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Singular value decomposition-based reconstruction algorithm for seismic traveltime tomography.

L P Song, S Y Zhang

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|February 13, 2008

Summary

This study introduces an improved seismic tomography method using singular value decomposition (SVD) with a variable regularization parameter. The novel approach enhances seismic data reconstruction accuracy compared to standard SVD techniques.

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Area of Science:

Geophysics
Seismic Imaging
Inverse Problems

Background:

Seismic transmission traveltime tomography is crucial for subsurface imaging.
Traditional methods using singular value decomposition (SVD) face limitations in handling ill-posed problems.
The need for robust reconstruction methods in geophysical exploration is significant.

Discussion:

The proposed method utilizes a variable regularization parameter, unlike fixed approaches.
Weighting matrices normalize the singular spectrum, improving problem scaling.
The regularization parameter increases with singular value index, mitigating noise from smaller components.

Key Insights:

The novel seismic tomography method demonstrates superior performance over truncated SVD and Tikhonov regularization.
Variable regularization effectively addresses the ill-posed nature of seismic inverse problems.
Optimized singular value decomposition enhances the accuracy of traveltime tomography.

Outlook:

Further research could explore adaptive regularization strategies for dynamic geological settings.
Application of this method to real-world seismic exploration data is warranted.
Potential for integration with other geophysical inversion techniques exists.