Full Waveform Inversion Using Beat Signal Envelopes
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Solution Overview
Problem
Seismic data is band limited due to hardware limitations, making low-frequency data unavailable and leading to issues like nonlinearity and cycle-skipping in full waveform inversion (FWI), which prevents accurate modeling of large underground structures.
Innovation Solution
The method involves converting seismic data from the time domain to the frequency domain, extracting data from signals at two close frequencies, generating simulated data, calculating a gradient of a cost function, and using this information to update a velocity model, thereby extracting low wavenumber data from beat signals to mitigate cycle-skipping and nonlinearity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If full waveform inversion is performed using band-limited seismic data, then processing can be completed with available hardware, but low-frequency information is missing causing cycle-skipping and local minima problems
Solution Approach 1:
The patent uses beat signals as an intermediary mechanism to indirectly obtain low-frequency information. By multiplying two high-frequency signals with slightly different frequencies, a beat signal is generated whose envelope contains the frequency difference (low-frequency component). This beat signal serves as a mediator that provides the missing low-frequency information without requiring direct low-frequency measurements, thus resolving the contradiction between using available band-limited data and needing low-frequency information for accurate inversion.
2Measurement precision
If high-frequency seismic data is used for inversion, then processing detail is improved, but cycle-skipping increases and large structures cannot be identified
Solution Approach 1:
The patent merges high-frequency data (providing detailed resolution) with low-frequency information derived from beat signals (providing large-scale structural context). The method combines the original high-frequency seismic data with the low-frequency envelope information from beat signals to create a composite dataset that contains both fine details and broad structural information, thereby simultaneously achieving high measurement precision and the ability to detect large structures without cycle-skipping issues.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for the reconstruction of underground formation models without the limitations of cycle-skipping and local minima, enabling the identification of large structures by utilizing low wavenumber information from high-frequency seismic data.
Implementation Method 1
extracting low wavenumber data from beat signals to mitigate cycle-skipping and nonlinearity
Data Source
AI summary
A full wave inversion (FWI) may utilize an Amplitude-Frequency-Differentiation (AFD) or a Phase-Frequency-Differentiation (PFD) operation to form a velocity model of a subterranean formation utilizing recovered low wavenumber data. Received seismic data is processes to isolate two data signals at different frequencies. In an AFD operation, the two data signals are summed and the data of the envelope of the summed function is used for the FWI. In a PFD operation, the phase data of the quotient of the two data signals is used for the FWI. The FWI proceeds iteratively utilizing either the AFD or PFD data or with single frequency data until the cost function of the AFD or PFD is satisfied.