Stable combustion of a high-velocity gas in a heated boundary layer

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Mechanisms of crustal deformation in the western US

The deformation processes in the western United States were studied, considering both deterministic models and random or statistical models. The role of the intracrustal delamination and mechanisms of crustal thinning were also examined. The application of fractal techniques to understand how the crust is deforming was studied in complex regions. Work continued on the development of a fractal based model for deformation in the western United States. Fractal studies were also extended to the study of topography and the geoid

Properties of the lithosphere and asthenosphere deduced from geoid observations

Data from the GEOS-3 and SEASAT Satellites provided a very accurate geoid map over the oceans. Broad bathymetric features in the oceans such as oceanic swells and plateaus are fully compensated. It is shown that the geoid anomalies due to the density structures of the lithosphere are proportional to the first moment of the density distribution. The deepening of the ocean basins is attributed to thermal isostasy. The thickness of the oceanic lithosphere increases with age due to the loss of heat to the sea floor. Bathymetry and the geoid provide constraints on the extent of this heat loss. Offsets in the geoid across major fracture zones can also be used to constrain this problem. Geoid bathymetry correlations show that the Hawaiian and Bermuda swells and the Cape Verde Rise are probably due to lithospheric thinning

Implications of convection in the Moon and the terrestrial planets

The early thermal and chemical evolution of the Moon is discussed. The rubidium-strontium, neodymium-samarium, and uranium-thorium-lead systems were studied. The relation of source region heterogeneity to the mixing associated with mantle convection is considered. Work on the application of fractal concepts to planetary geology and geophysics is also discussed. The fractal concept was applied to fragmentation, including the frequency-size distribution of meteorites, asteroids and particulate matter produced by impacts

An Exactly Soluble Hierarchical Clustering Model: Inverse Cascades, Self-Similarity, and Scaling

We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how this model can provide a general explanation for the behavior of several models that has been described as ``self-organized critical,'' including forest-fire, sandpile, and slider-block models.Comment: Resubmitted to Physical Review E; document prepared using RevTe

Correlation of data on strain accumulation adjacent to the San Andreas Fault with available models

Theoretical and numerical studies of deformation on strike slip faults were performed and the results applied to geodetic observations performed in the vicinity of the San Andreas Fault in California. The initial efforts were devoted to an extensive series of finite element calculations of the deformation associated with cyclic displacements on a strike-slip fault. Measurements of strain accumulation adjacent to the San Andreas Fault indicate that the zone of strain accumulation extends only a few tens of kilometers away from the fault. There is a concern about the tendency to make geodetic observations along the line to the source. This technique has serious problems for strike slip faults since the vector velocity is also along the fault. Use of a series of stations lying perpendicular to the fault whose positions are measured relative to a reference station are suggested to correct the problem. The complexity of faulting adjacent to the San Andreas Fault indicated that the homogeneous elastic and viscoelastic approach to deformation had serious limitations. These limitation led to the proposal of an approach that assumes a fault is composed of a distribution of asperities and barriers on all scales. Thus, an earthquake on a fault is treated as a failure of a fractal tree. Work continued on the development of a fractal based model for deformation in the western United States. In order to better understand the distribution of seismicity on the San Andreas Fault system a fractal analog was developed. The fractal concept also provides a means of testing whether clustering in time or space is a scale-invariant process

Anisotropy in Fracking: A Percolation Model for Observed Microseismicity

Hydraulic fracturing (fracking) using high pressures and a low viscosity fluid allow the extraction of large quantiles of oil and gas from very low permeability shale formations. The initial production of oil and gas at depth leads to high pressures and an extensive distribution of natural fractures which reduce the pressures. With time these fractures heal, sealing the remaining oil and gas in place. High volume fracking opens the healed fractures allowing the oil and gas to flow the horizontal productions wells. We model the injection process using invasion percolation. We utilize a 2D square lattice of bonds to model the sealed natural fractures. The bonds are assigned random strengths and the fluid, injected at a point, opens the weakest bond adjacent to the growing cluster of opened bonds. Our model exhibits burst dynamics in which the clusters extends rapidly into regions with weak bonds. We associate these bursts with the microseismic activity generated by fracking injections. A principal object of this paper is to study the role of anisotropic stress distributions. Bonds in the $y$-direction are assigned higher random strengths than bonds in the $x$-direction. We illustrate the spatial distribution of clusters and the spatial distribution of bursts (small earthquakes) for several degrees of anisotropy. The results are compared with observed distributions of microseismicity in a fracking injection. Both our bursts and the observed microseismicity satisfy Gutenberg-Richter frequency-size statistics.Comment: 14 pages, 10 figure

Self-organized criticality: Does it have anything to do with criticality and is it useful?

International audienceThree aspects of complexity are fractals, chaos, and self-organized criticality. There are many examples of the applicability of fractals in solid-earth geophysics, such as earthquakes and landforms. Chaos is widely accepted as being applicable to a variety of geophysical phenomena, for instance, tectonics and mantle convection. Several simple cellular-automata models have been said to exhibit self-organized criticality. Examples include the sandpile, forest fire and slider-blocks models. It is believed that these are directly applicable to landslides, actual forest fires, and earthquakes, respectively. The slider-block model has been shown to clearly exhibit deterministic chaos and fractal behaviour. The concept of self-similar cascades can explain self-organized critical behaviour. This approach also illustrates the similarities and differences with critical phenomena through association with the site-percolation and diffusion-limited aggregation models