Generalized Simulated Annealing Optimization Used In Conjunction With Damped Least Squares Techniques

1987 ◽  
Author(s):  
Gregory K. Hearn
Keyword(s):  
Simulated Annealing ◽  
Least Squares ◽  
Damped Least Squares ◽  
Least Squares Techniques

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

A Bounded Variation Approach to Inverse Interferometry

1995 ◽  
Author(s):  
B. G. Fitzpatrick ◽  
S. L. Keeling ◽  
S. G. Rock
Keyword(s):  
Least Squares ◽  
Flow Measurement ◽  
Optical Methods ◽  
Optical Data ◽  
Reconstruction Technique ◽  
Direct Inversion ◽  
Variation Approach ◽  
Mathematical Techniques ◽  
Traditional Approaches ◽  
Least Squares Techniques

Abstract A least squares reconstruction technique is examined for determining flow-field densities from optical data. Nonintrusive optical methods have long been used for flow visualization; however, the goal of this work is to devise mathematical techniques with which optical data can be used for quantitative flow measurement. The ill-posedness of density computation from interferogram measurements is recognized as a serious limitation in direct inversion methods. Here, least squares techniques employing compactness constraints are developed to avoid the difficulties encountered in traditional approaches.

Sign in / Sign up

Export Citation Format

Share Document