Wavefield Extrapolation Avoiding Spatial Aliasing
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Solution Overview
Problem
Marine seismic surveys face challenges in processing pressure and velocity wavefield data due to spatial aliasing, which results in unreliable images of subterranean formations, especially when receiver separations exceed half the reflected wavefield wavelengths.
Innovation Solution
A method that decomposes pressure and vertical velocity wavefields into up-going and down-going components using a slowness vector calculated from measured pressure and horizontal velocity wavefields, allowing for extrapolation while avoiding spatial aliasing disruptions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If receivers are separated by large distances to cover larger survey areas, then survey coverage and productivity are improved, but spatial aliasing occurs making the recorded wavefield unreliable
Solution Approach 1:
The patent introduces an intermediary mathematical model (wave equation propagator) that relates observed wavefields at receiver locations to extrapolated wavefields at intermediate locations. This propagator acts as a mediator that allows accurate wavefield reconstruction despite large receiver separations, effectively bridging the gap between sparse measurements and continuous wavefield representation.
Solution Approach 2:
The patent transitions from spatial domain processing to frequency-wavenumber domain processing by applying Fourier transforms. This dimensional transformation allows the wavefield extrapolation to be performed in the frequency-wavenumber domain where aliasing effects are mitigated, and then transformed back to obtain accurate spatial wavefield images despite large receiver separations.
2Reliability
If receivers are spaced closer than half the wavelength to avoid spatial aliasing, then wavefield recording reliability is improved, but survey coverage and productivity deteriorate
Solution Approach 1:
The patent applies preliminary wavefield extrapolation to predicted receiver locations before performing the actual imaging process. By pre-calculating what the wavefield should look like at densely spaced locations based on the sparsely sampled actual data, the method enables high-resolution imaging without requiring physically dense receiver spacing, thus maintaining reliability while improving productivity.
3Device complexity
If traditional wavefield extrapolation methods are used with sparsely spaced receivers, then processing simplicity is maintained, but spatial aliasing disruptions occur reducing imaging reliability
Solution Approach 1:
The patent replaces traditional mechanical/spatial extrapolation methods with a mathematical field-theory-based approach using the wave equation propagator in the frequency-wavenumber domain. This substitution allows the system to achieve accurate wavefield extrapolation without being constrained by physical receiver spacing, eliminating spatial aliasing disruptions while maintaining computational tractability through efficient Fourier-based algorithms.
Data Source
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AI summary
Methods and Systems for extrapolating wavefields while avoiding disruptions due to spatial aliasing are disclosed. Pressure wavefields measured with pressure sensors and vertical and horizontal velocity wavefields measured with three-axial motions sensors may be spatially aliased in at least one horizontal direction. The pressure wavefield and/or the vertical velocity wavefield are decomposed into one of an up-going wavefield and a down-going wavefield. The up-going or down-going wavefield is extrapolated using an extrapolator that depends on components of a slowness vector. In order to avoid disruptions in the extrapolated wavefield due to spatial aliasing, the components of the slowness vector are calculated from the measured pressure wavefield and the two horizontal velocity wavefields.