New method produces improved surface stress rate maps

Earthquakes occur when the tectonic strain that has gradually built up along a fault is suddenly released. Measurements of the amount of Earth’s surface deformation over time, or the rate of stress, can be used in seismic hazard models to predict where earthquakes will occur. One way scientists estimate the strain rate is via orbiting satellites and detailed measurements of how much GPS stations are moving across the Earth’s surface.

However, there are challenges to the use of such geodetic data. The stations provide measurements at specific locations only and are not evenly distributed – creating a continuous map of the strain rate requires scientists to make estimates to fill in the data gaps. These interpolated data add uncertainty to the resulting mathematical models.

To address these issues, Pagani et al. Developed a multidimensional Bayesian method for estimating surface stress rates in the southwestern United States, with a focus on the San Andreas Fault. Their method essentially divided the study area into non-overlapping triangles and calculated velocities within each triangle by incorporating measurements from GPS stations located inside.

The team didn’t rely on just one model. They used the inverse Markov chain’s Monte Carlo algorithm to produce up to hundreds of thousands of these models, with slightly modified coordinates for those two-dimensional triangles. Indeed, across these models, even the number of triangles can vary – since the method is multidimensional, the authors did not specify any parameters in advance. Finally, they pooled all of these models together to create a final map of the continuous stress rate.

Using the test data, the authors found that their approach handled data errors and uneven distribution of data better than the standard B spline interpolation scheme. In addition, because the approach included information from many models, it produced a set of stress rate estimates at each point and probabilities for those values.

When the team used the new approach to calculate stress rates around the San Andreas Fault System, they found their map consistent with previous studies. It even successfully identified the creeping sections of the fault system from the locked ones. Researchers can use the newly described technique to develop other strain rate maps, and it can generally be applied to other interpolation problems in the Earth sciences. (Journal of Geophysical Research: Solid Earth, https://doi.org/10.1029/2021JB021905, 2021)

—Jack Lee, science writer

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