Constrained Least Squares Spectral Analysis for Seismic Resolution

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Solution Overview

Problem

Conventional seismic spectral decomposition methods, such as the Short Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT), face challenges in achieving high temporal and frequency resolution, particularly in cases where seismic events are near other arrivals, leading to interference and spectral smearing, which affects the accuracy of layer thickness determination and hydrocarbon detection.

Innovation Solution

The development of Constrained Least Squares Spectral Analysis (CLSSA) computes Fourier Series coefficients directly within a moving time window using truncated sinusoidal kernels, applying constraints to reduce window smearing and enhance resolution, allowing for better determination of spectral characteristics of interfering reflections.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If the Short Time Fourier Transform (STFT) is used for spectral decomposition, then frequency resolution is improved, but temporal resolution deteriorates due to window smearing effects

Engineering Contradiction:

Improvefrequency resolutionVSAvoidtemporal resolution

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent replaces the conventional STFT mechanical system with a constrained least-squares spectral analysis system that uses truncated sinusoidal kernels and iterative optimization. This substitution eliminates the window smearing effect inherent in STFT while maintaining frequency resolution, thereby resolving the contradiction between frequency and temporal resolution.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent changes the fundamental parameters of spectral analysis by using constrained least-squares optimization with truncated sinusoidal kernels instead of standard Fourier transforms. This parameter change allows the system to achieve high frequency resolution without the temporal smearing caused by windowing in STFT, effectively resolving the resolution trade-off.

Inventive Principle:

Principle #35Parameter changes

2Loss of time

If the Continuous Wavelet Transform (CWT) is used for spectral decomposition, then temporal resolution is improved, but frequency resolution deteriorates at low frequencies

Engineering Contradiction:

Improvetemporal resolutionVSAvoidfrequency resolution

Core Design Contradiction:

Loss of timeVSMeasurement precision

Solution Approach 1:

The patent substitutes CWT with constrained least-squares spectral analysis using truncated sinusoidal kernels. This replacement maintains the temporal resolution advantages of wavelet-based methods while correcting the frequency resolution deficiencies at low frequencies through constrained optimization, thus resolving the frequency-resolution trade-off.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent changes the analytical approach from CWT to constrained least-squares spectral analysis, which allows simultaneous optimization of temporal and frequency resolution. The constrained optimization framework enables accurate frequency estimation at low frequencies while maintaining good temporal resolution, eliminating the resolution trade-off present in CWT.

Inventive Principle:

Principle #35Parameter changes

3Loss of time

If a short time window is used to isolate nearby seismic events, then temporal isolation is improved, but frequency resolution deteriorates due to window smearing

Engineering Contradiction:

Improvetemporal isolationVSAvoidfrequency resolution

Core Design Contradiction:

Loss of timeVSMeasurement precision

Solution Approach 1:

The patent replaces STFT with constrained least-squares spectral analysis that uses truncated sinusoidal kernels. This substitution enables the system to achieve both temporal isolation and frequency resolution simultaneously, as the constrained optimization eliminates window smearing while maintaining the benefits of short-time windowing for isolating nearby seismic events.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent converts the harmful window smearing effect into a beneficial constraint-based optimization problem. By formulating the spectral analysis as a constrained least-squares problem with truncated sinusoidal kernels, the system transforms the windowing limitation into an advantage, achieving sharp spectral peaks and accurate frequency estimation even with short time windows.

Inventive Principle:

Principle #22Blessing in disguise (Convert harm into benefit)

Data Source

PatentUS9507042B2System and method for constrained least-squares spectral processing and analysis of seismic data

Publication Date: 2016.11.29 LUMINA GEOPHYSICAL LLC

AI summary

An inversion-based algorithm for computing the time frequency analysis of reflection seismograms using constrained least-squares spectral analysis is formulated and applied to modeled seismic waveforms and real seismic data. The Fourier series coefficients are computed as a function of time directly by inverting a basis of truncated sinusoidal kernels for a moving time window. Spectra may be provided that have reduced window smearing for a given window length relative to the discrete Fourier transform irrespective of window shape, and a time-frequency analysis with a combination of time and frequency resolution that is superior to the short time Fourier transform and the continuous wavelet transform. The reduction in spectral smoothing enables enhanced determination of spectral characteristics of interfering reflections within a short window. The degree of resolution improvement relative to the short time Fourier transform increases as window length decreases.