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Geology topics

B.R. Julian

Publications and source records attributed to B.R. Julian.

At least 19 recordsLinked to original sources
USGS2010

Time-dependent seismic tomography

Of methods for measuring temporal changes in seismic-wave speeds in the Earth, seismic tomography is among those that offer the highest spatial resolution. 3-D tomographic methods are commonly applied in this context by inverting seismic wave arrival time data sets from different epochs independently and assuming that differences in the derived structures represent real temporal variations. This assumption is dangerous because the results of independent inversions would differ even if the structure in the Earth did not change, due to observational errors and differences in the seismic ray distributions. The latter effect may be especially severe when data sets include earthquake swarms or aftershock sequences, and may produce the appearance of correlation between structural changes and seismicity when the wave speeds are actually temporally invariant. A better approach, which makes it possible to assess what changes are truly required by the data, is to invert multiple data sets simultaneously, minimizing the difference between models for different epochs as well as the rms arrival-time residuals. This problem leads, in the case of two epochs, to a system of normal equations whose order is twice as great as for a single epoch. The direct solution of this system would require twice as much memory and four times as much computational effort as would independent inversions. We present an algorithm, tomo4d, that takes advantage of the structure and sparseness of the system to obtain the solution with essentially no more effort than independent inversions require. No claim to original US government works Journal compilation ?? 2010 RAS.

Geophysical Journal International↗
USGS2010

On possible plume-guided seismic waves

Hypothetical thermal plumes in the Earth's mantle are expected to have low seismic-wave speeds and thus would support the propagation of guided elastic waves analogous to fault-zone guided seismic waves, fiber-optic waves, and acoustic waves in the oceanic SOund Fixing And Ranging channel. Plume-guided waves would be insensitive to geometric complexities in the wave guide, and their dispersion would make them distinctive on seismograms and would provide information about wave-guide structure that would complement seismic tomography. Detecting such waves would constitute strong evidence of a new kind for the existence of plumes. A cylindrical channel embedded in an infinite medium supports two classes of axially symmetric elastic-wave modes, torsional and longitudinal-radial. Torsional modes have rectilinear particle motion tangent to the cylinder surface. Longitudinal-radial modes have elliptical particle motion in planes that include the cylinder axis, with retrograde motion near the axis. The direction of elliptical particle motion reverses with distance from the axis: once for the fundamental mode, twice for the first overtone, and so on. Each mode exists only above its cut-off frequency, where the phase and group speeds equal the shear-wave speed in the infinite medium. At high frequencies, both speeds approach the shear-wave speed in the channel. All modes have minima in their group speeds, which produce Airy phases on seismograms. For shear wave-speed contrasts of a few percent, thought to be realistic for thermal plumes in the Earth, the largest signals are inversely dispersed and have dominant frequencies of about 0.1-1 Hz and durations of 15-30 sec. There are at least two possible sources of observable plume waves: (1) the intersection of mantle plumes with high-amplitude core-phase caustics in the deep mantle; and (2) ScS-like reflection at the core-mantle boundary of downward-propagating guided waves. The widespread recent deployment of broadband seismometers makes searching for these waves possible.

Bulletin of the Seismological Society of America↗
USGS2005

Time-dependent seismic tomography of the Coso geothermal area, 1996-2004

The permanent 18-station network of three-component digital seismometers at the seismically active Coso geothermal area, California, provides high-quality microearthquake (MEQ) data that are well suited to investigating temporal variations in structure related to processes within the geothermal reservoir. A preliminary study [Julian, et al., 2003; Julian, et al., 2004] comparing data from 1996 and 2003 found significant variations in the ratio of the seismic wave-speeds, Vp/Vs, at shallow depths over this time interval. This report describes results of a more detailed study of each year from 1996 through 2004.

Conference Paper↗
USGS2004

Non-double-couple microearthquakes at Long Valley caldera, California, provide evidence for hydraulic fracturing

Most of 26 small (0.4≲ M ≲3.1) microearthquakes at Long Valley caldera in mid-1997, analyzed using data from a dense temporary network of 69 digital three-component seismometers, have significantly non-double-couple focal mechanisms, inconsistent with simple shear faulting. We determined their mechanisms by inverting P - and S -wave polarities and amplitude ratios using linear-programming methods, and tracing rays through a three-dimensional Earth model derived using tomography. More than 80% of the mechanisms have positive (volume increase) isotropic components and most have compensated linear-vector dipole components with outward-directed major dipoles. The simplest interpretation of these mechanisms is combined shear and extensional faulting with a volume-compensating process, such as rapid flow of water, steam, or CO 2 into opening tensile cracks. Source orientations of earthquakes in the south moat suggest extensional faulting on ESE-striking subvertical planes, an orientation consistent with planes defined by earthquake hypocenters. The focal mechanisms show that clearly defined hypocentral planes in different locations result from different source processes. One such plane in the eastern south moat is consistent with extensional faulting, while one near Casa Diablo Hot Springs reflects en echelon right-lateral shear faulting. Source orientations at Mammoth Mountain vary systematically with location, indicating that the volcano influences the local stress field. Events in a ‘spasmodic burst’ at Mammoth Mountain have practically identical mechanisms that indicate nearly pure compensated tensile failure and high fluid mobility. Five earthquakes had mechanisms involving small volume decreases, but these may not be significant. No mechanisms have volumetric moment fractions larger than that of a force dipole, but the reason for this fact is unknown.

California↗
USGS2003

Three-dimensional crustal structure of Long Valley caldera, California, and evidence for the migration of CO2 under Mammoth Mountain

A temporary network of 69 three-component seismic stations captured a major seismic sequence in Long Valley caldera in 1997. We performed a tomographic inversion for crustal structure beneath a 28 km ?? 16 km area encompassing part of the resurgent dome, the south moat, and Mammoth Mountain. Resolution of crustal structure beneath the center of the study volume was good down to ???3 km below sea level (???5 km below the surface). Relatively high wave speeds are associated with the Bishop Tuff and lower wave speeds characterize debris in the surrounding moat. A low-Vp/Vs anomaly extending from near the surface to ???1 km below sea level beneath Mammoth Mountain may represent a CO2 reservoir that is supplying CO2-rich springs, venting at the surface, and killing trees. We investigated temporal variations in structure beneath Mammoth Mountain by differencing our results with tomographic images obtained using data from 1989/1990. Significant changes in both Vp and Vs were consistent with the migration of CO2 into the upper 2 km or so beneath Mammoth Mountain and its depletion in peripheral volumes that correlate with surface venting areas. Repeat tomography is capable of detecting the migration of gas beneath active silicic volcanoes and may thus provide a useful volcano monitoring tool.

Journal of Geophysical Research B: Solid Earth↗
USGS2002

Imaging the mantle beneath Iceland using integrated seismological techniques

Using a combination of body wave and surface wave data sets to reveal the mantle plume and plume head, this study presents a tomographic image of the mantle structure beneath Iceland to 400 km depth. Data comes primarily from the PASSCAL-HOTSPOT deployment of 30 broadband instruments over a period of 2 years, and is supplemented by data from the SIL and ICEMELT networks. Three sets of relative teleseismic body wave arrival times are generated through cross correlation: S and SKS arrivals at 0.03–0.1 Hz, and P and PKIKP arrivals at 0.03–0.1 and 0.8–2.0 Hz. Prior to inversion the crustal portion of the travel time anomalies is removed using the crustal model ICECRTb. This step has a significant effect on the mantle velocity variations imaged down to a depth of ∼250 km. Inversion of relative arrival times only provides information on lateral velocity variations. Surface waves are therefore used to provide absolute velocity information for the uppermost mantle beneath Iceland. The average wave number for the Love wave fundamental mode at 0.020 and 0.024 Hz is measured and used to invert for the average S velocity. Combination of the body wave and surface wave information reveals a predominantly horizontal low-velocity anomaly extending from the Moho down to ∼250 km depth, interpreted as a plume head. Below the plume head a near-cylindrical low-velocity anomaly with a radius of ∼100 km and peak V P and V S anomalies of −2% and −4%, respectively, extends down to the maximum depth of resolution at 400 km. Within the plume head, in the uppermost mantle above the core of the plume, there is a relatively high velocity with a maximum V P and V S anomaly of +2%. This high-velocity anomaly may be the result of the extreme degree of melt extraction necessary to generate the thick (46 km) crust in central Iceland. Comparison of the plume volumetric flux implied by our images, the crustal generation rate, and the degree of melting suggested by rare earth element inversions, suggests that (1) mantle material must be flowing horizontally away from the plume core faster than the overlying lithosphere and (2) the bulk of the plume material does not participate in melting beneath Iceland.

Journal of Geophysical Research B: Solid Earth↗
USGS2002

Plume-driven plumbing and crustal formation in Iceland

Through combination of surface wave and body wave constraints we derive a three-dimensional (3-D) crustal S velocity model and Moho map for Iceland. It reveals a vast plumbing system feeding mantle plume melt into upper crustal magma chambers where crustal formation takes place. The method is based on the partitioned waveform inversion to which we add additional observations. Love waves from six local events recorded on the HOTSPOT- SIL networks are fitted, S n travel times from the same events measured, previous observations of crustal thickness are added, and all three sets of constraints simultaneously inverted for our 3-D model. In the upper crust (0–15 km) an elongated low-velocity region extends along the length of the Northern, Eastern and Western Neovolcanic Zones. The lowest velocities (−7%) are found at 5–10 km below the two most active volcanic complexes: Hekla and Bárdarbunga-Grímsvötn. In the lower crust (>15 km) the low-velocity region can be represented as a vertical cylinder beneath central Iceland. The low-velocity structure is interpreted as the thermal halo of pipe work which connects the region of melt generation in the uppermost mantle beneath central Iceland to active volcanoes along the neovolcanic zones. Crustal thickness in Iceland varies from 15–20 km beneath the Reykjanes Peninsula, Krafla and the extinct Snæfellsnes rift zone, to 46 km beneath central Iceland. The average crustal thickness is 29 km. The variations in thickness can be explained in terms of the temporal variation in plume productivity over the last ∼20 Myr, the Snæfellsnes rift zone being active during a minimum in plume productivity. Variations in crustal thickness do not depart significantly from an isostatically predicted crustal thickness. The best fit linear isostatic relation implies an average density jump of 4% across the Moho. Rare earth element inversions of basalt compositions on Iceland suggest a melt thickness (i.e., crustal thickness) of 15–20 km, given passive upwelling. The observed crustal thickness of up to 46 km implies active fluxing of source material through the melt zone by the mantle plume at up to 3 times the passive rate.

Journal of Geophysical Research B: Solid Earth↗
USGS2002

Seismic evidence for a tilted mantle plume and north-south mantle flow beneath Iceland

Shear waves converted from compressional waves at mantle discontinuities near 410- and 660-km depth recorded by two broadband seismic experiments in Iceland reveal that the center of an area of anomalously thin mantle transition zone lies at least 100 km south of the upper-mantle low-velocity anomaly imaged tomographically beneath the hotspot. This offset is evidence for a tilted plume conduit in the upper mantle, the result of either northward flow of the Icelandic asthenosphere or southward flow of the upper part of the lower mantle in a no-net-rotation reference frame. ?? 2002 Elsevier Science B.V. All rights reserved.

Earth and Planetary Science Letters↗
USGS2001

Seismic tomography shows that upwelling beneath Iceland is confined to the upper mantle

We report the results of the highest-resolution teleseismic tomography study yet performed of the upper mantle beneath Iceland. The experiment used data gathered by the Iceland Hotspot Project, which operated a 35-station network of continuously recording, digital, broad-band seismometers over all of Iceland 1996-1998. The structure of the upper mantle was determined using the ACH damped least-squares method and involved 42 stations, 3159 P-wave, and 1338 S-wave arrival times, including the phases P, pP, sP, PP, SP, PcP, PKIKP, pPKIKP, S, sS, SS, SKS and Sdiff. Artefacts, both perceptual and parametric, were minimized by well-tested smoothing techniques involving layer thinning and offset-and-averaging. Resolution is good beneath most of Iceland from ??? 60 km depth to a maximum of ??? 450 km depth and beneath the Tjornes Fracture Zone and near-shore parts of the Reykjanes ridge. The results reveal a coherent, negative wave-speed anomaly with a diameter of 200-250 km and anomalies in P-wave speed, Vp, as strong as -2.7 per cent and in S-wave speed, Vs, as strong as -4.9 per cent. The anomaly extends from the surface to the limit of good resolution at ??? 450 km depth. In the upper ??? 250 km it is centred beneath the eastern part of the Middle Volcanic Zone, coincident with the centre of the ??? 100 mGal Bouguer gravity low over Iceland, and a lower crustal low-velocity zone identified by receiver functions. This is probably the true centre of the Iceland hotspot. In the upper ??? 200 km, the low-wave-speed body extends along the Reykjanes ridge but is sharply truncated beneath the Tjornes Fracture Zone. This suggests that material may flow unimpeded along the Reykjanes ridge from beneath Iceland but is blocked beneath the Tjornes Fracture Zone. The magnitudes of the Vp, Vs and Vp/Vs anomalies cannot be explained by elevated temperature alone, but favour a model of maximum temperature anomalies <200 K, along with up to ??? 2 per cent of partial melt in the depth range ??? 100-300 km beneath east-central Iceland. The anomalous body is approximately cylindrical in the top 250 km but tabular in shape at greater depth, elongated north-south and generally underlying the spreading plate boundary. Such a morphological change and its relationship to surface rift zones are predicted to occur in convective upwellings driven by basal heating, passive upwelling in response to plate separation and lateral temperature gradients. Although we cannot resolve structure deeper than ??? 450 km, and do not detect a bottom to the anomaly, these models suggest that it extends no deeper than the mantle transition zone. Such models thus suggest a shallow origin for the Iceland hotspot rather than a deep mantle plume, and imply that the hotspot has been located on the spreading ridge in the centre of the north Atlantic for its entire history, and is not fixed relative to other Atlantic hotspots. The results are consistent with recent, regional full-thickness mantle tomography and whole-mantle tomography images that show a strong, low-wave-speed anomaly beneath the Iceland region that is confined to the upper mantle and thus do not require a plume in the lower mantle. Seismic and geochemical observations that are interpreted as indicating a lower mantle, or core-mantle boundary origin for the North Atlantic Igneous Province and the Iceland hotspot should be re-examined to consider whether they are consistent with upper mantle processes.

Geophysical Journal International↗
USGS2000

Period doubling and other nonlinear phenomena in volcanic earthquakes and tremor

Evidence of subharmonic period-doubling cascades has recently been recognized in seismograms of volcanic tremor from several volcanoes. This phenomenon occurs only in nonlinear systems, and is the commonest route by which such systems change from periodic to chaotic behavior. It is predicted to occur in a model of volcanic tremor excitation by flow-induced vibration, and it might well also occur in other volcano-seismic source process. If the possibility of period doubling is not taken into account in interpreting spectra of tremor and long-period earthquakes, then low-frequency "sub-harmonic" oscillations may be mis-identified as normal modes of a linear acoustic resonator, leading to errors of an order of magnitude or more in inferred magma-body dimensions. This example illustrates the importance of nonlinear phenomena in attempts to understand volcano-seismic phenomena physically. Linear systems are fundamentally incapable of causing earthquakes or exciting tremor, so nonlinearity is essential to any theory of volcano-seismic phenomena. Nonlinear processes are in many respects qualitatively different from linear ones. A few of their characteristics that might be relevant in volcanoes include the possibility: (1) that damping might increase, rather than decrease, oscillation frequencies; and (2) that these frequencies might be functions of the amplitude of oscillation, so that temporal variations in spectral peak frequencies might not be manifestations of changes of conditions within the magmatic system.

Journal of Volcanology and Geothermal Research↗
USGS2000

Constraints on a plume in the mid-mantle beneath the Iceland region from seismic array data

Teleseismic P waves passing through low-wave-speed bodies in the mantle are refracted, causing anomalies in their propagation directions that can be measured by seismometer arrays. Waves from earthquakes in the eastern Pacific and western North America arriving at the NORSAR array in Norway and at seismic stations in Scotland pass beneath the Iceland region at depths of ~ 1000-2000 km. Waves arriving at NORSAR have anomalous arrival azimuths consistent with a low-wave-speed body at a depth of ~ 1500 km beneath the Iceland-Faeroe ridge with a maximum diameter of ~ 250 km and a maximum wave-speed contrast of ~ 1.5 per cent. This agrees well with whole-mantle tomography results, which image a low-wave-speed body at this location with a diameter of ~ 500 km and a wave-speed anomaly of ~ 0.5 per cent, bearing in mind that whole-mantle tomography, because of its limited resolution, broadens and weakens small anomalies. The observations cannot resolve the location of the body, and the anomaly could be caused in whole or in part by larger bodies farther away, for example by a body imaged beneath Greenland by whole-mantle tomography.

Geophysical Journal International↗
USGS2000

A geometricla error in some Computer Programs based on the Aki-Christofferson-Husebye (ACH) Method of Teleseismic Tomography

Some computer programs based on the Aki-Christofferson-Husebye (ACH) method of teleseismic tomography contain an error caused by identifying local grid directions with azimuths on the spherical Earth. This error, which is most severe in high latitudes, introduces systematic errors into computed ray paths and distorts inferred Earth models. It is best dealt with by explicity correcting for the difference between true and grid directions. Methods for computing these directions are presented in this article and are likely to be useful in many other kinds of regional geophysical studies that use Cartesian coordinates and flat-earth approximations.

Bulletin of the Seismological Society of America↗
USGS1999

The thin hot plume beneath Iceland

We present the results of a seismological investigation of the frequency-dependent amplitude variations across Iceland using data from the HOTSPOT array currently deployed there. The array is composed of 30 broad-band PASSCAL instruments. We use the parameter t(*), defined in the usual manner from spectral ratios (Halderman and Davis 1991), to compare observed S-wave amplitude variations with those predicted due to both anelastic attenuation and diffraction effects. Four teleseismic events at a range of azimuths are used to measure t(*). A 2-D vertical cylindrical plume model with a Gaussian-shaped velocity anomaly is used to model the variations. That part of t(*) caused by attenuation was estimated by tracing a ray through IASP91, then superimposing our plume model velocity anomaly and calculating the path integral of 1/vQ. That part of t(*) caused by diffraction was estimated using a 2-D finite difference code to generate synthetic seismograms. The same spectral ratio technique used for the data was then used to extract a predicted t(*). The t(*) variations caused by anelastic attenuation are unable to account for the variations we observe, but those caused by diffraction do. We calculate the t(*) variations caused by diffraction for different plume models and obtain our best-fit plume, which exhibits good agreement between the observed and measured t(*). The best-fit plume model has a maximum S-velocity anomaly of - 12 per cent and falls to 1/e of its maximum at 100 km from the plume centre. This is narrower than previous estimates from seismic tomography, which are broadened and damped by the methods of tomography. This velocity model would suggest greater ray theoretical traveltime delays than observed. However, we find that for such a plume, wave-front healing effects at frequencies of 0.03-0.175 Hz (the frequency range used to pick S-wave arrivals) causes a 40 per cent reduction in traveltime delay, reducing the ray theoretical delay to that observed.

Geophysical Journal International↗
USGS1999

Source processes of industrially-induced earthquakes at the Geysers geothermal area, California

Microearthquake activity at The Geysers geothermal area, California, mirrors the steam production rate, suggesting that the earthquakes are industrially induced. A 15-station network of digital, three-component seismic stations was operated for one month in 1991, and 3,900 earthquakes were recorded. Highly-accurate moment tensors were derived for 30 of the best recorded earthquakes by tracing rays through tomographically derived 3-D VP and VP / VS structures, and inverting P-and S-wave polarities and amplitude ratios. The orientations of the P-and T-axes are very scattered, suggesting that there is no strong, systematic deviatoric stress field in the reservoir, which could explain why the earthquakes are not large. Most of the events had significant non-double-couple (non-DC) components in their source mechanisms with volumetric components up to ???30% of the total moment. Explosive and implosive sources were observed in approximately equal numbers, and must be caused by cavity creation (or expansion) and collapse. It is likely that there is a causal relationship between these processes and fluid reinjection and steam withdrawal. Compensated linear vector dipole (CLVD) components were up to 100% of the deviatoric component. Combinations of opening cracks and shear faults cannot explain all the observations, and rapid fluid flow may also be involved. The pattern of non-DC failure at The Geysers contrasts with that of the Hengill-Grensdalur area in Iceland, a largely unexploited water-dominated field in an extensional stress regime. These differences are poorly understood but may be linked to the contrasting regional stress regimes and the industrial exploitation at The Geysers.

Geophysics↗
USGS1998

Non-double-couple earthquakes. 1. Theory

Historically, most quantitative seismological analyses have been based on the assumption that earthquakes are caused by shear faulting, for which the equivalent force system in an isotropic medium is a pair of force couples with no net torque (a “double couple,” or DC). Observations of increasing quality and coverage, however, now resolve departures from the DC model for many earthquakes and find some earthquakes, especially in volcanic and geothermal areas, that have strongly non-DC mechanisms. Understanding non-DC earthquakes is important both for studying the process of faulting in detail and for identifying nonshear-faulting processes that apparently occur in some earthquakes. This paper summarizes the theory of “moment tensor” expansions of equivalent-force systems and analyzes many possible physical non-DC earthquake processes. Contrary to long-standing assumption, sources within the Earth can sometimes have net force and torque components, described by first-rank and asymmetric second-rank moment tensors, which must be included in analyses of landslides and some volcanic phenomena. Non-DC processes that lead to conventional (symmetric second-rank) moment tensors include geometrically complex shear faulting, tensile faulting, shear faulting in an anisotropic medium, shear faulting in a heterogeneous region (e.g., near an interface), and polymorphic phase transformations. Undoubtedly, many non-DC earthquake processes remain to be discovered. Progress will be facilitated by experimental studies that use wave amplitudes, amplitude ratios, and complete waveforms in addition to wave polarities and thus avoid arbitrary assumptions such as the absence of volume changes or the temporal similarity of different moment tensor components.

Reviews of Geophysics↗
USGS1998

Non-double-couple earthquakes 2. Observations

Most studies assume that earthquakes have double-couple (DC) source mechanisms, corresponding to shear motion on planar faults. However, many well-recorded earthquakes have radiation patterns that depart radically from this model, indicating fundamentally different source processes. Seismic waves excited by advective processes, such as landslides and volcanic eruptions, are consistent with net forces rather than DCs. Some volcanic earthquakes also have single-force mechanisms, probably because of advection of magmatic fluids. Other volcanic earthquakes have mechanisms close to compensated linear vector dipoles and may be caused by magmatic intrusions. Shallow earthquakes in volcanic or geothermal areas and mines often have mechanisms with isotropic components, indicating volume changes of either explosive or implosive polarity. Such mechanisms are consistent with failure involving both shear and tensile faulting, which may be facilitated by high-pressure, high-temperature fluids. In mines, tunnels are cavities that may close. Deep-focus earthquakes occur within zones of polymorphic phase transformations in the upper mantle at depths where stick-slip instability cannot occur. Their mechanisms tend to be deviatoric (volume conserving), but non-DC, and their source processes are poorly understood. Automatic global moment tensor services routinely report statistically significant non-DC components for large earthquakes, but detailed reexamination of individual events is required to confirm such results.

Reviews of Geophysics↗
USGS1998

Three-dimensional seismic structure and moment tensors of non-double-couple earthquakes at the Hengill-Grensdalur volcanic complex, Iceland

The volcanic and geothermal areas of Iceland are rich sources of non-double-couple (non-DC) earthquakes. A state-of-the-art digital seismometer network deployed at the Hengill–Grensdalur volcanic complex in 1991 recorded 4000 small earthquakes. We used the best recorded of these to determine 3-D V P and V P /V S structure tomographically and accurate earthquake moment tensors. The V P field is dominated by high seismic wave speed bodies interpreted as solidified intrusions. A widespread negative (−4 per cent) V P /V S anomaly in the upper 4km correlates with the geothermal field, but is too strong to be caused solely by the effect of temperature upon liquid water or the presence of vapour, and requires in addition mineralogical or lithological differences between the geothermal reservoir and its surroundings. These may be caused by geothermal alteration. Well-constrained moment tensors were obtained for 70 of the best-recorded events by applying linear programming methods to P - and S -wave polarities and amplitude ratios. About 25 per cent of the mechanisms are, within observational error, consistent with DC mechanisms consistent with shear faulting. The other 75 per cent have significantly non-DC mechanisms. Many have substantial explosive components, one has a substantial implosive component, and the deviatoric component of many is strongly non-DC. Many of the non-DC mechanisms are consistent, within observational error, with simultaneous tensile and shear faulting. However, the mechanisms occupy a continuum in source-type parameter space and probably at least one additional source process is occurring. This may be fluid flow into newly formed cracks, causing partial compensation of the volumetric component. Studying non-shear earthquakes such as these has great potential for improving our understanding of geothermal processes and earthquake source processes in general.

Geophysical Journal International↗