Earthquake Location and Relocation

Notebooks: codes/earthquake_location.ipynb

How to locate an earthquake?

How to locate an earthquake?

Optimization (Inverse) problem

• Minimize the difference between observed and predicted values

How to solve an optimization/inversion problem?

• Forward function
• Objective/Loss function
• Gradient
• Optimizer

Locating Earthquake using absolute arrival times

notebook

Loss function:

• Mean squared error (MSE), loss:
• Absolute error, loss:

Locating Earthquake using relative arrival times

notebook

Loss function:

HypoDD: Double-difference earthquake location

HypoDD: Double-difference earthquake location

GrowClust: A Hierarchical Clustering Algorithm for Relative Earthquake Relocation

Review: clusering

Uncertainty

• Aleatoric uncertainty
  • The irreducible part of the uncertainty
  • Uncertainty due to inherent randomness, e.g., the outcome of flipping a coin
• Epistemic uncertainty
  • The reducible part of the uncertainty
  • Uncertainty due to lack of knowledge, e.g., lack of data

Uncertainty Quantification

• Standard deviation of slope and intercept of linear regression
• Bootstrapping
• Markov Chain Monte Carlo (MCMC)
• Hamiltonian Monte Carlo (HMC)
• Stein Variational Gradient Descent (SVGD)
• Dropout as a Bayesian Approximation

HypoSVI: Hypocentre inversion with Stein variational inference