Search USGSSearch

SEARCH · Search USGS

Results for “Journal of Geophysical Research F: Earth Surface”

Search indexed USGS publications on groundwater, aquifers, geologic maps, mineral resources and earthquakes. Explore source records by subject and place.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

122 records · Page 7Linked to original sources

Experimental deformation of topaz crystals: Possible embrittlement by intracrystalline water

Crystallographically oriented single‐crystal prisms of gem quality topaz (composition AlSiO (OH− F) where x = 0.04 ± 0.01) were deformed at a confining pressure of 1.50 GPa, a temperature of 800°C, and a strain rate of 2×10 s. Under nearly identical conditions, all crystals of anhydrous rock‐forming minerals that have been tested to date, such as olivine, quartz, feldspars, pyroxenes, and refractory oxides, deform plastically; in contrast, our topaz crystals failed by brittle fracture regardless of the orientation of the compression direction. No optical evidence for plastic deformation was detected. Another suite of experiments with compression perpendicular to the (001) cleavage at = 100°–950°C and a strain rate of 2×10 s displayed two regimes of behavior: (1) at >400°C, fracture strength was independent of temperature, and fracture occurred on one or two surfaces parallel to {103}; (2) at <400°C, the fracture strength increased rapidly with decreasing temperature, no macroscopic stress drop was observed, and many closely spaced conjugate fractures formed on (103) and (103). The anomalous brittleness of topaz compared to anhydrous silicate and oxide crystals indicates that intracrystalline “water” plays a role in the embrittlement. We suggest that water within the topaz crystals promotes fracture in ways similar to the mechanisms of slow crack growth aided by environmental moisture.

Journal of Geophysical Research B: Solid Earth

Meteorites on Mars observed with Mars Exploration Rovers

Reduced weathering rates due to the lack of liquid water and significantly greater typical surface ages should result in a higher density of meteorites on the surface of Mars compared to Earth. Several meteorites were identified among the rocks investigated during Opportunity's traverse across the sandy Meridiani plains. Heat Shield Rock is a IAB iron meteorite and has been officially recognized as 'Meridiani Planum.' Barberton is olivine-rich and contains metallic Fe in the form of kamacite, suggesting a meteoritic origin. It is chemically most consistent with a mesosiderite silicate clast. Santa Catarina is a brecciated rock with a chemical and mineralogical composition similar to Barberton. Barberton, Santa Catarina, and cobbles adjacent to Santa Catarina may be part of a strewn field. Spirit observed two probable iron meteorites from its Winter Haven location in the Columbia Hills in Gusev Crater. Chondrites have not been identified to date, which may be a result of their lower strengths and probability to survive impact at current atmospheric pressures. Impact craters directly associated with Heat Shield Rock, Barberton, or Santa Catarina have not been observed, but such craters could have been erased by eolian-driven erosion.

Journal of Geophysical Research E: Planets

Overview of the Mars Pathfinder Mission: Launch through landing, surface operations, data sets, and science results

Mars Pathfinder successfully landed at Ares Vallis on July 4, 1997, deployed and navigated a small rover about 100 m clockwise around the lander, and collected data from three science instruments and ten technology experiments. The mission operated for three months and returned 2.3 Gbits of data, including over 16,500 lander and 550 rover images, 16 chemical analyses of rocks and soil, and 8.5 million individual temperature, pressure and wind measurements. Path‐finder is the best known location on Mars, having been clearly identified with respect to other features on the surface by correlating five prominent horizon features and two small craters in lander images with those in high‐resolution orbiter images and in inertial space from two‐way ranging and Doppler tracking. Tracking of the lander has fixed the spin pole of Mars, determined the precession rate since Viking 20 years ago, and indicates a polar moment of inertia, which constrains a central metallic core to be between 1300 and ∼2000 km in radius. Dark rocks appear to be high in silica and geochemically similar to anorogenic andesites; lighter rocks are richer in sulfur and lower in silica, consistent with being coated with various amounts of dust. Rover and lander images show rocks with a variety of morphologies, fabrics and textures, suggesting a variety of rock types are present. Rounded pebbles and cobbles on the surface as well as rounded bumps and pits on some rocks indicate these rocks may be conglomerates (although other explanations are also possible), which almost definitely require liquid water to form and a warmer and wetter past. Air‐borne dust is composed of composite silicate particles with a small fraction of a highly magnetic mineral, interpreted to be most likely maghemite; explanations suggest iron was dissolved from crustal materials during an active hydrologic cycle with maghemite freeze dried onto silicate dust grains. Remote sensing data at a scale of a kilometer or greater and an Earth analog correctly predicted a rocky plain safe for landing and roving with a variety of rocks deposited by catstrophic floods, which are relatively dust free. The surface appears to have changed little since it formed billions of years ago, with the exception that eolian activity may have deflated the surface by ∼3–7 cm, sculpted wind tails, collected sand into dunes, and eroded ventifacts (fluted and grooved rocks). Pathfinder found a dusty lower atmosphere, early morning water ice clouds, and morning near‐surface air temperatures that changed abruptly with time and height. Small scale vortices, interpreted to be dust devils, were observed repeatedly in the afternoon by the meteorology instruments and have been imaged.

Journal of Geophysical Research E: Planets

Hydrologic effects on water level changes associated with episodic fault creep near Parkfield, California

As part of the Parkfield, California, earthquake prediction experiment, water level is monitored in a well 460 m from the main trace of the San Andreas fault on Middle Mountain, in the preparation zone of the anticipated Parkfield earthquake. The well configuration allows water level to be monitored in two fluid reservoirs at depths of 85 and 250 m below land surface. During 1987, water level changes were recorded during 12 of the 18 episodes of accelerated fault creep detected by a creep meter spanning the fault trace 750 m northwest of the well. The creep-related water level changes in the shallow reservoir have durations of less than 1 day, whereas in the deeper reservoir the changes persist for as long as 2 months. These data suggest that the transient nature of the water level changes in the shallow interval is due to vertical flow to the water table and is not evidence that creep events propagate past the well. Phase leads of earth tidal constituents in the water level data from the shallow interval relative to the same constituents in the local volume strain tide support the interpretation of significant flow to the water table at periods of 1 day or less. The form of the water level changes in the deep interval is affected by horizontal flow to the well bore. This effect can be removed from the water level records using a theoretical response curve constrained by the phases of earth tidal constituents in the deep interval relative to the local volume strain tide. For the events where the signal in the shallow interval has been large enough to measure, the sizes of the simultaneous water level changes in the two reservoirs are consistent with the same amounts of volume strain occurring at both depths.

Journal of Geophysical Research Solid Earth

Brittle regime slip partitioned damage and deformation mechanisms along the eastern Denali fault zone in southwestern, Yukon

Rare bedrock exposures of the eastern Denali fault zone in southwestern Yukon allow for the measurement, sampling, and analyses of brittle regime fault slip data and deformation mechanisms to explore relations to far field, oblique plate motions. Host rock lithologies and associated slip surfaces show episodic damage zone‐related deformation and calcite ± hematite ± chlorite related hydrothermal fluid flow. This regional scale network of asymmetric fault damage is spatially and kinematically linked to a discrete and narrow fault core. Fault network observations, orientations, slip data, and strain inversions document a slip partitioned strike‐slip fault system with locally and mutually overprinting strike‐, oblique‐, and dip‐slip components. Microstructural analyses reveal crystal plastic and co‐seismic brittle deformation mechanisms active in a narrow range of upper crustal temperature, pressure, fluid, and chemical conditions. The net damage related slip is not exclusively formed by a single kinematic system, but rather a fully partitioned, time integrated system likely operative for much of the fault's brittle regime evolution temporally constrained by previously published thermochronometric data. Although the fault slip data was collected from outcrop‐scale exposures at sites tens of kilometers apart, results show remarkable correlation between fault kinematics and plate motions along the ∼580 km long eastern Denali fault segment. End member, subhorizontal, northeast directed reverse and north directed dextral strike slip fault strain axes closely reflect relative plate motion interactions over at least the last 30 m.y. and act as a proxy for far‐field stresses compatible with the kinematics of the damage zone network.

Alaska

Fluid expulsion sites on the Cascadia accretionary prism: mapping diagenetic deposits with processed GLORIA imagery

Point-discharge fluid expulsion on accretionary prisms is commonly indicated by diagenetic deposition of calcium carbonate cements and gas hydrates in near-surface (<10 m below seafloor; mbsf) hemipelagic sediment. The contrasting clastic and diagenetic lithologies should be apparent in side scan images. However, sonar also responds to variations in bottom slope, so unprocessed images mix topographic and lithologic information. We have processed GLORIA imagery from the Oregon continental margin to remove topographic effects. A synthetic side scan image was created initially from Sea Beam bathymetric data and then was subtracted iteratively from the original GLORIA data until topographic features disappeared. The residual image contains high-amplitude backscattering that we attribute to diagenetic deposits associated with fluid discharge, based on submersible mapping, Ocean Drilling Program drilling, and collected samples. Diagenetic deposits are concentrated (1) near an out-of-sequence thrust fault on the second ridge landward of the base of the continental slope, (2) along zones characterized by deep-seated strikeslip faults that cut transversely across the margin, and (3) in undeformed Cascadia Basin deposits which overlie incipient thrust faults seaward of the toe of the prism. There is no evidence of diagenetic deposition associated with the frontal thrust that rises from the dècollement. If the dècollement is an important aquifer, apparently the fluids are passed either to the strike-slip faults which intersect the dècollement or to the incipient faults in Cascadia Basin for expulsion. Diagenetic deposits seaward of the prism toe probably consist dominantly of gas hydrates.

Cascadia Basin

Findings and lessons learned from the assessment of the Mexico-United States transboundary San Pedro and Santa Cruz aquifers: The utility of social science in applied hydrologic research

Study Region This study region encompasses the Transboundary San Pedro and Santa Cruz aquifers which are shared between the states of Sonora (Mexico) and Arizona (US). Special regional considerations include a semi-arid climate, basin-fill aquifers with predominantly montane recharge areas, economic drivers in the mining, trade, and military sectors, groundwater-dependent cities with expanding cones of depression, interbasin groundwater transfers, ground- and surface-water contamination, and protected aquatic and riparian habitats that act as significant migration corridors for hundreds of species, including some that are threatened and endangered. Study Focus We focus on lessons learned from the hydrologic assessment of the Transboundary San Pedro and Santa Cruz aquifers. We conducted the work, in two phases: (1) laying the groundwork and (2) implementation. The “laying the groundwork” phase consisted of binational meetings with stakeholders and key actors (agencies and individuals), and the development of an understanding of the physical, institutional, historical, and socio-political context. This led to signing of the binational Transboundary Aquifer Assessment Program (TAAP) agreement in 2009 and detailed the process for cooperation and coordination in the assessment of shared aquifers. The implementation phase began with an agreement to proceed with the study of four “focus” aquifers (Santa Cruz, San Pedro, Mesilla (Conejos-Médanos in Mexico), and Hueco Bolson (Bolsón del Hueco in Mexico)) and development of associated technical teams. Though we do include a brief discussion of the lessons learned from the physical science portion of the study, the results have been described and published elsewhere. The bulk of the paper instead focuses on the findings and lessons learned from the integration of social-science perspectives into a largely physical-science based program, since there is a growing recognition of the need for this type of approach especially in the management and assessment of transboundary aquifers. New Hydrological Insights for the Region The Sonora-Arizona effort succeeded because both countries were adequately represented, and because of flexibility of skills and ability of teams comprising both university and government scientists. Teams included social and earth scientists. Including the social sciences was critical to research design and implementation, and to addressing the cultural, institutional, and socio-political contexts of transboundary aquifer assessment. Significant components of the continuing implementation phase include strategic planning, data compilation and analysis, cross-border integration of datasets, geophysical and geochemical surveys, and internal, peer, and stakeholder engagement.

Arizona, Sonora

Continuous monitoring of surface deformation at Long Valley Caldera, California, with GPS

Continuous Global Positioning System (GPS) measurements at Long Valley Caldera, an active volcanic region in east central California, have been made on the south side of the resurgent dome since early 1993. A site on the north side of the dome was added in late 1994. Special adaptations for autonomous operation in remote regions and enhanced vertical precision were made. The data record ongoing volcanic deformation consistent with uplift and expansion of the surface above a shallow magma chamber. Measurement precisions (1 standard error) for “absolute” position coordinates, i.e., relative to a global reference frame, are 3–4 mm (north), 5–6 mm (east), and 10–12 mm (vertical) using 24 hour solutions. Corresponding velocity uncertainties for a 12 month period are about 2 mm/yr in the horizontal components and 3–4 mm/yr in the vertical component. High precision can also be achieved for relative position coordinates on short (less than 10 km) baselines using broadcast ephemerides and observing times as short as 3 hours, even when data are processed rapidly on site. Comparison of baseline length changes across the resurgent dome between the two GPS sites and corresponding two-color electronic distance measurements indicates similar extension rates within error (∼2 mm/yr) once we account for a random walk noise component in both systems that may reflect spurious monument motion. Both data sets suggest a pause in deformation for a 3.5 month period in mid-1995, when the extension rate across the dome decreased essentially to zero. Three dimensional positioning data from the two GPS stations suggest a depth (5.8±1.6 km) and location (west side of the resurgent dome) of a major inflation center, in agreement with other geodetic techniques, near the top of a magma chamber inferred from seismic data. GPS systems similar to those installed at Long Valley can provide a practical method for near real-time monitoring and hazard assessment on many active volcanoes.

Journal of Geophysical Research B: Solid Earth

Effects of compression direction on the plasticity and rheology of hydrolytically weakened synthetic quartz crystals at atmospheric pressure

A hydrothermally grown synthetic quartz crystal with 370±60 ppm hydroxyl impurity was cut into right rectangular prisms in eight crystallographic orientations. We compressed the prisms under constant axial force corresponding to a uniaxial stress of 140.0±0.5 MPa, and temperatures of 510° and 750°C. All but one of the samples sustained permanent axial strains of 2–3%. We established the operating slip systems from specimen shape change, slip bands and dislocation etch pits on polished surfaces, crystallographic orientation changes, stress optical features in thin sections, and transmission electron microscopy. The observed creep behavior and plasticity divided the samples into three groups: (1) Crystals compressed at 45° to [0001] and [ ] and those compressed ⊥( ) and ⊥( ) deformed principally by slip parallel to [0001]. Creep rates were relatively high and were not strongly sensitive to test temperature. Dislocation arrays approximately parallel to ( ) are common. Dislocation loops are elongate parallel to [0001], indicating that the edge segments were more mobile than the screw segments. (2) The second group of samples were loaded normal to [0001] in three orientations: ⊥( ), ⊥( ), and at 45° to ( ). These samples deformed primarily by { } 〈a〉 slip with some evidence for secondary slip on the other systems. They were more creep resistant than the first group and displayed a much higher sensitivity of creep rate to test temperature. Dislocation loops are very elongate parallel to [0001], indicating that the screw dislocation segments were much more mobile than the edge segments. (3) A sample compressed parallel to [0001] at 750°C crept at a barely detectable rate (∼10 s) and no optical scale slip features were observed. These results confirm our earlier work on one orientation each from groups 1 and 2, which indicated a strong creep anisotropy for this same crystal. This creep anisotropy parallels a remarkably similar anisotropy in the diffusivity of impurities in quartz, suggesting a causal relationship between impurity diffusion and creep associated with hydrolytic weakening. Appendix Tables A1‐A5 are available with entire article on microfiche. Order from American Geophysical Union, 2000 Florida Avenue, N.W., Washington, DC 20009. Document B84‐004; $2.50. Payment must accompany order.

Journal of Geophysical Research B: Solid Earth

Färoe-Iceland Ridge Experiment: 1. Crustal structure of northeastern Iceland

Results from the F&auml;roe-Iceland Ridge Experiment (FIRE) constrain the crustal thickness as 19 km under the Northern Volcanic Zone of Iceland and 35 km under older Tertiary areas of northeastern Iceland. The Moho is defined by strong P wave and S wave reflections. Synthetic seismogram modeling of the Moho reflection indicates mantle velocities of at least 8.0 km/s beneath the Tertiary areas of northeastern Iceland and at least 7.9 km/s beneath the neovolcanic zone. Crustal diving rays resolve the structure of the upper and lower crust. Surface P wave velocities are 1.1&ndash;4.0 km/s in Quaternary rocks and are rather higher, 4.4&ndash;4.7 km/s, in the Tertiary basalts that outcrop elsewhere. The highest crustal P wave velocities observed directly from diving rays are 7.1 km/s, from rays that turn at 24 km depth. Velocities of 7.35 km/s at the base of the crust are inferred from extrapolation of the lower crustal velocity gradient (0.024 s &minus;1 ). A Poisson's ratio of approximately 0.27, equivalent to an S wave to P wave travel time ratio of 1.78, is measured throughout the crust east of the neovolcanic zone. The Poisson's ratio and the steep Moho topography (in places up to 30&deg; from the horizontal) indicate that the entire crust outside the neovolcanic zone is cool (<800&deg;C). Gravity data are well matched by a velocity/density conversion of our seismic crustal model and indicate a region of low mantle density beneath the neovolcanic zone, believed to be due to elevated mantle temperatures. The crustal thickness in the neovolcanic zone is consistent with geochemical estimates of the melt generation, placing constraints on the flow within the Iceland mantle plume.

Journal of Geophysical Research B: Solid Earth

Locating shallow seismic sources with waves scattered by surface topography: Validation of the method at the Nevada Test Site

Accurate and robust source location is fundamental in seismology. Previously, we proposed a new full waveform location method using waves scattered by topography near the source, and we demonstrated its potential in obtaining accurate source location using synthetic data. In the work presented here, we validate this method with observed seismic data from the 1993 Non-Proliferation Experiment, a chemical explosion with a precisely known location in a region with moderate topography at the Nevada Test Site. We select the first arrivals (Pn/Pg) and their immediate codas to determine the source location and compare our solution with the known location. We use a collocated-grid finite-difference method to calculate the strain Green’s tensor in a grid-search volume containing the source, and obtain three-component synthetic waveforms at 12 broadband seismic stations at regional distances using source-receiver reciprocity. We assess the solution using a least-squares misfit between the observed and synthetic waveforms. When scattered coda waves are incorporated, the best solution is within a few hundreds of meters of the exact source location, and the estimated uncertainty of the solution is reduced compared to the waveform based solution using only the P waves. The solution is robust to the choice of the frequency content and to the addition of random velocity heterogeneity. We conclude that the full waveform source location method is effective for real seismic data, though more validation tests like this one are needed to further understand its efficacy for source-station geometry, roughness of topography, signal quality and other factors.

Nevada

Orbital and in-situ investigation of periodic bedrock ridges in Glen Torridon, Gale Crater, Mars

Wind has been the dominant agent of landscape modification on Mars for the past ~3 billion years. Among the diversity of features formed by aeolian abrasion on the surface of Mars are periodic bedrock ridges (PBRs), a relatively recently recognized class of erosional bedforms on Mars for which Earth analogues are rare. Gale crater, the field site for NASA’s Mars Science Laboratory Curiosity rover since it landed there in 2012, contains a diverse and extensive record of aeolian deposition and erosion. This study focuses on a series of periodic, linear bedrock ridges that occur within the Fe/Mg-smectite clay-bearing Glen Torridon region of Aeolis Mons (informally Mount Sharp). During Curiosity’s exploration of the Glen Torridon region between sols ~2300-3080, the rover drove through this field of ridges, providing the first opportunity for the in situ observation of these enigmatic erosional features. This study characterizes the Glen Torridon ridges using orbiter and rover data to determine their morphology, spatial distribution, compositional and material properties, and association with other aeolian features in the area. Based on these observations, the Glen Torridon ridges are interpreted to be consistent with an origin as wind-eroded periodic bedrock ridges carved during the most recent exhumation of Mount Sharp into the present-day mound. Although there is evidence for multidirectional winds in the Glen Torridon region based on the orientation of modern ripples, megaripples, TARs and other bedrock indicators, the consistent orientation of the Glen Torridon ridges, coupled with morphologic asymmetries within the ridges, support formation and elongation of the Glen Torridon PBRs forms parallel to a net regional northerly wind direction in and around Gale crater.

Journal of Geophysical Research E: Planets

Imaging spectroscopy: Earth and planetary remote sensing with the USGS Tetracorder and expert systems

Imaging spectroscopy is a tool that can be used to spectrally identify and spatially map materials based on their specific chemical bonds. Spectroscopic analysis requires significantly more sophistication than has been employed in conventional broadband remote sensing analysis. We describe a new system that is effective at material identification and mapping: a set of algorithms within an expert system decision‐making framework that we call Tetracorder. The expertise in the system has been derived from scientific knowledge of spectral identification. The expert system rules are implemented in a decision tree where multiple algorithms are applied to spectral analysis, additional expert rules and algorithms can be applied based on initial results, and more decisions are made until spectral analysis is complete. Because certain spectral features are indicative of specific chemical bonds in materials, the system can accurately identify and map those materials. In this paper we describe the framework of the decision making process used for spectral identification, describe specific spectral feature analysis algorithms, and give examples of what analyses and types of maps are possible with imaging spectroscopy data. We also present the expert system rules that describe which diagnostic spectral features are used in the decision making process for a set of spectra of minerals and other common materials. We demonstrate the applications of Tetracorder to identify and map surface minerals, to detect sources of acid rock drainage, and to map vegetation species, ice, melting snow, water, and water pollution, all with one set of expert system rules. Mineral mapping can aid in geologic mapping and fault detection and can provide a better understanding of weathering, mineralization, hydrothermal alteration, and other geologic processes. Environmental site assessment, such as mapping source areas of acid mine drainage, has resulted in the acceleration of site cleanup, saving millions of dollars and years in cleanup time. Imaging spectroscopy data and Tetracorder analysis can be used to study both terrestrial and planetary science problems. Imaging spectroscopy can be used to probe planetary systems, including their atmospheres, oceans, and land surfaces.

Journal of Geophysical Research E: Planets

Resonance of a fluid-driven crack: Radiation properties and implications for the source of long-period events and harmonic tremor

A dynamic source model is presented, in which a three-dimensional crack containing a viscous compressible fluid is excited into resonance by an impulsive pressure transient applied over a small area ΔS of the crack surface. The crack excitation depends critically on two dimensionless parameters called the crack stiffness, C = ( b /μ)( L / d ), and viscous damping loss, F = (12η L )/(ρ ƒ d 2 α), where b is the bulk modulus, η is the viscosity, ρ ƒ is the density of the fluid, μ is the rigidity, α is the compressional velocity of the solid, L is the crack length, and d is the crack thickness. The first parameter characterizes the ability of the crack to vibrate and shapes the spectral signature of the source, and the second quantifies the effect of fluid viscosity on the duration of resonance. Resonance is sustained by a very slow wave trapped in the fluid-filled crack. This guided wave, called the crack wave, is similar to the tube wave propagating in a fluid-filled borehole; it is inversely dispersive, showing a phase velocity that decreases with increasing wavelength, and its wave speed is always lower than the acoustic velocity of the fluid, decreasing rapidly as the crack stiffness increases. The source spectrum shows many sharp peaks characterizing the individual modes of vibration of the crack; the variation of spectral shape, both in the number and width of peaks, is surprisingly complex, reflecting the interference between the lateral and longitudinal modes of resonance, as well as nodes for these modes. The far-field spectrum is marked by narrow-band dominant and subdominant peaks that reflect the interaction of the various source modes. The frequency of the dominant spectral peak radiated by the source is independent of the radiation direction. The frequency, bandwidth, and spacing of the resonant peaks are strongly dependent on the crack stiffness, larger values of the stiffness factor shifting these peaks to lower frequencies and decreasing their bandwidth. The excitation of a particular mode depends on the position of the trigger and on the extent of the crack surface affected by the pressure transient. Fluid viscosity decreases the amplitudes of the main spectral peaks, smears out the finer structure of the spectrum, and greatly reduces the duration of the radiated signal. The energy loss by radiation is stronger for high frequencies, producing a seismic signature that is marked by a high-frequency content near the onset of the signal and dominated by a longer-period component of much longer duration in the signal coda. Such signature is in harmony with those displayed by long-period events observed on active volcanoes and in hydrofracture experiments. The very low velocity which is possible in a crack with high stiffness ( C ≥ 100) also provides an attractive explanation for very long period tremor, such as type 2 tremor at Aso volcano, Japan, without the requirement of an unrealistically large magma container. The standing wave pattern set up on the crack surface by the sustained resonance in the fluid is observable in the near field of the crack, suggesting that the location and extent of the source may be estimated from the mapping of the pattern of nodes and antinodes seen in its vicinity. According to the model, the long-period event and harmonic tremor share the same source but differ in the boundary conditions for fluid flow and in the triggering mechanism setting up the resonance of the source, the former being viewed as the impulse response of the tremor generating system and the latter representing the excitation due to more complex forcing functions.

Journal of Geophysical Research Solid Earth