Complex Wavelet Full Waveform Inversion for Seismic Data
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Solution Overview
Problem
Traditional Full Waveform Inversion (FWI) methods face challenges with high non-linearity and cycle-skip errors, and uncertainties in density models lead to unreliable amplitude modeling, necessitating a new cost function to improve the accuracy of subsurface parameter extraction.
Innovation Solution
The implementation of a complex wavelet-based cost function that separates kinematics and dynamics through phase and amplitude, using transforms like Dual-Tree Complex Wavelet Transform (DTCWT) and Curvelet Transform, to focus on kinematics or dynamics separately, reducing non-linearity and enhancing convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If traditional least-squares cost function is used in FWI, then the method is simple to implement, but it suffers from high non-linearity and cycle-skip errors leading to poor convergence
Solution Approach 1:
The patent transforms the data from time domain to frequency domain using Fourier transform, and further decomposes it using wavelet transform. This parameter transformation allows the cost function to operate on frequency-specific components, reducing the non-linearity issue that plagues traditional time-domain least-squares FWI and enabling more reliable convergence.
Solution Approach 2:
The patent segments the seismic data into different frequency components through wavelet transform decomposition. By processing each frequency band separately and combining results, the method avoids the cycle-skip errors that occur when trying to invert the full bandwidth data at once, thus improving convergence reliability.
2Loss of information
If amplitude information is used in the cost function, then more information is available for inversion, but uncertainties in density models make amplitude modeling unreliable
Solution Approach 1:
The patent extracts only the phase information from the wavelet-transformed data, deliberately excluding amplitude information from the cost function. This extraction of essential phase characteristics while discarding unreliable amplitude data allows the inversion to proceed with trustworthy information, avoiding the pitfalls of uncertain amplitude modeling.
3Loss of information
If full bandwidth data is processed simultaneously, then the inversion uses all available information, but the high non-linearity causes convergence difficulties
Solution Approach 1:
The patent segments the full bandwidth data into multiple frequency bands using wavelet transform. By inverting each frequency band separately and combining the results, the method maintains data utilization while reducing the non-linearity complexity that would otherwise prevent convergence of the full bandwidth inversion.
Data Source
AI summary
A method for seismic exploration using a full waveform inversion, FWI, the method including receiving an initial velocity model V of the subsurface, receiving recorded data d related to the subsurface, generating synthetic data u related to the subsurface, using the initial velocity model V and a source signature of a source S, transforming the recorded data d and the synthetic data u, with a complex wavelet transform, into complex wavelet transformed recorded data d′ and complex wavelet transformed synthetic data u′, respectively, updating the initial velocity model V using the FWI to generate an updated velocity model, based on a cost function J which depends on the complex wavelet transformed recorded data d′ and the complex wavelet transformed synthetic data u′, and generating an image of a surveyed subsurface formation.