features not readily apparent in the seismic data. Several formulations exist for obtaining coherence estimates. The first three generations of coherence algorithms at Amoco are based, respectively, on cross correlation, semblance, and an eigendecomposition of the data covariance matrix. Application of these three generations to data from the Gulf of Mexico indicates that the implementation of the eigenstructure approach described in this paper produces the most robust results. This paper first introduces the basic eigenstructure approach for computing coherence followed by a comparison on data from the Gulf of Mexico. Next, Appendix A develops a theoretical connection between the well‐known semblance and the less well‐known eigenstructure measures of coherence in terms of the eigenvalues of the data covariance matrix. Appendix B further extends the analysis by comparing the semblance- and eigenstructure‐based coherence measures in the presence of additive uncorrelated noise.

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