Microseismic Event Localization Error Analysis Using Cramer-Rao Bound
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Solution Overview
Problem
Current seismic monitoring technologies face inaccuracies in microseismic event localization due to seismic background energy and uncertainties in wave propagation, leading to poor understanding of localization errors and their impact on interpreting resource extraction processes like fracking, and challenges in displaying event data effectively.
Innovation Solution
The method involves computing and displaying microseismic event localization errors using the Cramer-Rao Bound to gauge estimation accuracy, deriving optimal weightings for least-squares methods, and representing event positions as error ellipses with varying transparency to convey localization variance, allowing for improved survey design and interpretation of stimulated volumes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional microseismic event localization methods are used, then event locations can be estimated, but localization accuracy is poor due to seismic background energy and wave propagation uncertainties
Solution Approach 1:
The patent implements feedback by computing the Cramer-Rao Bound (CRB) for each microseismic event location estimate and using this bound information to adjust the visualization and interpretation process. The CRB computation provides feedback on the theoretical minimum variance achievable, allowing operators to understand localization quality and adjust survey design or interpretation accordingly.
Solution Approach 2:
The patent changes the parameter representation from simple point locations to probability density functions characterized by mean position and Cramer-Rao Bound variance values. This parameter transformation allows the system to convey both location estimates and their uncertainties, resolving the contradiction between providing location estimates and maintaining reliability understanding.
2Ease of operation
If simple point location displays are used, then event positions are easy to visualize, but uncertainty and error information is lost
Solution Approach 1:
The patent adds another dimension to the display by representing each event location not as a simple point but as a probability distribution characterized by mean position and variance (CRB) values. This dimensional expansion from 3D space to 5D space (x, y, z, variance_x, variance_y) allows uncertainty information to be preserved while maintaining visualizability through appropriate graphical representations like error ellipses or transparency variations.
3Ease of manufacture
If uniform weighting is applied in least-squares localization, then computation is simple, but location accuracy is suboptimal
Solution Approach 1:
The patent changes the weighting parameter in the least-squares optimization from uniform weights to weights derived from the Cramer-Rao Bound. By computing optimal weights based on the inverse of the CRB variance for each measurement, the system achieves suboptimal localization accuracy improvement while maintaining reasonable computational complexity through efficient CRB computation.
Data Source
AI summary
According certain aspects, embodiments of the invention consider the problem of microseismic event localization from a parameter estimation perspective, and include a method and system for computing and displaying characteristics of event localization errors. According to certain other aspects, embodiments of the invention include techniques for deriving aggregate statistics from a set of event location estimates, including methods for computing and displaying the probability that an event occurred in any given volume, and methods for describing and displaying the smallest volume that contains a specified percentage of the event probability or expected to contain the specified percentage of the events.