Marine Seismic Source Deghosting Using Complex Laplace Transform
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Solution Overview
Problem
Current methods for deghosting marine seismic data are unstable at spectral notches, leading to irreparable artifacts and reduced resolving power, especially when operating without prior knowledge of the subsurface.
Innovation Solution
The method employs a complex Laplace frequency parameter with a nonzero real part to transform seismic data from the space-time domain to the spectral domain, using an iterative conjugate gradient scheme with a physically-based preconditioner to solve source deghosting equations, ensuring stability across the full seismic bandwidth.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional deghosting methods are used, then processing can be performed without prior subsurface knowledge, but the results become unstable at spectral notches causing artifacts
Solution Approach 1:
The patent changes the fundamental parameter of the frequency domain transformation by using a complex Laplace frequency parameter with a nonzero real part instead of the conventional purely imaginary frequency parameter. This parameter change stabilizes the deghosting process at spectral notches while maintaining the ability to process data without prior subsurface knowledge
Solution Approach 2:
The patent introduces an iterative conjugate gradient scheme with a physically-based preconditioner as an intermediary computational mechanism. This intermediary process solves the system of equations in a stable manner, bridging the gap between the transformed seismic data and the final deghosted result, particularly at problematic spectral notches
2Measurement precision
If full-bandwidth deghosting is attempted, then resolving power improves, but instability at spectral notches creates artifacts
Solution Approach 1:
By modifying the frequency parameter to include a nonzero real part in the complex Laplace domain, the patent enables stable full-bandwidth processing. This parameter modification allows the system to maintain stability across the entire frequency spectrum including spectral notches, thereby achieving full resolving power without artifacts
Solution Approach 2:
The iterative conjugate gradient scheme incorporates a physically-based preconditioner that provides feedback during the solution process. This feedback mechanism continuously adjusts the solution to maintain stability at spectral notches while preserving the full bandwidth information needed for high resolving power
Data Source
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AI summary
Seismic data recorded in a marine streamer are obtained, sorted as a common receiver gather. A complex Laplace frequency parameter is used to transform the seismic data from a space-time domain to a spectral domain. An iterative conjugate gradient scheme, using a physically-based preconditioner, is applied to the transformed seismic data, to provide a least squares solution to a normal set of equations for a source deghosting system of equations. The solution is inverse-transformed back to a space-time domain to provide source deghosted seismic data, which is useful for imaging the earth's subsurface.