Efficient analysis and representation of geophysical processes using localized spherical basis functions

While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of these naturally admit spectral representations, or they may need to be extracted from data collected globally, e.g. by satellites that circumnavigate the Earth. Wavelets are often used to study such nonstationary processes. On the sphere, however, many of the known constructions are somewhat limited. And in particular, the notion of `dilation' is hard to reconcile with the concept of a geological region with fixed boundaries being responsible for generating the signals to be analyzed. Here, we build on our previous work on localized spherical analysis using an approach that is firmly rooted in spherical harmonics. We construct, by quadratic optimization, a set of bandlimited functions that have the majority of their energy concentrated in an arbitrary subdomain of the unit sphere. The `spherical Slepian basis' that results provides a convenient way for the analysis and representation of geophysical signals, as we show by example. We highlight the connections to sparsity by showing that many geophysical processes are sparse in the Slepian basis.Comment: To appear in the Proceedings of the SPIE, as part of the Wavelets XIII conference in San Diego, August 200

Geoid, topography, and convection-driven crustal deformation on Venus

High-resolution Magellan images and altimetry of Venus reveal a wide range of styles and scales of surface deformation that cannot readily be explained within the classical terrestrial plate tectonic paradigm. The high correlation of long-wavelength topography and gravity and the large apparent depths of compensation suggest that Venus lacks an upper-mantle low-viscosity zone. A key difference between Earth and Venus may be the degree of coupling between the convecting mantle and the overlying lithosphere. Mantle flow should then have recognizable signatures in the relationships between surface topography, crustal deformation, and the observed gravity field

Distribution of slip from 11 M_w > 6 earthquakes in the northern Chile subduction zone

We use interferometric synthetic aperture radar, GPS, and teleseismic data to constrain the relative location of coseismic slip from 11 earthquakes on the subduction interface in northern Chile (23°–25°S) between the years 1993 and 2000. We invert body wave waveforms and geodetic data both jointly and separately for the four largest earthquakes during this time period (1993 M_w 6.8; 1995 M_w 8.1; 1996 M_w 6.7; 1998 M_w 7.1). While the location of slip in the teleseismic-only, geodetic-only, and joint slip inversions is similar for the small earthquakes, there are differences for the 1995 M_w 8.1 event, probably related to nonuniqueness of models that fit the teleseismic data. There is a consistent mislocation of the Harvard centroid moment tensor locations of many of the 6 6 earthquakes, as well as three M_w > 7 events from the 1980s. All of these earthquakes appear to rupture different portions of the fault interface and do not rerupture a limited number of asperities

How do we understand and visualize uncertainty?

Geophysicists are often concerned with reconstructing subsurface properties using observations collected at or near the surface. For example, in seismic migration, we attempt to reconstruct subsurface geometry from surface seismic recordings, and in potential field inversion, observations are used to map electrical conductivity or density variations in geologic layers. The procedure of inferring information from indirect observations is called an inverse problem by mathematicians, and such problems are common in many areas of the physical sciences. The inverse problem of inferring the subsurface using surface observations has a corresponding forward problem, which consists of determining the data that would be recorded for a given subsurface configuration. In the seismic case, forward modeling involves a method for calculating a synthetic seismogram, for gravity data it consists of a computer code to compute gravity fields from an assumed subsurface density model. Note that forward modeling often involves assumptions about the appropriate physical relationship between unknowns (at depth) and observations on the surface, and all attempts to solve the problem at hand are limited by the accuracy of those assumptions. In the broadest sense then, exploration geophysicists have been engaged in inversion since the dawn of the profession and indeed algorithms often applied in processing centers can all be viewed as procedures to invert geophysical data

Fluctuation and Commensurability Effect of Exciton Density Wave

At low temperatures, indirect excitons formed at the in-plane electron-hole interface in a coupled quantum well structure undergo a spontaneous transition into a spatially modulated state. We report on the control of the instability wavelength, measurement of the dynamics of the exciton emission pattern, and observation of the fluctuation and commensurability effect of the exciton density wave. We found that fluctuations are strongly suppressed when the instability wavelength is commensurate with defect separation along the exciton density wave. The commensurability effect is also found in numerical simulations within the model describing the exciton density wave in terms of an instability due to stimulated processes

Flexural analysis of uplifted rift flanks on Venus

Knowledge of the thermal structure of a planet is vital to a thorough understanding of its general scheme of tectonics. Since no direct measurements of heat flow or thermal gradient are available for Venus, most estimates have been derived from theoretical considerations or by analog with the Earth. The flexural response of the lithosphere to applied loads is sensitive to regional thermal structure. Under the assumption that the yield strength as a function of depth can be specified, the temperature gradient can be inferred from the effective elastic plate thickness. Previous estimates of the effective elastic plate thickness of Venus range from 11-18 km for the foredeep north of Uorsar Rupes to 30-60 km for the annular troughs around several coronae. Thermal gradients inferred for these regions are 14-23 K km(exp -1) and 4-9 K km(exp -1) respectively. In this study, we apply the same techniques to investigate the uplifted flanks of an extensional rift. Hypotheses for the origin of uplifted rift flanks on Earth include lateral transport of heat from the center of the rift, vertical transport of heat by small-scale convection, differential thinning of the lithosphere, dynamical uplift, and isostatic response to mechanical uploading of the lithosphere. The 1st hypothesis is considered the dominant contributor to terrestrial rift flanks lacking evidence for volcanic activity, particularly for rift structures that are no longer active. In this study, we model the uplifted flanks of a venusian rift as the flexural response to a vertical end load

JWalk: a tool for lazy, systematic testing of java classes by design introspection and user interaction

Popular software testing tools, such as JUnit, allow frequent retesting of modified code; yet the manually created test scripts are often seriously incomplete. A unit-testing tool called JWalk has therefore been developed to address the need for systematic unit testing within the context of agile methods. The tool operates directly on the compiled code for Java classes and uses a new lazy method for inducing the changing design of a class on the fly. This is achieved partly through introspection, using Java’s reflection capability, and partly through interaction with the user, constructing and saving test oracles on the fly. Predictive rules reduce the number of oracle values that must be confirmed by the tester. Without human intervention, JWalk performs bounded exhaustive exploration of the class’s method protocols and may be directed to explore the space of algebraic constructions, or the intended design state-space of the tested class. With some human interaction, JWalk performs up to the equivalent of fully automated state-based testing, from a specification that was acquired incrementally

Dyson's Brownian Motion and Universal Dynamics of Quantum Systems

We establish a correspondence between the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler et al between the space-time correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit and a set of two-variable correlations for disordered quantum systems calculated by them. Multiple variable correlation functions are, however, shown to be inequivalent for the two cases.Comment: 10 pages, revte