Seismic Frequency Expansion Using Fast Sparse Inversion
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Solution Overview
Problem
The lack of lower-frequency and higher-frequency components in seismic data due to land and marine data acquisition limitations leads to local minima in full waveform inversion results, reducing precision and resolution.
Innovation Solution
A frequency expansion method based on fast sparse inversion using a pre-constructed filtering operator, Fourier transform, and a Lagrange multiplier method to iteratively solve a frequency inversion objective function, ensuring the preservation of original frequency components while expanding missing frequencies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If traditional seismic data acquisition methods are used, then data collection is simpler and faster, but lower-frequency and higher-frequency components are lost due to land filtering effect, artificial seismic source limitations, and geophone distortion
Solution Approach 1:
The patent applies preliminary action by performing frequency expansion processing before full waveform inversion. The method first expands the frequency spectrum of the seismic data to recover lost low-frequency and high-frequency components, then uses this expanded data for inversion. This preliminary frequency restoration prevents the inversion from getting trapped in local minima and improves the accuracy of subsurface imaging without requiring complex hardware modifications.
Solution Approach 2:
The patent introduces an intermediary frequency expansion algorithm that acts as a bridge between the limited-frequency seismic data and the full-frequency requirements of waveform inversion. This intermediary processing step synthesizes the missing frequency components by leveraging the sparsity of seismic signals in the frequency domain, effectively mediating between the acquisition limitations and inversion requirements without direct hardware changes.
2Measurement precision
If full waveform inversion is performed with incomplete frequency data, then processing time is reduced, but precision of process and interpretation of seismic signal is dramatically reduced due to local minimum
Solution Approach 1:
The patent applies preliminary action by performing frequency expansion processing before full waveform inversion. The method first expands the frequency spectrum of the seismic data to recover lost low-frequency and high-frequency components, then uses this expanded data for inversion. This preliminary frequency restoration prevents the inversion from getting trapped in local minima and improves the accuracy of subsurface imaging without requiring complex hardware modifications.
3Measurement precision
If frequency expansion processing is applied to recover missing frequencies, then precision and resolution are improved, but calculation complexity increases
Solution Approach 1:
The patent applies parameter changes by transforming the seismic data from the time domain to the frequency domain using Fourier transform, and then applying sparsity constraints in the frequency domain. This parameter transformation allows the frequency expansion to be performed more efficiently by exploiting the sparsity property of seismic signals in the frequency domain, reducing the computational burden compared to time-domain methods.
Solution Approach 2:
The patent applies local quality by applying different processing strategies to different frequency bands. The frequency expansion algorithm selectively restores low-frequency components using sparsity constraints while preserving the integrity of high-frequency components. This localized approach to frequency restoration optimizes computational resources by focusing processing efforts where they are most needed.
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
Enhances precision and resolution of seismic data processing by effectively continuing missing frequencies, reducing calculation complexity, and improving signal-to-noise ratio.
Implementation Method 1
performing Fourier transform on the filtered pre-stack seismic data, and obtaining transformed pre-stack seismic data
Implementation Method 2
constructing a frequency inversion objective function based on the filtered pre-stack seismic data and a sparse inversion algorithm
Data Source
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Figure 6(a)~8(b)
AI summary
The present invention relates to the technical field of seismic data processing, and provides a frequency expansion method and apparatus based on fast sparse inversion, and a readable storage medium. The method comprises: acquiring pre-stack seismic data; filtering the pre-stack seismic data by using a filter operator to obtain filtered pre-stack seismic data; performing Fourier transform on the filtered pre-stack seismic data to obtain transformed pre-stack seismic data; on the basis of the filtered pre-stack seismic data and a sparse inversion algorithm, constructing a frequency inversion objective function by taking the transformed pre-stack seismic data as a constraint condition; and iterating the frequency inversion objective function by using a Lagrange multiplier method, updating the filtered pre-stack seismic data until the update amount of the updated filtered pre-stack seismic data is smaller than a preset update threshold or the number of iterations reaches a preset iteration threshold, and outputting the updated filtered pre-stack seismic data. The method has the advantages of high frequency inversion precision and a high data signal-to-noise ratio, a reduced calculation amount in a data processing process, and a reduced calculation cost.