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Temporal stress changes caused by earthquakes: A review

Earthquakes can change the stress field in the Earth’s lithosphere as they relieve and redistribute stress. Earthquake-induced stress changes have been observed as temporal rotations of the principal stress axes following major earthquakes in a variety of tectonic settings. The stress changes due to the 2011 Mw9.0 Tohoku-Oki, Japan, earthquake were particularly well documented. Earthquake stress rotations can inform our understanding of earthquake physics, most notably addressing the long-standing problem of whether the Earth’s crust at plate boundaries is “strong” or “weak.” Many of the observed stress rotations, including that due to the Tohoku-Oki earthquake, indicate near-complete stress drop in the mainshock. This implies low background differential stress, on the order of earthquake stress drop, supporting the weak crust model. Earthquake stress rotations can also be used to address other important geophysical questions, such as the level of crustal stress heterogeneity and the mechanisms of postseismic stress reloading. The quantitative interpretation of stress rotations is evolving from those based on simple analytical methods to those based on more sophisticated numerical modeling that can capture the spatial-temporal complexity of the earthquake stress changes.

Journal of Geophysical Research B: Solid Earth

Climatic impact of glacial cycle polar motion: Coupled oscillations of ice sheet mass and rotation pole position

Precessional motion of Earth's rotation axis relative to its orbit is a well-known source of long-period climatic variation. It is less well appreciated that growth and decay of polar ice sheets perturb the symmetry of the global mass distribution enough that the geographic location of the rotation axis will change by at least 15 km and possibly as much as 100 km during a single glacial cycle. This motion of the pole will change the seasonal and latitudinal pattern of temperatures. We present calculations, based on a diurnal average energy balance, which compare the summer and winter temperature anomalies due to a 1° decrease in obliquity with those due to a 1° motion of the rotation pole toward Hudson Bay. Both effects result in peak temperature perturbations of about 1° Celsius. The obliquity change primarily influences the amplitude of the seasonal cycle, while the polar motion primarily changes the annual mean temperatures. The polar motion induced temperature anomaly is such that it will act as a powerful negative feedback on ice sheet growth. We also explore the evolution of the coupled system composed of ice sheet mass and pole position. Oscillatory solutions result from the conflicting constraints of rotational and thermal stability. A positive mass anomaly on an otherwise featureless Earth is in rotational equilibrium only at the poles or the equator. The two polar equilibria are rotationally unstable, and the equatorial equilibrium, though rotationally stable, is thermally unstable. We find that with a plausible choice for the strength of coupling between the thermal and rotational systems, relatively modest external forcing can produce significant response at periods of 10 4 –10 6 years, but it strongly attenuates polar motion at longer periods. We suggest that these coupled oscillations may contribute to the observed dominance of 100 kyr glacial cycles since the mid-Pleistocene and will tend to stabilize geographic patterns that are suitable to glaciations.

Journal of Geophysical Research B: Solid Earth

Crustal velocity field near the big bend of California's San Andreas fault

We use geodetic data spanning the 1920–1992 interval to estimate the horizontal velocity field near the big bend segment of California's San Andreas fault (SAF). More specifically, we estimate a horizontal velocity vector for each node of a two-dimensional grid that has a 15-min-by-15-min mesh and that extends between latitudes 34.0°N and 36.0°N and longitudes 117.5°W and 120.5°W. For this estimation process, we apply bilinear interpolation to transfer crustal deformation information from geodetic sites to the grid nodes. The data include over a half century of triangulation measurements, over two decades of repeated electronic distance measurements, a decade of repeated very long baseline interferometry measurements, and several years of Global Positioning System measurements. Magnitudes for our estimated velocity vectors have formal standard errors ranging from 0.7 to 6.8 mm/yr. Our derived velocity field shows that (1) relative motion associated with the SAF exceeds 30 mm/yr and is distributed on the Earth's surface across a band (>100 km wide) that is roughly centered on this fault; (2) when velocities are expressed relative to a fixed North America plate, the motion within our primary study region has a mean orientation of N44°W ± 2° and the surface trace of the SAF is congruent in shape to nearby contours of constant speed yet this trace is oriented between 5° and 10° counterclockwise relative to these contours; and (3) large strain rates (shear rates > 150 nrad/yr and/or areal dilatation rates < −150 nstr/yr) exist near the Garlock fault, near the White Wolf fault, and in the Ventura basin.

Journal of Geophysical Research B: Solid Earth

Pore fluid pressure, apparent friction, and Coulomb failure

Many recent studies of stress-triggered seismicity rely on a fault failure model with a single free parameter, the apparent coefficient of friction, presumed to be a material constant with possible values 0 ≤ μ′ ≤ 1. These studies may present a misleading view of fault strength and the role of pore fluid pressure in earthquake failure. The parameter μ′ is intended to incorporate the effects of both friction and pore pressure, but is a material constant only if changes in pore fluid pressure induced by changes in stress are proportional to the normal stress change across the potential failure plane. Although specific models of fault zones permit such a relation, neither is it known that fault zones within the Earth behave this way, nor is this behavior expected in all cases. In contrast, for an isotropic homogeneous poroelastic model the pore pressure changes are proportional to changes in mean stress, μ′ is not a material constant, and −∞ ≤ μ′ ≤ +∞. Analysis of the change in Coulomb failure stress for tectonically loaded reverse and strike-slip faults shows considerable differences between these two pore pressure models, suggesting that such models might be distinguished from one another using observations of triggered seismicity (e.g., aftershocks). We conclude that using the constant apparent friction model exclusively in studies of Coulomb failure stress is unwise and could lead to significant errors in estimated stress change and seismic hazard.

Journal of Geophysical Research B: Solid Earth

Mass addition at Mount St. Helens, Washington, inferred from repeated gravity surveys

Measurements of subtle changes in the Earth’s gravityfield can provideinformation on the addition/loss of mass (e.g., magma or aqueousfluids) beneath a volcano. In this study, wemeasured gravity at Mount St. Helens from 2010 to 2016 to investigate possible mass changes followingthe 2004–2008 dome-forming eruption. The raw gravity measurements were corrected for changes in themass and shape of Crater Glacier and for deformation of the volcanic edifice to obtain residual gravity values.We found positive residual gravity changes that we interpret as evidence for partial recharge of the magmareservoir that fed the 2004–2008 eruption and/or for accumulation of groundwater in one or more shallowaquifers. Most of the gravity signal can be explained by groundwater accumulation; magma recharge is notrequired. However, there is additional evidence for at least partial recharge from seismic, deformation, andgeochemical observations

Washington

Insights into shallow magmatic processes at Kīlauea Volcano, Hawaiʻi, from a multiyear continuous gravity time series

Continuous gravity data collected near the summit eruptive vent at Kīlauea Volcano, Hawaiʻi, during 2011–2015 show a strong correlation with summit-area surface deformation and the level of the lava lake within the vent over periods of days to weeks, suggesting that changes in gravity reflect variations in volcanic activity. Joint analysis of gravity and lava level time series data indicates that over the entire time period studied, the average density of the lava within the upper tens to hundreds of meters of the summit eruptive vent remained low—approximately 1000–1500 kg/m 3 . The ratio of gravity change (adjusted for Earth tides and instrumental drift) to lava level change measured over 15 day windows rose gradually over the course of 2011–2015, probably reflecting either (1) a small increase in the density of lava within the eruptive vent or (2) an increase in the volume of lava within the vent due to gradual vent enlargement. Superimposed on the overall time series were transient spikes of mass change associated with inflation and deflation of Kīlauea's summit and coincident changes in lava level. The unexpectedly strong mass variations during these episodes suggest magma flux to and from the shallow magmatic system without commensurate deformation, perhaps indicating magma accumulation within, and withdrawal from, void space—a process that might not otherwise be apparent from lava level and deformation data alone. Continuous gravity data thus provide unique insights into magmatic processes, arguing for continued application of the method at other frequently active volcanoes.

Hawaii

Short-period strain (0.1–105 s): Near-source strain field for an earthquake (ML 3.2) near San Juan Bautista, California

Measurements of dilational earth strain in the frequency band 25–10 −5 Hz have been made on a deep borehole strainmeter installed near the San Andreas fault. These data are used to determine seismic radiation fields during nuclear explosions, teleseisms, local earthquakes, and ground noise during seismically quiet times. Strains of less than 10 −10 on these instruments can be clearly resolved at short periods (< 10 s) and are recorded with wide dynamic range digital recorders. This permits measurement of the static and dynamic strain variations in the near field of local earthquakes. Noise spectra for earth strain referenced to 1 (strain) 2 /Hz show that strain resolution decreases at about 10 dB per decade of frequency from −150 dB at 10 −4 Hz to −223 dB at 10 Hz. Exact expressions are derived to relate the volumetric strain and displacement field for a homogeneous P wave in a general viscoelastic solid as observed on colocated dilatometers and seismometers. A rare near-field recording of strain and seismic velocity was obtained on May 26, 1984, from an earthquake ( M L 3.2) at a hypocentral distance of 3.2 km near the San Andreas fault at San Juan Bautista, California. While the data indicate no precursory strain release at the 5 × 10 −11 strain level, a coseismic strain release of 1.86 nanostrain was observed. This change in strain is consistent with that calculated from a simple dislocation model of the event. Ground displacement spectra, determined from the downhole strain data and instrument-corrected surface seismic data, suggest that source parameters estimated from surface recordings may be contaminated by amplification effects in near-surface low-velocity materials.

California

Long period seismicity and very long period infrasound driven by shallow magmatic degassing at Mount Pagan, Mariana Islands

Long period (LP) seismicity and very long period infrasound (iVLP) were recorded during continuous degassing from Mount Pagan, Mariana Islands, in July 2013 to January 2014. The frequency content of the LP and iVLP events and delay times between the two arrivals were remarkably stable and indicate nearly co-located sources. Using phase-weighted stacking over similar events to dampen noise, we find that the LP source centroid is located 60&thinsp;m below and 180&thinsp;m west of the summit vent. The moment tensor reveals a volumetric source modeled as resonance of a subhorizontal sill intersecting a dike. We model the seismoacoustic wavefields with a coupled earth-air 3-D finite difference code. The ratios of pressure to velocity measured at the infrasound arrays are an order of magnitude larger than the synthetic ratios, so the iVLP is not the result of LP energy transmitting into the atmosphere at its epicenter. Based on crater shape and dimensions determined by structure from motion, we model the iVLP as acoustic resonance of an exponential horn. The source of the continuous plume from gas analysis is shallow magmatic degassing, which repeatedly pressurized the dike-sill portion of the conduit over the 7&thinsp;months of observation. Periodic gas release caused the geologically controlled sill to partially collapse and resonate, while venting of gas at the surface triggered resonance in the crater. LP degassing only accounts for ~12% of total degassing, indicating that most degassing is relatively aseismic and that multiple active pathways exist beneath the vent.

Mount Pagan

Tidal triggering of low frequency earthquakes near Parkfield, California: Implications for fault mechanics within the brittle-ductile transition

Studies of nonvolcanic tremor (NVT) have established the significant impact of small stress perturbations on NVT generation. Here we analyze the influence of the solid earth and ocean tides on a catalog of ∼550,000 low frequency earthquakes (LFEs) distributed along a 150 km section of the San Andreas Fault centered at Parkfield. LFE families are identified in the NVT data on the basis of waveform similarity and are thought to represent small, effectively co-located earthquakes occurring on brittle asperities on an otherwise aseismic fault at depths of 16 to 30 km. We calculate the sensitivity of each of these 88 LFE families to the tidally induced right-lateral shear stress (RLSS), fault-normal stress (FNS), and their time derivatives and use the hypocentral locations of each family to map the spatial variability of this sensitivity. LFE occurrence is most strongly modulated by fluctuations in shear stress, with the majority of families demonstrating a correlation with RLSS at the 99% confidence level or above. Producing the observed LFE rate modulation in response to shear stress perturbations requires low effective stress in the LFE source region. There are substantial lateral and vertical variations in tidal shear stress sensitivity, which we interpret to reflect spatial variation in source region properties, such as friction and pore fluid pressure. Additionally, we find that highly episodic, shallow LFE families are generally less correlated with tidal stresses than their deeper, continuously active counterparts. The majority of families have weaker or insignificant correlation with positive (tensile) FNS. Two groups of families demonstrate a stronger correlation with fault-normal tension to the north and with compression to the south of Parkfield. The families that correlate with fault-normal clamping coincide with a releasing right bend in the surface fault trace and the LFE locations, suggesting that the San Andreas remains localized and contiguous down to near the base of the crust. The deep families that have high sensitivity to both shear and tensile normal stress perturbations may be indicative of an increase in effective fault contact area with depth. Synthesizing our observations with those of other LFE-hosting localities will help to develop a comprehensive understanding of transient fault slip below the “seismogenic zone” by providing constraints on parameters in physical models of slow slip and LFEs.

California

Inference of postseismic deformation mechanisms of the 1923 Kanto earthquake

Coseismic slip associated with the M7.9, 1923 Kanto earthquake is fairly well understood, involving slip of up to 8 m along the Philippine Sea-Honshu interplate boundary under Sagami Bay and its onland extension. Postseismic deformation after the 1923 earthquake, however, is relatively poorly understood. We revisit the available deformation data in order to constrain possible mechanisms of postseismic deformation and to examine the consequences for associated stress changes in the surrounding crust. Data from two leveling lines and one tide gage station over the first 7-8 years postseismic period are of much greater amplitude than the corresponding expected interseismic deformation during the same period, making these data suitable for isolating the signal from postseismic deformation. We consider both viscoelastic models of asthenosphere relaxation and afterslip models. A distributed coseismic slip model presented by Pollitz et al. (2005), combined with prescribed parameters of a viscoelastic Earth model, yields predicted postseismic deformation that agrees with observed deformation on mainland Honshu from Tokyo to the Izu peninsula. Elsewhere (southern Miura peninsula; Boso peninsula), the considered viscoelastic models fail to predict observed deformation, and a model of ???1 in shallow afterslip in the offshore region south of the Boso peninsula, with equivalent moment magnitude Mw = 7.0, adequately accounts for the observed deformation. Using the distributed coseismic slip model, layered viscoelastic structure, and a model of interseismic strain accumulation, we evaluate the post-1923 stress evolution, including both the coseismic and accumulated postseismic stress changes and those stresses contributed by interseismic loading. We find that if account is made for the varying tectonic regime in the region, the occurrence of both immediate (first month) post-1923 crustal aftershocks as well as recent regional crustal seismicity is consistent with the predicted stress pattern. This suggests that the influence of the 1923 earthquake on regional seismicity is fairly predictable and has persisted for at least seven decades following the earthquake.

Journal of Geophysical Research B: Solid Earth

A global search inversion for earthquake kinematic rupture history: Application to the 2000 western Tottori, Japan earthquake

[1] We present a two-stage nonlinear technique to invert strong motions records and geodetic data to retrieve the rupture history of an earthquake on a finite fault. To account for the actual rupture complexity, the fault parameters are spatially variable peak slip velocity, slip direction, rupture time and risetime. The unknown parameters are given at the nodes of the subfaults, whereas the parameters within a subfault are allowed to vary through a bilinear interpolation of the nodal values. The forward modeling is performed with a discrete wave number technique, whose Green's functions include the complete response of the vertically varying Earth structure. During the first stage, an algorithm based on the heat-bath simulated annealing generates an ensemble of models that efficiently sample the good data-fitting regions of parameter space. In the second stage (appraisal), the algorithm performs a statistical analysis of the model ensemble and computes a weighted mean model and its standard deviation. This technique, rather than simply looking at the best model, extracts the most stable features of the earthquake rupture that are consistent with the data and gives an estimate of the variability of each model parameter. We present some synthetic tests to show the effectiveness of the method and its robustness to uncertainty of the adopted crustal model. Finally, we apply this inverse technique to the well recorded 2000 western Tottori, Japan, earthquake ( Mw 6.6); we confirm that the rupture process is characterized by large slip (3-4 m) at very shallow depths but, differently from previous studies, we imaged a new slip patch (2-2.5 m) located deeper, between 14 and 18 km depth.

Tottori

Strain accumulation and rotation in western Nevada, 1993-2000

The positions of 44 GPS monuments in an array extending from the Sierra Nevada at the latitude of Reno to near Austin, Nevada, have been measured several times in the 1993–2000 interval. The western half of the array spans the Walker Lane belt, whereas the eastern half spans the central Nevada seismic zone (CNSZ). The principal strain rates in the Walker Lane belt are 29.6 ± 5.3 nstrain yr −1 N88.4°E ± 5.4° and −12.8 ± 6.0 nanostrain yr −1 N01.6°W ± 5.4°, extension reckoned positive, and the clockwise (as seen from above the Earth) rotation rate about a vertical axis is 13.6 ± 4.0 nrad yr −1 . The quoted uncertainties are standard deviations. The motion in the Walker Lane belt can then be represented by a zone striking N35°W subject to 16.8 ± 4.9 nstrain yr −1 extension perpendicular to it and 19.5 ± 4.0 nstrain yr −1 right-lateral, simple shear across it. The N35°W strike of the zone is the same as the direction of the local tangent to the small circle drawn about the Pacific-North America pole of rotation. The principal strain rates for the CNSZ are 46.2 ± 11.0 nstrain yr −1 N49.9°W ± 6.0° and −13.6 ± 6.1 nstrain yr −1 N40.1°E ± 6.0°, and the clockwise rotation rate about a vertical axis is 20.3 ± 6.3 nrad yr −1 . The motion across the CNSZ can then be represented by a zone striking N12°E subject to 32.6 ± 11.0 nstrain yr −1 extension perpendicular to it and 25.1 ± 6.3 nstrain yr −1 right-lateral, simple shear across it. The N12°E strike of the zone is similar to the strikes of the faults (Rainbow Mountain, Fairview Peak, and Dixie Valley) within it.

California, Nevada

Diffuse flow hydrothermal manganese mineralization along the active Mariana and southern Izu-Bonin arc system, western Pacific

Abundant ferromanganese oxides were collected along 1200 km of the active Izu-Bonin-Mariana arc system. Chemical compositions and mineralogy show that samples were collected from two deposit types: Fe-Mn crusts of mixed hydrogenetic/hydrothermal origin and hydrothermal Mn oxide deposits; this paper addresses only the second type. Mn oxides cement volcaniclastic and biogenic sandstone and breccia layers (Mn sandstone) and form discrete dense stratabound layers along bedding planes and within beds (stratabound Mn). The Mn oxide was deposited within coarse-grained sediments from diffuse flow systems where precipitation occurred below the seafloor. Deposits were exposed at the seabed by faulting, mass wasting, and erosion. Scanning electron microscopy and microprobe analyses indicate the presence of both amorphous and crystalline 10 ?? and 7 ?? manganate minerals, the fundamental chemical difference being high water contents in the amorphous Mn oxides. Alternation of amorphous and crystalline laminae occurs in many samples, which likely resulted from initial rapid precipitation of amorphous Mn oxides from waxing pulses of hydrothermal fluids followed by precipitation of slow forming crystallites during waning stages. The chemical composition is characteristic of a hydrothermal origin including strong fractionation between Fe (mean 0.9 wt %) and Mn (mean 48 wt %) for the stratabound Mn, generally low trace metal contents, and very low rare earth element and platinum group element contents. However, Mo, Cd, Zn, Cu, Ni, and Co occur in high concentrations in some samples and may be good indicator elements for proximity to the heat source or to massive sulfide deposits. For the Mn sandstones, Fe (mean-8.4%) and Mn (12.4%) are not significantly fractionated because of high Fe contents in the volcaniclastic material. However, the proportion of hydrothermal Fe (nondetrital Fe) to total Fe is remarkably constant (49-58%) for all the sample groups, regardless of the degree of Mn mineralization. Factor analyses indicate various mixtures of two dominant components: hydrothermal Mn oxide for the stratabound Mn and detrital aluminosilicate for the Mn-cemented sandstone; and two minor components, hydrothermal Fe oxyhydroxide and biocarbonate/biosilica. Our conceptual model shows that Mn mineralization was produced by hydrothermal convection cells within arc volcanoes and sedimentary prisms that occur along, the flanks and within calderas. The main source of hydrothermal fluid was seawater that penetrated through fractures, faults, and permeable volcanic edifices. The fluids were heated by magma, enriched in metals by leaching of basement rocks and sediments, and mixed with magmatic fluids and gases. Dikes and sills may have been another source of heat that drove small-scale circulation within sedimentary prisms. Copyright 2008 by the American Geophysical Union.

Journal of Geophysical Research B: Solid Earth

Isotopic and trace element variations in the Ruby Batholith, Alaska, and the nature of the deep crust beneath the Ruby and Angayucham Terranes

Thirty-six samples from plutons of the Ruby batholith of central Alaska were collected and analyzed for 22 trace elements, and many were analyzed for the isotopic compositions of Sr, Nd, O, and Pb in order to delimit the processes that produced the diversity of granodioritic to granitic compositions, to deduce the nature of the source of magmas at about 110 Ma, and to characterize the deep crust beneath the Ruby and Angayucham terranes. Plutons of the batholith show a substantial range in initial 87 Sr/ 86 Sr (SIR) of 0.7055&ndash;0.7235 and a general decrease from southwest to northeast. Initial 143 Nd/ 144 Nd (NIR) have a range of 0.51150&ndash;0.51232 and generally increase from southwest to northeast. The &delta; 18 O values for most whole rocks have a range of +8.4 to +11.8 and an average of +10.3&permil;. Rb, Cs, U, and Th show large ranges of concentration, generally increase as SiO 2 increases, and are higher in southwest than in northeast plutons. Sr, Ba, Zr, Hf, Ta, Sc, Cr, Co, and Zr show large ranges of concentration and generally decrease as SiO 2 increases. Rare earth elements (REE) show fractionated patterns and negative Eu anomalies. REE concentrations and anomalies are larger in the southwest than in the northeast plutons. Uniformity of SIR and NIR in Sithylemenkat and Jim River plutons suggests a strong role for fractional crystallization or melting of uniform magma sources at depth. Isotopic variability in Melozitna, Ray Mountains, Hot Springs, and Kanuti plutons suggests complex magmatic processes such as magma mixing and assimilation, probably combined with fractional crystallization, or melting of a complex source at depth. The large variations in SIR and NIR in the batholith require a variation in source materials at depth. The southwestern plutons probably had dominantly siliceous sources composed of metamorphosed Proterozoic and Paleozoic upper crustal rocks. The northeastern plutons probably had Paleozoic sources that were mixtures of siliceous and intermediate to mafic crustal rocks. The inferred sources could well have been the higher-metamorphic-grade lithologic equivalents of the exposed Proterozoic(?) to Paleozoic schists, orthogneisses, and metavolcanic rocks of Ruby terrane, the silicic portions of which are quite radiogenic. The deeper crustal sources that gave rise to most of the batholithic magmas are inferred to be similar under both the Ruby metamorphic terrane and the Angayucham ophiolitic terrane.

Alaska

Correlated errors in geodetic time series: Implications for time-dependent deformation

Analysis of frequent trilateration observations from the two-color electronic distance measuring networks in California demonstrate that the noise power spectra are dominated by white noise at higher frequencies and power law behavior at lower frequencies. In contrast, Earth scientists typically have assumed that only white noise is present in a geodetic time series, since a combination of infrequent measurements and low precision usually preclude identifying the time-correlated signature in such data. After removing a linear trend from the two-color data, it becomes evident that there are primarily two recognizable types of time-correlated noise present in the residuals. The first type is a seasonal variation in displacement which is probably a result of measuring to shallow surface monuments installed in clayey soil which responds to seasonally occurring rainfall; this noise is significant only for a small fraction of the sites analyzed. The second type of correlated noise becomes evident only after spectral analysis of line length changes and shows a functional relation at long periods between power and frequency of 1/ƒ α , where ƒ is frequency and α≈2. With α=2, this type of correlated noise is termed random-walk noise, and its source is mainly thought to be small random motions of geodetic monuments with respect to the Earth's crust, though other sources are possible. Because the line length changes in the two-color networks are measured at irregular intervals, power spectral techniques cannot reliably estimate the level of 1/ƒ α noise. Rather, we also use here a maximum likelihood estimation technique which assumes that there are only two sources of noise in the residual time series (white noise and random-walk noise) and estimates the amount of each. From this analysis we find that the random-walk noise level averages about 1.3 mm/√yr and that our estimates of the white noise component confirm theoretical limitations of the measurement technique. In addition, the seasonal noise can be as large as 3 mm in amplitude but typically is less than 0.5 mm. Because of the presence of random-walk noise in these time series, modeling and interpretation of the geodetic data must account for this source of error. By way of example we show that estimating the time-varying strain tensor (a form of spatial averaging) from geodetic data having both random-walk and white noise error components results in seemingly significant variations in the rate of strain accumulation; spatial averaging does reduce the size of both noise components but not their relative influence on the resulting strain accumulation model.

Journal of Geophysical Research B: Solid Earth

Displacement field for an edge dislocation in a layered half-space

The displacement field for an edge dislocation in an Earth model consisting of a layer welded to a half-space of different material is found in the form of a Fourier integral following the method given by Weeks et al. [1968]. There are four elementary solutions to be considered: the dislocation is either in the half-space or the layer and the Burgers vector is either parallel or perpendicular to the layer. A general two-dimensional solution for a dip-slip faulting or dike injection (arbitrary dip) can be constructed from a superposition of these elementary solutions. Surface deformations have been calculated for an edge dislocation located at the interface with Burgers vector inclined 0°, 30°, 60°, and 90° to the interface for the case where the rigidity of the layer is half of that of the half-space and the Poisson ratios are the same. Those displacement fields have been compared to the displacement fields generated by similarly situated edge dislocations in a uniform half-space. The surface displacement field produced by the edge dislocation in the layered half-space is very similar to that produced by an edge dislocation at a different depth in a uniform half-space. In general, a low-modulus (high-modulus) layer causes the half-space equivalent dislocation to appear shallower (deeper) than the actual dislocation in the layered half-space.

Journal of Geophysical Research B: Solid Earth

Prodigious submarine landslides on the Hawaiian Ridge

The extensive area covered by major submarine mass wasting deposits on or near the Hawaiian Ridge has been delimited by systematic mapping of the Hawaiian exclusive economic zone using the side‐looking sonar system GLORIA. These surveys show that slumps and debris avalanche deposits are exposed over about 100,000 km 2 of the ridge and adjacent seafloor from Kauai to Hawaii, covering an area more than 5 times the land area of the islands. Some of the individual debris avalanches are more than 200 km long and about 5000 km 3 in volume, ranking them among the largest on Earth. The slope failures that produce these deposits begin early in the history of individual volcanoes when they are small submarine seamounts, culminate near the end of subaerial shield building, and apparently continue long after dormancy. Consequently, landslide debris is an important element in the internal structure of the volcanoes. The dynamic behavior of the volcanoes can be modulated by slope failure, and the structural features of the landslides are related to elements of the volcanoes including rift zones and fault systems. The landslides are of two general types, slumps and debris avalanches. The slumps are slow moving, wide (up to 110 km), and thick (about 10 km) with transverse blocky ridges and steep toes. The debris avalanches are fast moving, long (up to 230 km) compared to width, and thinner (0.05–2 km); they commonly have a well‐defined amphitheater at their head and hummocky terrain in the lower part. Oceanic disturbance caused by rapid emplacement of debris avalanches may have produced high‐level wave deposits (such as the 365‐m elevation Hulopoe Gravel on Lanai) that are found on several islands. Most present‐day submarine canyons were originally carved subaerially in the upper parts of debris avalanches. Subaerial canyon cutting was apparently promoted by the recently steepened and stripped slopes of the landslide amphitheaters.

Journal of Geophysical Research B: Solid Earth

Origin of Hawaiian tholeiite: A metasomatic model

Two voluminous magma types generated in the mantle underlying the Pacific plate are mid‐ocean ridge tholeiite (MORB) erupted at the East Pacific Rise spreading center and Hawaiian tholeiite (HT) erupted above the Hawaiian hot spot or melting anomaly. MORB has low initial 87 Sr/ 86 Sr ratios and low amounts of all incompatible trace elements including rare earths; chondrite‐normalized patterns are depleted in light rare earths. HT, by contrast, has higher initial 87 Sr/ 86 Sr and higher amounts of incompatible trace elements; chondrite‐nor‐malized patterns are enriched in the middle and light rare earths. HT is generally poorer in CaO and Al 2 O 3 and much richer in total iron and TiO 2 compared with MORB having the same MgO content. Primary magma compositions for the two volcanic systems are calculated in Fe‐Mg equilibrium with residual olivine (Fo 92 ). MORB is generated by partial melting of a trace element depleted Iherzolite source leaving a residual assemblage dominated by olivine and orthopyroxene. The percentage of partial melting for a primary magma containing 15% MgO is calculated to be 35–42% in a source mantle having a heavy rare earth content of 3×chondrite and 33–35% MgO. HT, represented by Kilauea tholeiite, is generated by partial melting of a mixture of unmelted and residual mantle for MORB which has been modified by metasomatic addition of a nephelinitic fluid, amphibole, and minor amounts of apatite and Fe‐bearing phases such as sulfide and magnetite/ilmenite. This model yields a picritic magma in equilbrium with magnesian dunite at high (>40%) degrees of partial melting. The source also has 35% MgO before partial melting. Melting in both systems in polyvariant and not controlled by lower‐temperature invariant equilibria. The low‐velocity zone is considered to be the source of metasomatic fluids that are driven upward into the lowermost lithosphere in response to a thermal plume. Picritic primary magmas are produced by shear melting, localized in the zone of thinned and metasomatized lithosphere beneath Hawaii. Melt extraction is rapid and episodic at intervals of months to decades; magma is not stored in the mantle but passes upward to a plexus of storage reservoirs located 2–6 km beneath the surface of Kilauea. Kilauea primary magmas fractionate olivine during upward transport to reach bulk compositions of 13–14% MgO in storage. Different magma batches erupted to the surface, distinguished by different major and minor element compositons compared at similar MgO content, represent combinations of differing degrees of metasomatic enrichment, differing degrees of partial melting, and some effects of premelting mantle heterogeneity.

Hawaii