Bayesian Polarity Determination for Seismic Signal Uncertainty
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Solution Overview
Problem
Existing methods for determining first-motion polarities in seismic data often rely on binary classification, which does not account for measurement uncertainty and can be error-prone, especially in noisy environments, limiting their effectiveness in source inversion and fracture characterization.
Innovation Solution
A Bayesian approach that calculates the probability of polarity as a positive or negative polarity from a noisy time series, incorporating uncertainty into the polarity assessment, allowing for quantitative evaluation and integration into earthquake source inversion methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If binary classification is used for polarity determination, then the process is simple and fast, but measurement uncertainty cannot be quantified and errors increase in noisy environments
Solution Approach 1:
The patent transforms the binary polarity classification (positive/negative) into a continuous probability scale (0 to 1) by calculating the area under the curve of the product of the seismic trace and a template waveform. This parameter change allows quantitative assessment of measurement uncertainty while maintaining computational efficiency, directly resolving the contradiction between measurement precision and method complexity.
2Reliability
If manual polarity picking is used, then measurement uncertainty can be assessed through pick quality indicators, but the process is time consuming and incompatible with automated workflows
Solution Approach 1:
The patent implements an automated system that performs polarity determination and uncertainty assessment without human intervention. The method calculates probability values automatically by processing the seismic trace through mathematical operations (correlation with template, area under curve calculation), enabling the system to serve itself and eliminating the need for manual picking while maintaining reliability through quantitative uncertainty measures.
Solution Approach 2:
The patent replaces the manual mechanical process of polarity picking with an automated computational system. The human eye and judgment are substituted by algorithmic processing that calculates probability values based on the product of the seismic trace and template waveform, achieving both automation and quantitative uncertainty assessment simultaneously.
3Productivity
If automatic polarity determination methods are used, then productivity is high and workflows are automated, but they produce binary classification results without quantitative uncertainty values
Solution Approach 1:
The patent adds a new dimension to automatic polarity determination by introducing a probability value (continuous dimension from 0 to 1) that represents measurement uncertainty. Instead of merely classifying polarity as binary, the method calculates the area under the curve of the trace-template product, creating an additional informational dimension that quantifies uncertainty while maintaining automated processing and high productivity.
Data Source
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AI summary
A device for assigning to the unknown onset of a signal in a noisy time series a probability of that onset having a signed excursion away from the trace mean including one or more means arranged to: define a polarity at a given time sample by reference to the sign of the amplitude difference between the extrema immediately before and after the given time sample in the time series; define a positive and a negative polarity probability density function; take the respective products of the positive and negative polarity probability density functions with an onset probability density function defining the probability that the onset of the signal occurs at a given time sample; and marginalize the respective products of the positive and negative polarity probability density functions with the onset probability density function over time to estimate final probabilities that the onset has a positive or a negative polarity.