Neural network can explain the physics of an earthquake ruptureMachine Learning Approach to Earthquake Rupture DynamicsSabber AhamedBlockedUnblockFollowFollowingJun 19Damage due to earthquakes poses a threat to humans worldwide.

To estimate the hazard, scientists use historical earthquake data and ground motion recorded by seismometers at different locations.

However, the current approaches are mostly empirical and may not capture the full range of ground shaking in future large earthquakes due to a lack of historical geological data.

This leads to significant uncertainties in hazard estimates.

Not only that, due to the lack of sufficient historical data, scientists mostly rely on simulated data, which is computationally expensive.

In this article, I will explain a workflow to predict if an earthquake can break a fault using machine learning.

The project was part of my Ph.

D.

thesis at the Center for Earthquake research and information(CERI), The University of Memphis.

Eric.

G.

Daub is also the co-author of this paper who supervised me and the project.

Recently we submitted the paper on Arxiv: https://arxiv.

org/abs/1906.

06250.

In the remaining of the article, I will be discussing the potentiality of machine learning algorithms in predicting real surface fault rupture and estimating seismic hazard.

I will also explain the complex pattern of the learned parameters that helps to reveal the mechanics of an earthquake rupture processEarthquake rupture domainFigure-1: Rupture domainWe produced a set of 2,000 rupture simulations varying the fault geometry (height and width), and the material properties (Out of plain stress, In plain stress, shear stress, friction drop, dynamic friction coefficient) illustrated in figure-1.

We used an open source numerical simulation code fdfault developed by Eric.

The domain is 32 km in length and 24 kilometers wide across the fault.

The diagram shows a zoomed view of the fault for better visualization of the barrier.

Earthquake initiates at the nucleation patch (red) which is ten kilometers from the curved geometric barrier.

Based on the geometry and properties of the fault, some of the earthquakes were able to break through the fault and some did not.

To keep it simple, we made it a binary classification problem.

More details can be found in the paper.

Shallow neural networkAlthough we used two random forests and a neural network to create predictive models, in this article, I mostly focus on the neural network especially the explanation of the learned parameters that helped us to reveal the mechanics of earthquake rupture process.

Figure-2: Schematic diagram of the neural network topology used in the workThe above Figure-2 illustrates the schematic diagram of the neural network topology we use in this work.

The network has one hidden layer with 12 units.

The eight input parameters are mapped to these 12 units, producing a 12 X 8 weight matrix for the model.

As each input enters a unit, the output of the previous unit is multiplied by its weight.

The unit then adds all these new inputs, which determines the output value of the intermediate unit.

We then apply a nonlinear activation function ReLu to the output weight, which passes all the values greater than zero and set any negative output to be zero.

Finally, the hidden layers combine the 12 outputs with the output layer and use the resulting weight to make predictions.

Explain model parameters and the get the physicsFigure-3: The parameters learned by the NNThe weights learned by the neural network allow us to gain some insight into the combinations of input parameters that are most predictive of the ability of the rupture to propagate.

To visualize the weights, we constructed the weights versus neural units matrix plot.

This is illustrated in Figure-2.

The left panel shows the model weights mapping the eight inputs (horizontal) to the twelve hidden units (vertical).

The right panel shows the weights that combine the hidden units into the one output unit on the right.

The color scale indicates the range of weights.

The weights in the model range from negative values to positive values which indicate inhibitory or excitatory influences.

If the output layer weight is positive for a particular unit, then the parameter combination is a good predictor of rupture propagation, while a negative weight indicates the parameter combination is a good predictor of rupture arrest.

Similarly, weights mapping the inputs to the hidden units that are positive indicators signify that large values of that input unit favor rupture.

If the output unit has a negative weight, then large weights for a hidden unit indicate that large values of that parameter are predictive of the arrest.

The weights provide insight into which parameter combinations are most predictive of rupture.

Parameters illustrated in figure-2 provide insights into the parameter combinations and their influence on determining the rupture propagation.

For example, unit-4 has a large negative output weight.

The unit has a large negative weight of shear stress, friction drop, and slip-weakening distance while height, half-width, OP, IP normal stress, dynamic friction coefficient, and friction drop have positive weight.

This indicates that if a fault has low shear stress, and low friction drop, but high compressive OP, IP normal stress, high dynamic friction coefficient, height, and half-width then it is likely that rupture would not propagate but arrest.

On the other hand, unit-8 has a substantial positive output weight.

The OP, IP normal and dynamic friction coefficient has a large negative weight while friction drop, slip-weakening distance, shear stress have high positive weight.

Note that these are essentially the opposite values from those in unit-4, indicating a single underlying pattern in the data.

Therefore, based on input data the model has determined exactly how to best combine the various input parameters in a more sophisticated way.

Robustness of the learned parametersFigure-3: The illustration shows the coefficient of determination (R2 score) among the weights learned by fifteen neural network modelsWe confirmed that the parameter combinations found by the ANN approach are robust by repeating the fitting procedure.

We developed an additional 15 neural network models with the same training data set, but different initial weights to see if the models find the same features that are predictive of rupture.

The average testing accuracy of the models is 83%.

Although the final weights vary slightly from model to model, they exhibit high correlation when sorted in ascending order based on their output weight.

Figure-4 shows the determination of coefficient (R2 score) among the parameters (in ascending order) learned by the models.

Model-11 has the smallest correlation with the other model while models-10, and 12 have high correlations.

Even though model-11 has the lowest correlation coefficient of 0.

71 with model-1, it is high enough that it still contains similar patterns as the other models.

The highly correlated weights indicate that the models are picking up on consistent features regardless of the random way that the model is initialized.

ConclusionComputationally, the models are highly efficient.

Once the training simulations are computed, and the machine learning algorithms are trained, the models can make a prediction within a fraction of a second.

This has the potential to allow for the results of dynamic rupture simulations to be incorporated into other complex calculations such as inversions or probabilistic seismic hazard analysis, something that would not be ordinarily possible.

The method can also be applied to other complex rupture problems such as branching faults, fault stepovers, and other complex heterogeneities where the physics of earthquake rupture propagation is not fully understood.

Machine learning provides a new way of approaching this complex, nonlinear problem, and helps scientists understand how the underlying geophysical parameters are related to the resulting slip and ground motions, thus helping us constrain future seismic hazard and risk.

Thank you very much for reading.

I hope you enjoyed the whole series.

The full code can be found on Github.

Details of the paper can be found on Arxiv: https://arxiv.

org/abs/1906.

06250.

I would love to hear from you.

You can reach out to me:Email: sabbers@gmail.

comLinkedIn: https://www.

linkedin.

com/in/sabber-ahamed/Github: https://github.

com/msahamedMedium: https://medium.

com/@sabber/.