Frequency-Dependent Noise Factor for Tau-p Domain Stability

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Solution Overview

Problem

Current methods for transforming seismograms into tau-p space suffer from instability at low frequencies, leading to artifacts and poor sampling, which are not adequately addressed by frequency-independent noise factors.

Innovation Solution

The use of a frequency-dependent noise factor to stabilize the transformation matrix, which is generated based on the number of nonzero eigenvalues and eigenvalue distribution, allowing for precise transformation of seismic data into tau-p space.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If a frequency-independent noise factor is used to stabilize the transformation matrix, then the transformation can be performed, but the instability at low frequencies remains and artifacts are produced

Engineering Contradiction:

Improvestability of transformation matrixVSAvoidaccuracy of transformation

Core Design Contradiction:

ReliabilityVSManufacturing precision

Solution Approach 1:

The patent applies parameter changes by transitioning from a frequency-independent noise factor to a frequency-dependent noise factor. The noise factor is modified to be proportional to the average of the non-zero eigenvalues of the transformation matrix, which varies with frequency. This allows the stabilization parameter to adapt to the frequency-specific characteristics of the transformation matrix, particularly addressing the low-frequency instability while maintaining accuracy across the full frequency spectrum.

Inventive Principle:

Principle #35Parameter changes

2Reliability

If standard noise factor stabilization is applied, then some stability is achieved, but the spectral imbalance in the transform domain persists and affects deconvolution

Engineering Contradiction:

Improvestability of inversion methodVSAvoidspectral imbalance

Core Design Contradiction:

ReliabilityVSLoss of information

Solution Approach 1:

The patent applies local quality by making the noise factor frequency-dependent rather than uniform across all frequencies. The noise factor is specifically tailored to each frequency component based on the average of non-zero eigenvalues at that frequency. This localized approach allows different parts of the frequency spectrum to receive appropriate stabilization, particularly addressing the low-frequency region where eigenvalues are small, thereby correcting the spectral imbalance without introducing artifacts.

Inventive Principle:

Principle #3Local quality

3Productivity

If the transformation is performed with standard methods, then processing can be completed, but low frequencies are poorly sampled and lead to artifacts after inverse transformation

Engineering Contradiction:

Improveprocessing efficiencyVSAvoidsampling accuracy at low frequencies

Core Design Contradiction:

ProductivityVSManufacturing precision

Solution Approach 1:

The patent modifies the transformation parameter (noise factor) to be frequency-dependent, which improves the sampling accuracy at low frequencies without significantly impacting processing efficiency. By setting the noise factor proportional to the average of non-zero eigenvalues, the transformation naturally adapts to the frequency characteristics, providing better low-frequency sampling where needed while maintaining overall processing efficiency through the same transformation framework.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentEP2414866B1Method for stabilization of low frequencies in TAU-p domain filtering and deconvolution

Publication Date: 2020.03.11 SHELL OIL CO

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AI summary

Apparatuses and methods for collecting and analyzing seismic data (D) include a frequency dependent noise factor (e2) for stabilizing a transformation matrix (S). The noise factor (e2) is a function of a number of nonzero eigenvalues of the transformation matrix (S).