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Mapping heterogeneities through avalanche statistics.

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  • 1Max Planck Institute of Dynamics and Self-Organization, Am Fassberg 17, 37073 Göttingen, Germany soumyajyoti.biswas@ds.mpg.de.

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Summary
This summary is machine-generated.

This study models stress-bearing systems, revealing detection times for stress variations follow a scaling law. Earthquake data analysis shows a trade-off between spatial resolution and accuracy of Gutenberg-Richter b-values.

Keywords:
avalanche dynamicsb-value variationsearthquakesself-organized criticality

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Area of Science:

  • Statistical physics of fracture and earthquakes
  • Complex dynamical systems

Background:

  • Avalanche statistics in threshold-activated systems (e.g., earthquakes, power grids) depend on applied stress.
  • Understanding stress variations is crucial for predicting system behavior and failures.

Purpose of the Study:

  • To model threshold-activated avalanche dynamics and investigate detection times for local stress variations.
  • To analyze the scaling laws governing detection times based on stress feature magnitude.
  • To examine the spatial resolution-accuracy trade-off in earthquake exponent mapping.

Main Methods:

  • Developed a model for threshold-activated avalanche dynamics.
  • Investigated the time required to detect local variations in stress-bearing capacity.
  • Analyzed earthquake data (Sumatra, California) to map Gutenberg-Richter b-values.

Main Results:

  • Detection time follows a scaling law, with exponents dependent on whether the feature is weaker or stronger than its surroundings.
  • Demonstrated a trade-off between spatial resolution and accuracy of earthquake b-value maps.
  • Proposed a method to optimize both spatial resolution and accuracy in b-value mapping.

Conclusions:

  • The detection time of stress variations in dynamical systems is predictable via scaling laws.
  • Optimizing earthquake b-value mapping requires balancing spatial resolution and exponent accuracy.
  • Findings contribute to the statistical physics of fracture and earthquake prediction.