Reports on progress in physics the complex dynamics of earthquake fault systems: new approaches to forecasting and nowcasting of earthquakes

Charles Richter's observation that 'only fools and charlatans predict earthquakes,' reflects the fact that despite more than 100 years of effort, seismologists remain unable to do so with reliable and accurate results. Meaningful prediction involves specifying the location, time, and size of an earthquake before it occurs to greater precision than expected purely by chance from the known statistics of earthquakes in an area. In this context, 'forecasting' implies a prediction with a specification of a probability of the time, location, and magnitude. Two general approaches have been used. In one, the rate of motion accumulating across faults and the amount of slip in past earthquakes is used to infer where and when future earthquakes will occur and the shaking that would be expected. Because the intervals between earthquakes are highly variable, these long-term forecasts are accurate to no better than a hundred years. They are thus valuable for earthquake hazard mitigation, given the long lives of structures, but have clear limitations. The second approach is to identify potentially observable changes in the Earth that precede earthquakes. Various precursors have been suggested, and may have been real in certain cases, but none have yet proved to be a general feature preceding all earthquakes or to stand out convincingly from the normal variability of the Earth's behavior. However, new types of data, models, and computational power may provide avenues for progress using machine learning that were not previously available. At present, it is unclear whether deterministic earthquake prediction is possible. The frustrations of this search have led to the observation that (echoing Yogi Berra) 'it is difficult to predict earthquakes, especially before they happen.' However, because success would be of enormous societal benefit, the search for methods of earthquake prediction and forecasting will likely continue. In this review, we note that the focus is on anticipating the earthquake rupture before it occurs, rather than characterizing it rapidly just after it occurs. The latter is the domain of earthquake early warning, which we do not treat in detail here, although we include a short discussion in the machine learning section at the end.

Universality class for loopless invasion percolation models and a percolation avalanche burst model for hydraulic fracturing

Invasion percolation is a model that was originally proposed to describe growing networks of fractures. Here we describe a loopless algorithm on random lattices, coupled with an avalanche-based model for bursts. The model reproduces the characteristic b-value seismicity and spatial distribution of bursts consistent with earthquakes resulting from hydraulic fracturing ("fracking"). We test models for both site invasion percolation and bond invasion percolation. These have differences on the scale of site and bond lengths l. But since the networks are characterized by their large-scale behavior, l≪L, we find small differences between scaling exponents. Though data may not differentiate between models, our results suggest that both models belong to different universality classes.

Determination of the throat size distribution of a porous medium as an inverse optimization problem combining pore network modeling and genetic and hill climbing algorithms

The pore size distribution of a porous medium is often estimated from the retention curve or the invading fluid flow rate curve using simple relationships more or less explicitly based on the consideration that the porous medium is made of a bundle of cylindrical parallel tubes. This type of determination is tested using pore network simulations. Starting from two- or three-dimensional networks, the characteristics of which are known a priori, the estimation of the throat size distribution (TSD) is performed using the standard methods in the case of drainage. Results show a significant discrepancy with the input data. The disagreement is more pronounced when the fluid flow rate curve is employed together with the parallel tubes assumption. The physical origins of these shortcomings are identified. A method, based on pore network simulations combined with a genetic algorithm and the hill climbing algorithm, is then designed, which makes simultaneous use of the nonwetting fluid flow rate curve and the retention curve of the medium. Very significant improvement is achieved in the estimation of the TSD using this procedure.

Formation of a Stable Bridge between Two Disjoint Nanotubes with Single-File Chains of Water

It was recently demonstrated that stable water bridges can form between two relatively large disjoint nanochannels, such as carbon nanotubes (CNTs), under an applied pressure drop. Such bridges are relevant to fabrication of nanostructured materials, drug delivery, water desalination devices, hydrogen fuel cells, dip-pen nanolithography, and several other applications. If the nanotubes are small enough, however, then one has only single-file hydrogen-bonded chains of water molecules. The distribution of water in such nanotubes manifests unusual physical properties that are attributed to the low number of hydrogen bonds (HBs) formed in the channel since, on average, each water molecule in a single-file chain forms only 1.7 HBs, almost half of the value for bulk water. Using extensive molecular dynamics simulations, we demonstrate that stable bridges can form even between two small disjoint CNTs that contain single-file chains of water. The structure, stability, and properties of such bridges and their dependence on the applied pressure drop and the length of the gap between the two CNTs are studied in detail, as is the distribution of the HBs. We demonstrate, in particular, that the efficiency of flow through the bridge is at maximum at a specific pressure difference.

Loopless nontrapping invasion-percolation model for fracking

Recent developments in hydraulic fracturing (fracking) have enabled the recovery of large quantities of natural gas and oil from old, low-permeability shales. These developments include a change from low-volume, high-viscosity fluid injection to high-volume, low-viscosity injection. The injected fluid introduces distributed damage that provides fracture permeability for the extraction of the gas and oil. In order to model this process, we utilize a loopless nontrapping invasion percolation previously introduced to model optimal polymers in a strongly disordered medium and for determining minimum energy spanning trees on a lattice. We performed numerical simulations on a two-dimensional square lattice and find significant differences from other percolation models. Additionally, we find that the growing fracture network satisfies both Horton-Strahler and Tokunaga network statistics. As with other invasion percolation models, our model displays burst dynamics, in which the cluster extends rapidly into a connected region. We introduce an alternative definition of bursts to be a consecutive series of opened bonds whose strengths are all below a specified value. Using this definition of bursts, we find good agreement with a power-law frequency-area distribution. These results are generally consistent with the observed distribution of microseismicity observed during a high-volume frack.

Structure of drying fronts in three-dimensional porous media

Evaporation in a three-dimensional (3D) porous medium, a sand column saturated by water, was studied using synchrotron x-ray tomography. Three-dimensional images of the medium with a resolution of 7 μm were obtained during the evaporation. The entire column was scanned seven times, resulting in nearly 10(4) 2D cross sections and illustrating the spatial distribution of air, liquid, and solid phases at the pore scale. The results were analyzed in order to gain new insights and better understanding of the characteristics of the drying front that was formed when the liquid-filled pores were invaded by air, as well as the structure of the liquid phase as it was dried. The analysis indicates that the liquid phase has a self-similar fractal structure, with its fractal dimension D(f) in all the cross sections being a function of the water content or saturation. In addition, D(f) for the 3D liquid structure, as well as its density correlation function, were computed using the 3D images. A crossover length scale ξ was identified that separates the fractal regime from the compact geometry. For length scales r>ξ, the density correlation function approaches asymptotically the water content of the porous medium. The drying front is shown to be rough and multi-affine, rather than self-affine. Its properties were also computed using the 3D images. The roughness characteristics agree with those for imbibition in porous media, but not with those of fracture surfaces and crack lines.