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Although free oscillations of the Earth may be computed by many different methods, numerous practical considerations have led us to use a Rayleigh-Ritz formulation with piecewise cubic Hermite spline basis functions. By treating the resulting banded matrix equation as a generalized algebraic eigenvalue problem, we are able to achieve great accuracy and generality and a high degree of automation at a reasonable cost.
The proliferation of drilling expeditions focused on characterizing natural gas hydrate as a potential energy resource has spawned widespread interest in gas hydrate reservoir properties and associated porous media phenomena. Between 2017 and 2019, a Special Section of this journal compiled contributed papers elucidating interactions between gas hydrate and sediment based on laboratory, numerical modeling, and field studies. Motivated mostly by field observations in the northern Gulf of Mexico and offshore Japan, several papers focus on the mechanisms for gas hydrate formation and accumulation, particularly with vapor phase gas, not dissolved gas, as the precursor to hydrate. These studies rely on numerical modeling or laboratory experiments using sediment packs or benchtop micromodels. A second focus of the Special Section is the role of fines in inhibiting production of gas from methane hydrate, controlling the distribution of hydrate at a pore scale, and influencing the bulk behavior of seafloor sediments. Other papers fill knowledge gaps related to the physical properties of hydrate-bearing sediments and advance new approaches in coupled thermal-mechanical modeling of these sediments during hydrate dissociation. Finally, one study addresses the long-standing question about the fate of methane hydrate at the molecular level when CO2 is injected into natural reservoirs under hydrate-forming conditions.
The entire surface of the planet Venus is being mapped at global and regional scales (1:50,000,000 through 1:1,500,000) with synthetic aperture radar (SAR), radar altimeter, and radiometer measurements of physical properties from the Magellan spacecraft. The mapping includes SAR image mosaics, shaded relief maps, and topographic contour overlays made from altimetry data and by radargrammetric methods. Methods used include new techniques of radar image processing that became operational as a result of the Magellan mission. The area being mapped (at a resolution of 75 m/pixel) is roughly equivalent to that of Earth, including seafloors. The mapping is designed to support geologic and geophysical investigations.
Long-period global-scale electromagnetic induction studies of deep Earth conductivity are based almost exclusively on magnetovariational methods and require accurate models of external source spatial structure. We describe approaches to inverting for both the external sources and three-dimensional (3-D) conductivity variations and apply these methods to long-period ( T ≥1.2 days) geomagnetic observatory data. Our scheme involves three steps: (1) Observatory data from 60 years (only partly overlapping and with many large gaps) are reduced and merged into dominant spatial modes using a scheme based on frequency domain principal components. (2) Resulting modes are inverted for corresponding external source spatial structure, using a simplified conductivity model with radial variations overlain by a two-dimensional thin sheet. The source inversion is regularized using a physically based source covariance, generated through superposition of correlated tilted zonal (quasi-dipole) current loops, representing ionospheric source complexity smoothed by Earth rotation. Free parameters in the source covariance model are tuned by a leave-one-out cross-validation scheme. (3) The estimated data modes are inverted for 3-D Earth conductivity, assuming the source excitation estimated in step 2. Together, these developments constitute key components in a practical scheme for simultaneous inversion of the catalogue of historical and modern observatory data for external source spatial structure and 3-D Earth conductivity.
Seismic quiescence has attracted attention as a possible precursor to a large earthquake. However, sensitive detection of quiescence requires accurate modeling of normal aftershock activity. We apply the epidemic-type aftershock sequence (ETAS) model that is a natural extension of the modified Omori formula for aftershock decay, allowing further clusters (secondary aftershocks) within an aftershock sequence. The Hector Mine aftershock activity has been normal, relative to the decay predicted by the ETAS model during the 14 months of available data. In contrast, although the aftershock sequence of the 1992 Landers earthquake (M = 7.3), including the 1992 Big Bear earthquake (M = 6.4) and its aftershocks, fits very well to the ETAS up until about 6 months after the main shock, the activity showed clear lowering relative to the modeled rate (relative quiescence) and lasted nearly 7 years, leading up to the Hector Mine earthquake (M = 7.1) in 1999. Specifically, the relative quiescence occurred only in the shallow aftershock activity, down to depths of 5-6 km. The sequence of deeper events showed clear, normal aftershock activity well fitted to the ETAS throughout the whole period. We argue several physical explanations for these results. Among them, we strongly suspect aseismic slips within the Hector Mine rupture source that could inhibit the crustal relaxation process within "shadow zones" of the Coulomb's failure stress change. Furthermore, the aftershock activity of the 1992 Joshua Tree earthquake (M = 6.1) sharply lowered in the same day of the main shock, which can be explained by a similar scenario.
The Earth Observing-1 (EO-1) satellite was launched on November 21, 2000, as part of a one-year technology demonstration mission. The mission was extended because of the value it continued to add to the scientific community. EO-1 has now been operational for more than a decade, providing both multispectral and hyperspectral measurements. As part of the EO-1 mission, the Advanced Land Imager (ALI) sensor demonstrates a potential technological direction for the next generation of Landsat sensors. To evaluate the ALI sensor capabilities as a precursor to the Operational Land Imager (OLI) onboard the Landsat Data Continuity Mission (LDCM, or Landsat 8 after launch), its measured top-of-atmosphere (TOA) reflectances were compared to the well-calibrated Landsat 7 (L7) Enhanced Thematic Mapper Plus (ETM+) and the Terra Moderate Resolution Imaging Spectroradiometer (MODIS) sensors in the reflective solar bands (RSB). These three satellites operate in a near-polar, sun-synchronous orbit 705 km above the Earth's surface. EO-1 was designed to fly one minute behind L7 and approximately 30 minutes in front of Terra. In this configuration, all the three sensors can view near-identical ground targets with similar atmospheric, solar, and viewing conditions. However, because of the differences in the relative spectral response (RSR), the measured physical quantities can be significantly different while observing the same target. The cross-calibration of ALI with ETM+ and MODIS was performed using near-simultaneous surface observations based on image statistics from areas observed by these sensors over four desert sites (Libya 4, Mauritania 2, Arabia 1, and Sudan 1). The differences in the measured TOA reflectances due to RSR mismatches were compensated by using a spectral band adjustment factor (SBAF), which takes into account the spectral profile of the target and the RSR of each sensor. For this study, the spectral profile of the target comes from the near-simultaneous EO-1 Hyperion data over these sites. The results indicate that the TOA reflectance measurements for ALI agree with those of ETM+ and MODIS to within 5% after the application of SBAF.
As magma rises in volcanic systems, volatile species exsolve from the silicate melt and are emitted as gases into the atmosphere. Measuring the magnitude and composition of gas emissions from volcanoes provides insights into processes occurring deep within the Earth and helps constrain the impact of volcanic degassing on atmospheric chemistry. Optical remote sensing techniques allow volcanic gas emissions to be characterized without the need to access hazardous areas near active volcanic vents. This paper reviews the state of the art in ultraviolet and visible volcanic gas remote sensing from the ground, air, and space. Special attention is given to discussing the physics of atmospheric radiative transfer on which these techniques are based. The functionality and limitations of different remote sensing instruments are examined, making clear that the ideal choice of instrumentation will depend on the volcanic system to which it is applied and the sought measurement parameters. Common algorithms for determining trace gas column densities, gas burdens, and volcanic emission rates from measurements of spectral radiance are outlined and compared, showing how some algorithms attempt to model the physics of the measurement while others maximize sensitivity. Several examples demonstrate how remote sensing measurements continue to advance our understanding of volcanic systems and their impact on the atmosphere. Finally, a few promising directions of inquiry are suggested that could lead to improvements in remote sensing instrumentation and analysis techniques. By combining spectroscopic and imaging techniques, improving our understanding of atmospheric radiative transfer, expanding the suite of target gases, and increasing the coverage and frequency of observations, we stand to significantly improve our ability to detect and quantify volcanic gas emissions and gain new insights into important Earth-system processes.
In this study I show that simple heuristic models and numerical calculations suggest that an entire class of commonly invoked models of earthquake failure processes cannot explain triggering of seismicity by transient or "dynamic" stress changes, such as stress changes associated with passing seismic waves. The models of this class have the common feature that the physical property characterizing failure increases at an accelerating rate when a fault is loaded (stressed) at a constant rate. Examples include models that invoke rate state friction or subcritical crack growth, in which the properties characterizing failure are slip or crack length, respectively. Failure occurs when the rate at which these grow accelerates to values exceeding some critical threshold. These accelerating failure models do not predict the finite durations of dynamically triggered earthquake sequences (e.g., at aftershock or remote distances). Some of the failure models belonging to this class have been used to explain static stress triggering of aftershocks. This may imply that the physical processes underlying dynamic triggering differs or that currently applied models of static triggering require modification. If the former is the case, we might appeal to physical mechanisms relying on oscillatory deformations such as compaction of saturated fault gouge leading to pore pressure increase, or cyclic fatigue. However, if dynamic and static triggering mechanisms differ, one still needs to ask why static triggering models that neglect these dynamic mechanisms appear to explain many observations. If the static and dynamic triggering mechanisms are the same, perhaps assumptions about accelerating failure and/or that triggering advances the failure times of a population of inevitable earthquakes are incorrect.
The Nimbus III and IV satellites provide reflectance and emittance data from the earth's surface at 8-km resolution. These data have been used to derive a physical property of geologic materials termed '"thermal inertia" which appears to have great promise for discriminating surficial units. A thermal inertia map of part of Oman was produced from the Nimbus satellite measurements. Correlation of this map with a reconnaissance geologic map showed gross agreement with the major units but also suggested the need for some modifications of the reconnaissance map. Some of the anomalies were verified by comparison with a later, more detailed map; others remain unexplained and may indicate previously undiscriminated geologic units.
Scaling considerations indicate that miniature experiments can be used to test models of granular avalanches in which the effects of intergranular fluid and cohesion are negligible. To test predictions of a granular avalanche model described in a companion paper, we performed bench top experiments involving avalanches of dry sand across irregular basal topography that mimicked the complexity of natural terrain. The experiments employed a novel method of laser-assisted cartography to map the three-dimensional morphology of rapidly moving avalanches, thereby providing high-resolution data for comparison with model output. Model input consisted of two material properties (angles of internal and basal Coulomb friction of the sand), which were measured in independent tests, and of initial and boundary conditions that characterized the geometry of the experimental apparatus. Experimental results demonstrate that the model accurately predicts not only the gross behavior but also many details of avalanche motion, from initiation to deposition. We attribute this accuracy to a mathematical and computational formulation that conserves mass and momentum in three-dimensional physical space and satisfies the Coulomb equation in three-dimensional stress space. Our results support the hypothesis that a Coulomb proportionality between shear and normal stresses applies in moderately rapid granular flows and that complicated constitutive postulates are unnecessary if momentum conservation is strictly enforced in continuum avalanche models. Furthermore, predictions of our Coulomb continuum model contrast with those of a Coulomb point mass model, illustrating the importance of multidimensional modeling and model testing.
The interaction of the Juan de Fuca Ridge with the Cobb hot spot has had a considerable influence on the magmatism of the Axial Segment of the ridge, the second-order segment that overlies the hot spot. In addition to the construction of the large volcanic edifice of Axial Seamount, the Axial Segment has shallow bathymetry and a prevalence of constructional volcanic features along its 100-km length, suggesting that hot spot-derived magmas supplement and oversupply the ridge. Lavas are generally more primitive at Axial Seamount and more evolved in the Axial Segment rift zones, suggesting that fractional crystallization is enhanced with increasing distance from the hot spot because of a reduced magma supply and more rapid cooling. Although the Cobb hot spot is not an isotopically enriched plume, it produces lavas with some distinct geochemical characteristics relative to normal mid-ocean ridge basalt, such as enrichments in alkalis and highly incompatible trace elements, that can be used as tracers to identify the presence and prevalence of the hot spot influence along the ridge. These characteristics are most prominent at Axial Seamount and decline in gradients along the Axial Segment. The physical model that can best explain the geochemical observations is a scenario in which hot spot and mid-ocean ridge basalt (MORB) magmas mix to varying degrees, with the proportions controlled by the depth to the MORB source. Modeling of two-component mixing suggests that MORB is the dominant component in most Axial Segment basalts. Copyright 2005 by the American Geophysical Union.
The physical properties of gas hydrate-bearing sediments depend on the volume fraction and spatial distribution of the hydrate phase. The host sediment grain size and the state of effective stress determine the hydrate morphology in sediments; this information can be used to significantly constrain estimates of the physical properties of hydrate-bearing sediments, including the coarse-grained sands subjected to high effective stress that are of interest as potential energy resources. Reported data and physical analyses suggest hydrate-bearing sands contain a heterogeneous, patchy hydrate distribution, whereby zones with 100% pore-space hydrate saturation are embedded in hydrate-free sand. Accounting for patchy rather than homogeneous hydrate distribution yields more tightly constrained estimates of physical properties in hydrate-bearing sands and captures observed physical-property dependencies on hydrate saturation. For example, numerical modeling results of sands with patchy saturation agree with experimental observation, showing a transition in stiffness starting near the series bound at low hydrate saturations but moving toward the parallel bound at high hydrate saturations. The hydrate-patch size itself impacts the physical properties of hydrate-bearing sediments; for example, at constant hydrate saturation, we find that conductivity (electrical, hydraulic and thermal) increases as the number of hydrate-saturated patches increases. This increase reflects the larger number of conductive flow paths that exist in specimens with many small hydrate-saturated patches in comparison to specimens in which a few large hydrate saturated patches can block flow over a significant cross-section of the specimen.
The presence of fault-plane reflections in seismic images, besides indicating the locations of faults, offers a possible source of information on the properties of these poorly understood zones. To better understand the physical mechanism giving rise to fault-plane reflections in compacting sedimentary basins, we numerically model the full elastic wavefield via the spectral element method (SEM) for several different fault models. Using well log data from the South Eugene Island field, offshore Louisiana, we derive empirical relationships between the elastic parameters (e.g. P-wave velocity and density) and the effective-stress along both normal compaction and unloading paths. These empirical relationships guide the numerical modelling and allow the investigation of how differences in fluid pressure modify the elastic wavefield. We choose to simulate the elastic wave equation via SEM since irregular model geometries can be accommodated and slip boundary conditions at an interface, such as a fault or fracture, are implemented naturally. The method we employ for including a slip interface retains the desirable qualities of SEM in that it is explicit in time and, therefore, does not require the inversion of a large matrix. We performa complete numerical study by forward modelling seismic shot gathers over a faulted earth model using SEM followed by seismic processing of the simulated data. With this procedure, we construct post-stack time-migrated images of the kind that are routinely interpreted in the seismic exploration industry. We dip filter the seismic images to highlight the fault-plane reflections prior to making amplitude maps along the fault plane. With these amplitude maps, we compare the reflectivity from the different fault models to diagnose which physical mechanism contributes most to observed fault reflectivity. To lend physical meaning to the properties of a locally weak fault zone characterized as a slip interface, we propose an equivalent-layer model under the assumption of weak scattering. This allows us to use the empirical relationships between density, velocity and effective stress from the South Eugene Island field to relate a slip interface to an amount of excess pore-pressure in a fault zone. ?? 2007 The Authors Journal compilation ?? 2007 RAS.
Of all the filters applied to recordings of seismic waves, which include source, path, and site effects, the one we know most precisely is the instrument filter. Therefore, it behooves seismologists to accurately remove the effect of the instrument from raw seismograms. Applying instrument corrections allows analysis of the seismogram in terms of physical units (e.g., displacement or particle velocity of the Earth’s surface) instead of the output of the instrument (e.g., digital counts). The instrument correction can be considered the most fundamental processing step in seismology since it relates the raw data to an observable quantity of interest to seismologists. Complicating matters is the fact that, in practice, the term “instrument correction” refers to more than simply the seismometer. The instrument correction compensates for the complete recording system including the seismometer, telemetry, digitizer, and any anti‐alias filters. Knowledge of all these components is necessary to perform an accurate instrument correction. The subject of instrument corrections has been covered extensively in the literature (Seidl, 1980; Scherbaum, 1996). However, the prospect of applying instrument corrections still evokes angst among many seismologists—the authors of this paper included. There may be several reasons for this. For instance, the seminal paper by Seidl (1980) exists in a journal that is not currently available in electronic format and cannot be accessed online. Also, a standard method for applying instrument corrections involves the programs TRANSFER and EVALRESP in the Seismic Analysis Code (SAC) package (Goldstein et al. , 2003). The exact mathematical methods implemented in these codes are not thoroughly described in the documentation accompanying SAC.
Lava extrusion at erupting volcanoes causes rapid changes in topography and morphology on the order of tens or even hundreds of meters. Satellite radar provides a method for measuring changes in topographic height over a given time period to an accuracy of meters, either by measuring the width of radar shadow cast by steep sided features, or by measuring the difference in radar phase between two sensors separated in space. We measure height changes, and hence estimate extruded lava volume flux, at El Reventador, Ecuador, between 2011 and 2016, using data from the RADARSAT-2 and TanDEM-X satellite missions. We find that 39 new lava flows were extruded between 9 February 2012 and 24 August 2016, with a cumulative volume of 44.8M m 3 dense rock equivalent and a gradually decreasing eruption rate. The average dense rock rate of lava extrusion during this time is 0.31 ± 0.02 m 3 s −1 , which is similar to the long-term average from 1972 to 2016. Apart from a volumetrically small dyke opening event between 9 March and 10 June 2012, lava extrusion at El Reventador is not accompanied by any significant magmatic ground deformation. We use a simple physics-based model to estimate that the volume of the magma reservoir under El Reventador is greater than 3 km 3 . Our lava extrusion data can be equally well fit by models representing a closed reservoir depressurising during the eruption with no magma recharge, or an open reservoir with a time-constant magma recharge rate of up to 0.35 ± 0.01 m 3 s −1 .
Results from a highly idealized, 2-D computational model indicate that dynamic normal-stress rarefactions might cause friction reduction in long-runout landslides, but the physical relevance of the idealized dynamics has not been confirmed by experimental tests. More importantly, the model results provide no evidence that refutes alternative hypotheses about friction reduction mechanisms. One alternative hypothesis, which is strongly supported by field evidence, experimental data, and the predictions of a well-constrained computational model, involves development of high pore fluid pressures in deforming landslide material or overridden bed material. However, no scientific basis exists for concluding that a universal mechanism is responsible for friction reduction in all long-runout landslides.
A general computer code, developed to calculate anelastic reflection-refraction coefficients, energy flow, and the physical characteristics for general P , S -I, and S -II waves, quantitatively describes physical characteristics for wave fields in anelastic media that do not exist in elastic media. Consideration of wave fields incident on boundaries between anelastic media shows that scattered wave fields experience reductions in phase and energy speeds, increases in maximum attenuation and Q −1 , and directions of maximum energy flow distinct from phase propagation. Each of these changes in physical characteristics are shown to vary with angle of incidence. Finite relaxation times for anelastic media result in energy flow due to interaction of superimposed radiation fields and contribute to energy flow across anelastic boundaries for all angles of incidence. Agreement of theoretical and numerical results with laboratory measurements argues for the validity of the theoretical and numerical formulations incorporating inhomogeneous wave fields. The agreement attests to the applicability of the model and helps confirm the existence of inhomogeneous body waves and their associated set of distinct physical characteristics in the earth. The existence of such body waves in layered, low-loss anelastic solids implies the need to reformulate some seismological models of the earth. The exact anelastic formulation for a liquid-solid interface with no low-loss approximations predicts the existence of a range of angles of incidence or an anelastic Rayleigh window, through which significant amounts of energy are transmitted across the boundary. The window accounts for the discrepancy apparent between measured reflection data presented in early textbooks and predictions based on classical elasticity theory. Characteristics of the anelastic Rayleigh window are expected to be evident in certain sets of wide-angle, ocean-bottom reflection data and to be useful in estimating Q −1 for some ocean bottom reflectors.
Physical property measurements of sediment cores containing natural gas hydrate are typically performed on material exposed, at least briefly, to non-in situ conditions during recovery. To examine the effects of a brief excursion from the gas-hydrate stability field, as can occur when pressure cores are transferred to pressurized storage vessels, we measured physical properties on laboratory-formed sand packs containing methane hydrate and methane pore gas. After depressurizing samples to atmospheric pressure, we repressurized them into the methane-hydrate stability field and remeasured their physical properties. Thermal conductivity, shear strength, acoustic compressional and shear wave amplitudes, and speeds of the original and depressurized/repressurized samples are compared. X– ray computed tomography images track how the gas-hydrate distribution changes in the hydrate-cemented sands owing to the depressurizaton/repressurization process. Because depressurization-induced property changes can be substantial and are not easily predicted, particularly in water-saturated, hydrate-bearing sediment, maintaining pressure and temperature conditions throughout the core recovery and measurement process is critical for using laboratory measurements to estimate in situ properties.