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CRS regularization

In seismic exploration, CRS (Common Reflection Surface) is a method of processing seismic data that involves the estimation of a set of surfaces in the subsurface that have a common reflection point (CRP) for a given reflection time. This is done by analyzing the travel times and wavefront shapes of seismic waves recorded at different points on the Earth's surface.

The benefits of CRS compared to CDP (Common Depth Point) stacking include:

  1. Improved imaging of complex subsurface structures: CRS can handle the complex geometry of subsurface structures better than CDP stacking, especially in areas where the structure is not well defined.

  2. More accurate velocity estimation: CRS can provide more accurate velocity estimation by using a smaller set of parameters to describe the subsurface than CDP stacking.

  3. Reduction of noise: CRS can effectively suppress noise in seismic data, resulting in higher quality images of the subsurface.

  4. Better imaging of dipping reflectors: CRS can better handle dipping reflectors, which can be difficult to image with CDP stacking.

CRS regularization is a technique used to constrain the estimation of the CRS surfaces by incorporating prior information about the subsurface structure. It involves adding a regularization term to the objective function that is optimized during the estimation of the CRS surfaces. This term penalizes deviations from the expected behavior of the subsurface structure, based on prior knowledge or assumptions.

The regularization term helps to stabilize the inversion process and prevent overfitting, which can occur when the inversion process tries to fit the data too closely, resulting in noise amplification or incorrect subsurface imaging. Regularization can also help to improve the resolution of the estimated CRS surfaces by reducing the effects of noise and data inconsistencies.

There are different types of regularization methods used in CRS inversion, including:

  1. Tikhonov regularization: This is the most commonly used regularization method in seismic inversion. It involves adding a term that penalizes the squared values of the CRS parameters. The strength of the regularization is controlled by a regularization parameter, which balances the trade-off between data fitting and model regularization.

  2. Total Variation (TV) regularization: This method penalizes the variation in the CRS parameters along the reflection time axis, rather than their absolute values. TV regularization is effective in preserving sharp discontinuities and edges in the subsurface structure.

  3. Wavelet regularization: This method involves transforming the CRS surfaces into the wavelet domain and applying a penalty term that encourages sparsity in the wavelet coefficients. Wavelet regularization is useful for preserving sharp features and suppressing noise in the subsurface structure.


CRS regularization is an essential technique in seismic exploration for improving the accuracy and stability of the estimation of subsurface structures using the CRS method.

Overall, CRS provides a more robust and accurate method for seismic data processing and imaging compared to CDP stacking, especially in complex geological environments.


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