Neural network-based hydrology corrections for borehole strainmeters

Borehole strainmeters are remarkably precise instruments.  They are often installed to record deformation produced by earthquakes, postseismic slip, and slow earthquakes.  Strainmeters can record such tectonic deformation on timescales of minutes to months with a precision of 0.1 to 1 nanostrain; they record sub-Angstrom changes in borehole width.  

However, the instruments’ high precision also extends to non-tectonic signals.  The borehole width often changes by more than 1 Angstrom when it rains, when atmospheric pressure increases, and when snow loads the ground.  Thus if we want to take full advantage of the instruments and investigate tectonic deformation with high precision, we need to understand and remove the deformation produced by non-tectonic signals like water loading.

So in this study, I present several neural network-based models of hydrologic deformation.  Neural networks are ideal for this modelling as they can accommodate the nonlinearity of the system; 1 cm of rain will cause different deformation if it falls on saturated, winter soil than if it falls on dry, summer soil.  Further, neural networks can take advantage of the abundance of local weather data, including at short timescales.  In my initial modelling, I attempt to reproduce and predict strain as a function of current and past precipitation, atmospheric pressure, wind speed, and temperature.  For simplicity and ease of use, all these parameters are taken from the ECMWF reanalysis models.

I design two neural networks to model the observed strain, using physical intuition to limit the number of free parameters and thus improve the training.  The first network is simple; it creates 10 linear combinations of past rainfall, with exclusively positive weights, and then combines those linear combinations to predict the strain.  The second network also creates 10 linear combinations of past rainfall with positive weights.  But it multiplies those linear combinations of rain by nonlinear functions that could represent the state of the Earth and aquifers.  These nonlinear functions include dependencies on past rainfall, atmospheric pressure, wind speed, and temperature.

These networks train quickly, within a few minutes, and they do a reasonable job of producing the first-order features of the strain.  Both models accommodate more than 50% of the hydrologic signal on timescales of days.  Such modelling may or may not be interesting to hydrologists, but for those interested in tectonic deformation, reproducing and removing 50% of the hydrologic signal means removing 50% of the noise.

It is likely that a better developed and regularised model could remove much more of the noise, and we are continuing to add constraints, initial weights, and training schemes to improve the hydrologic modelling.