Convolutional quelling in seismic tomography

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 570-580 ◽  
Author(s):  
Keith A. Meyerholtz ◽  
Gary L. Pavlis ◽  
Sally A. Szpakowski

This paper introduces convolutional quelling as a technique to improve imaging of seismic tomography data. We show the result amounts to a special type of damped, weighted, least‐squares solution. This insight allows us to implement the technique in a practical manner using a sparse matrix, conjugate gradient equation solver. We applied the algorithm to synthetic data using an eight nearest‐neighbor smoothing filter for the quelling. The results were found to be superior to a simple, least‐squares solution because convolutional quelling suppresses side bands in the resolving function that lead to imaging artifacts.

2009 ◽  
Vol 26 (12) ◽  
pp. 2642-2654 ◽  
Author(s):  
M. Gilcoto ◽  
Emlyn Jones ◽  
Luis Fariña-Busto

Abstract An extended explanation of the hypothesis and equations traditionally used to transform between four-beam ADCP radial beam velocities and current velocity components is presented. This explanation includes a dissertation about the meaning of the RD Instrument error velocity and a description of the standard beam-to-current components transformation as a least squares solution. Afterward, the variance–covariance matrix associated with the least squares solution is found. Then, a robust solution for transforming radial beam velocities into current components is derived under the formality of a weighted least squares approach. The associated variance–covariance matrix is also formulated and theoretically proves that the modulus of its elements will be generally lower than the corresponding modulus of the variance–covariance matrix associated with the standard least squares solution. Finally, a comparison between the results obtained using the standard least squares solution and the results of the weighted least squares method, using a high-resolution ADCP dataset, is presented. The results show that, in this case, the weighted least squares solution provides variance estimations that are 4% lower over the entire record period (8 days) and 7% lower during a shorter, more energetic period (12 h).


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