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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:24:22 +0000Melt Segregation from Partially Molten Source Regions: The Importance of Melt Density and Source Region Size
https://resolver.caltech.edu/CaltechAUTHORS:20120821-160724340
Authors: Stolper, Edward; Walker, David; Hager, Bradford H.; Hays, James F.
Year: 1981
DOI: 10.1029/JB086iB07p06261
The compressibility of basic melt at 1 atmosphere is about an order of magnitude higher than that of mantle minerals. Consequently, the density contrast between melt and the principal residual crystals in mantle source regions is expected to decrease with increasing source region depth. The increasingly olivine-normative character of primary melts produced at greater depths is also expected to result in a decrease in this density contrast with increasing source region depth. Once vertical permeability is established by melt generated during partial melting, buoyancy-driven melt percolation can under some circumstances segregate melt from the residual crystals in its source region on a geologically rapid time scale. Limits to this process are provided by cooling of the source region (freezing melt in) and rigidity of the crystalline matrix (mechanically trapping melt). Source region size influences these limits strongly: consequently, small, partially molten diapirs (∼km in diameter) may be able to trap large melt fractions (≳30%), but larger source regions would be unable to do so. The reduction in density contrast with pressure reduces the buoyant force driving melt percolation and provides another limit to melt segregation. Diapirs at depth may thus stably contain large fractions of melt but may decompress and unload their melt during ascent; this effect would be enhanced in small diapirs and may be relevant to the genesis of komatiitic magma. Melt compression may also be a factor in explaining why the very different maximum depths inferred for typical basic melt segregation from source regions on different planets—∼500 km on the moon, ∼250 km on Mars, ∼100 km on earth—correspond to similar pressures (25–35 kbar); at greater pressures, melt may no longer be capable under ordinary conditions of segregating upwards by buoyancy. This may also help to explain why depleted peridotites overlie more fertile peridotites and how deep regions of the mantle are able to remain fertile over geologic time.https://authors.library.caltech.edu/records/v7cwm-jaa45Global isostatic geoid anomalies for plate and boundary layer models of the lithosphere
https://resolver.caltech.edu/CaltechAUTHORS:20180125-135055796
Authors: Hager, Bradford H.
Year: 1983
DOI: 10.1016/0012-821X(83)90025-0
Isostatic geoid anomalies are usually interpreted using a flat-earth, one-dimensional idealization. Isostatic anomalies on the spherical, self-gravitating earth differ from this idealization because: (1) degree one terms in the spherical harmonic expansion vanish; (2) each term in the spherical harmonic expansion is multiplied by (l + 2)/(l + 0.5) relative to the flat-earth case; (3) mass in cones rather than straight-sided columns is constant; and (4) further deformation of the earth is induced by the gravitational attraction of the deformation caused by the isostatic potential anomaly. When the effect of each of these is quantified, the second, third, and fourth nearly cancel, leaving the degree one, "over the horizon" effect providing the most important difference. Calculations of model isostatic geoid anomalies for the spherical analogues (developed here) of the plate and boundary layer thermal models show that this effect can bias estimates of geoid slopes by over 20%, although the effect is usually less than 5%. The geoid anomalies for these two models are quite different over old ocean basins, but they are unlikely to be distinguishable on the basis of global geoid observations owing to the presence of other larger perturbations in the geoid. Stripping the effects of plate aging and a hypothetical uniform, 35 km thick, isostatically-compensated continental crust from the observed geoid emphasizes that the largest-amplitude geoid anomaly is the geoid low of almost 120 m over West Antarctica. This anomaly is a factor of two greater in amplitude than the low of 60 m over Sri Lanka.https://authors.library.caltech.edu/records/3bm1w-zv286Subduction, back-arc spreading and global mantle flow
https://resolver.caltech.edu/CaltechAUTHORS:20171120-155732622
Authors: Hager, Bradford H.; O'Connell, Richard J.; Raefsky, Arthur
Year: 1983
DOI: 10.1016/0040-1951(83)90101-4
The shapes and orientations of Benioff zones beneath island arcs, interpreted as marking the location of subducted lithosphere, provide the best presently available constraints on the global convective flow pattern associated with plate motions. This global flow influences the dynamics of subduction. Subduction zone phenomena therefore provide powerful tests for models of mantle flow. We compute global flow models which, while simple, include those features which are best constrained, namely the observed plate velocities, applied as boundary conditions, and the density contrasts given by thermal models of the lithosphere and subducted slabs. Two viscosity structures are used; for one, flow is confined to the upper mantle, while for the other, flow extends throughout the mantle.
Instantaneous flow velocity vectors match observed Benioff zone dips and shapes for the model which allows mantle-wide flow but not for the upper mantle model, which has a highly contorted flow pattern. The effect of trench migration on particle trajectories is calculated; it is not important if subduction velocities are greater than migration rates. Two-dimensional finite element models show that including a coherent high viscosity slab does not change these conclusions. A coherent high viscosity slab extending deep into the upper mantle would significantly slow subduction if flow were confined to the upper mantle. The maximum earthquake magnitude, M_w, for island arcs correlates well with the age of the subducted slab and pressure gradient between the trench and back-arc region for the whole mantle, but not the upper mantle, flow model. The correlations with orientations of Benioff zones and seismic coupling strongly suggest that the global return flow associated with plate motions extends below 700 km. For both models, regions of back-arc spreading have asthenospheric shear pulling the back-arc toward the trench; regions without back-arc spreading have the opposite sense of shear, suggesting global flow strongly influences back-arc spreading.https://authors.library.caltech.edu/records/tsehr-2bf70Convection experiments in a centrifuge and the generation of plumes in a very viscous fluid
https://resolver.caltech.edu/CaltechAUTHORS:20141112-120154248
Authors: Nataf, H.-C; Hager, B. H.; Scott, R. F.
Year: 1984
«Plumes» originating from unstable· thermal boundary layers have been proposed to be the preferred mode of small-scale convection in the Earth's mantle. However, doubts have been cast on the validity of the extrapolation from laboratory to mantle-like conditions. In particular, it was feared that inertial effects might be the origin of the observed instabilities. In this paper, experiments are described fbr which inertial effects are negligible. A small aspect-ratio tank filled with a very viscous fluid (Pr = 106) is used to observe the behaviour of convection for Rayleigh numbers up to 6.3 x 10^5. These high values are reached by conducting the experiment in a centrifuge which provides a 130-fold increase in apparent gravity. Rotational effects are small, but cannot be totally dismissed In this geometry thermal boundary layer instabilities are indeed observed, and are found to be very similar to their lower Prandtl number counterparts. It is tentatively concluded that once given a certain degree of «vulnerability», convection can develop «plume»-like instabilities, even when the Prandtl number is infinite. The concept is applied to the earth's mantle and it is speculated that «plumes» could well be the dominant mode of small-scale convection under the lithospheric plates.https://authors.library.caltech.edu/records/c2jyf-tmc35A tomographic image of mantle structure beneath Southern California
https://resolver.caltech.edu/CaltechAUTHORS:20121017-115856637
Authors: Humphreys, Eugene; Clayton, Robert W.; Hager, Bradford H.
Year: 1984
DOI: 10.1029/GL011i007p00625
We determined the variations in seismic structure beneath southern California by using a tomographic method of inversion on teleseismic P delays recorded with the Southern California Array. The algorithm employed was a modified form of an Algebraic Reconstruction Technique (ART) used in medical X‐ray imaging. Deconvolution with an empirically estimated point spread function was also used to help in focusing the image.
The inversion reveals two prominent features beneath the region. The first is a thin, vertical wedge directly beneath the Transverse Ranges that is 2‐3% faster than the surrounding region. This feature deepens to the east, attaining a maximum depth of about 250 km beneath the San Bernardino Mountains. The second feature is a major zone of low velocity material that is 2‐4% slow under the Salton Trough rift valley, extending to a depth of about 125 km. Two possible explanations for the spatial association of the Transverse Ranges with the velocity anomaly below are lithospheric subduction or small‐scale sublithospheric convection in the region of the Big Bend of the San Andreas Fault. The low velocity anomaly beneath the Salton Trough is consistent with convective upwelling there.https://authors.library.caltech.edu/records/qcsec-hfg47Lower mantle heterogeneity, dynamic topography and the geoid
https://resolver.caltech.edu/CaltechAUTHORS:20121018-093742377
Authors: Hager, Bradford H.; Clayton, Robert W.; Richards, Mark A.; Comer, Robert P.; Dziewonski, Adam M.
Year: 1985
DOI: 10.1038/313541a0
Density contrasts in the lower mantle, inferred using seismic tomography, drive viscous flow; this results in kilometres of dynamically maintained topography at the core-mantle boundary and at the Earth's surface. The total gravity field due to interior density contrasts and dynamic boundary topography predicts the longest-wavelength components of the geoid remarkably well. Neglecting dynamic surface deformation leads to geoid anomalies of opposite sign to those observed.https://authors.library.caltech.edu/records/wg7d6-wrg54Mantle convection and the state of the Earth's interior
https://resolver.caltech.edu/CaltechAUTHORS:20130130-140422875
Authors: Hager, Bradford H.; Gurnis, Michael
Year: 1987
DOI: 10.1029/RG025i006p01277
During 1983–1986, the four year period covered by this review, emphasis in the study of mantle convection shifted away from fluid mechanical analysis of simple systems with uniform material properties and simple geometries, toward analyzing the effects of more complicated, presumably more realistic models.https://authors.library.caltech.edu/records/r7rtn-0dg02Finite Element Solution of Thermal Convection On A Hypercube
Concurrent Computer
https://resolver.caltech.edu/CaltechAUTHORS:20121119-131724167
Authors: Gurnis, Michael; Raefsky, Arthur; Lyzenga, Gregory A.; Hager, Bradford H.
Year: 1988
DOI: 10.1145/63047.63070
Numerical solutions to thermal convection flow problems
are vital to many scientific and engineering problems.
One fundamental geophysical problem is the thermal convection
responsible for continental drift and sea floor
spreading. The earth's interior undergoes slow creeping
flow (~cm/yr) in response to the buoyancy forces generated
by temperature variations caused by the decay of
radioactive elements and secular cooling. Convection in
the earth's mantle, the 3000 km thick solid layer between
the crust and core, is difficult to model for three reasons:
(1) Complex rheology -- the effective viscosity depends
exponentially on temperature, on pressure (or depth) and
on the deviatoric stress; (2) the buoyancy forces driving
the flow occur in boundary layers thin in comparison to the
total depth; and (3) spherical geometry -- the flow in the
interior is fully three dimensional. Because of these many
difficulties, accurate and realistic simulations of this process
easily overwhelm current computer speed and memory
(including the Cray XMP and Cray 2) and only simplified
problems have been attempted [e.g. Christensen and
Yuen, 1984; Gurnis, 1988; Jarvis and Peltier, 1982].
As a start in overcoming these difficulties, a number of
finite element formulations have been explored on hypercube
concurrent computers. Although two coupled equations
are required to solve this problem (the momentum
or Stokes equation and the energy or advection-diffusion
equation), we will concentrate our efforts on the solution
to the latter equation in this paper. Solution of the former
equation is discussed elsewhere [Lyzenga, et al, 1988].
We will demonstrate that linear speedups and efficiencies
of 99 percent are achieved for sufficiently large problems.https://authors.library.caltech.edu/records/rke4a-npe19Subduction zone earthquakes and stress in slabs
https://resolver.caltech.edu/CaltechAUTHORS:20190214-143453542
Authors: Vassiliou, M. S.; Hager, B. H.
Year: 1988
DOI: 10.1007/BF00874550
The pattern of seismicity as a function of depth in the world, and the orientation of stress axes of deep and intermediate earthquakes, are explained using viscous fluid models of subducting slabs, with a barrier in the mantle at 670 km. 670 km is the depth of a seismic discontinuity, and also the depth below which earthquakes do not occur. The barrier in the models can be a viscosity increase of an order of magnitude or more, or a chemical discontinuity where vertical velocity is zero. LongN versus depth, whereN is the number of earthquakes, shows (1) a linear decrease to about 250–300 km depth, (2) a minimum near that depth, and (3) an increase thereafter. Stress magnitude in a subducting slab versus depth, for a wide variety of models, shows the same pattern. Since there is some experimental evidence thatN is proportional toeκσ, where κ is a constant and σ is the stress magnitude, the agreement is encouraging. In addition, the models predict down-dip compression in the slab at depths below 400 km. This has been observed in earlier studies of earthquake stress axes, and we have confirmed it via a survey of events occurring since 1977 which have been analysed by moment tensor inversion. At intermediate depths, the models predict an approximate but not precise state of down-dip tension when the slab is dipping. The observations do not show an unambiguous state of down-dip tension at intermediate depths, but in the majority of regions the state of stress is decidedly closer to down-dip tension than it is to down-dip compression. Chemical discontinuities above 670 km, or phase transitions with an elevation of the boundary in the slab, predict, when incorporated into the models, stress peaks which are not mirrored in the profile of seismicity versus depth. Models with an asthenosphere and mesosphere of appropriate viscosity can not only explain the state of stress observed in double Benioff zones, but also yield stress magnitude profiles consistent with observed seismicity. Models where a nonlinear rheology is used are qualitatively consistent with the linear models.https://authors.library.caltech.edu/records/n0mjd-we356Controls of the structure of subducted slabs
https://resolver.caltech.edu/CaltechAUTHORS:20130305-082158626
Authors: Gurnis, Michael; Hager, Bradford H.
Year: 1988
DOI: 10.1038/335317a0
Numerical simulations of subducting slabs are formulated in which the shape and dip of the slab are determined by the dynamics of the flow, rather than imposed a priori. The dip of slabs is a function of the time since the initiation of subduction. Slabs fold, develop a kink in dip, and thicken on entry into a high-viscosity lower mantle. Comparison of the simulations with seismic observations suggest that the lower mantle is at least 10–30 times more viscous than the upper mantle.https://authors.library.caltech.edu/records/60wq0-v6823Constraints on the Structure of Mantle Convection Using Seismic Observations, Flow Models, and the Geoid
https://resolver.caltech.edu/CaltechAUTHORS:20121002-141328164
Authors: Hager, Bradford H.; Clayton, Robert W.
Year: 1989
The establishment of the theory of plate tectonics in the late 1960s has left
little doubt that the mantle is convecting. The plates themselves form the cold
upper thermal boundary layer of the mantle convection system; the cooling of
oceanic plates as they move away from midoceanic ridges provides the
mechanism by which the Earth loses most of its heat (e.g., Sclater et al.,
1980; O'Connell and Hager, 1980). The mantle is in turn cooled by the cold
slabs that plunge into Earth's interior at subduction zones.
Although plate tectonics implies that convective motions in the mantle are
the dominant mechanism for heat transport, and we can measure the surface
motions associated with it, we are remarkably ignorant of even the gross
features of the interior flow field associated with this mantle circulation. Only
at subduction zones, where seismicity presumably marks the particle trajectories
of the cold descending boundary layer, do we have direct evidence for
the interior flow pattern and state of stress. Most of what is understood, or
thought to be understood, about convection in the Earth's interior is based on
comparison of simplified models to observations taken at the surface.
Examples of these models of mantle convection are given in the other
chapters of this book, as well as in the general geophysical literature. These
include studies of convection in media with uniform rheology (Busse, this
volume; Jarvis and Peltier, this volume), interpretation of travel time anomalies
from deep earthquakes in terms of simple thermal models of subducted
slabs (Jordan eta!., this volume), interpretation of geochemical anomalies in
terms of models of the distribution of mantle heterogeneities (Hart and
Zindler, this volume), and interpretation of changes in the Earth's shape and
rotational parameters in terms of models of mantle rheology (Peltier, this
volume).
In order to be useful, models must be simple enough to understand, and
yet contain enough of the essential physics to be applicable. The line
between oversimplification and overwhelming complexity is a fine one, and
its positioning is a matter of subjective judgement, particularly when some
observations have a fairly small signal to noise ratio. The ultimate test of a
particular model is whether it can satisfy, within their uncertainties, the
observations. If it cannot it must be rejected, although unfortunately, the
converse is not true. The more types of observations a model can satisfy,
however, the more likely it is to be correct.https://authors.library.caltech.edu/records/n21w7-jrw19Long-wavelength variations in Earth's geoid: physical models and dynamical implications
https://resolver.caltech.edu/CaltechAUTHORS:20141113-131525233
Authors: Hager, B. H.; Richards, M. A.
Year: 1989
DOI: 10.1098/rsta.1989.0038
The seismic velocity anomalies resolved by seismic tomography are associated with variations in density that lead to convective flow and to dynamically maintained topography at the Earth's surface, the core--mantle boundary (CMB), and any interior chemical boundaries that might exist. The dynamic topography resulting from a given density field is very sensitive to viscosity structure and to chemical stratification. The mass anomalies resulting from dynamic topography have a major effect on the geoid, which places strong constraints on mantle structure. Almost 90% of the observed geoid can be explained by density anomalies inferred from tomography and a model of subducted slabs, along with the resulting dynamic topography predicted for an Earth model with a low-viscosity asthenosphere (ca. 10^(20) Pa s) overlying a moderate viscosity (ca. 10^(22.5) Pa s) lower mantle. This viscosity stratification would lead to rapid mixing in the asthenosphere, with little mixing in the lower mantle. Chemically stratified models can also explain the geoid, but they predict hundreds of kilometres of dynamic topography at the 670 km discontinuity, a prediction currently unsupported by observation. A low-viscosity or chemically distinct D" layer tends to decouple CMB topography from convective circulation in the overlying mantle. Dynamic topography at the surface should result in long-term changes in eustatic sea level.https://authors.library.caltech.edu/records/x9acw-df593Long-wavelength variations in Earth's geoid: physical models and dynamical implications
https://resolver.caltech.edu/CaltechAUTHORS:20200929-143507118
Authors: Hager, B. H.; Richards, M. A.
Year: 1989
DOI: 10.1098/rsta.1989.0038
The seismic velocity anomalies resolved by seismic tomography are associated with variations in density that lead to convective flow and to dynamically maintained topography at the Earth's surface, the core-mantle boundary (CMB), and any interior chemical boundaries that might exist. The dynamic topography resulting from a given density field is very sensitive to viscosity structure and to chemical stratification. The mass anomalies resulting from dynamic topography have a major effect on the geoid, which places strong constraints on mantle structure. Almost 90% of the observed geoid can be explained by density anomalies inferred from tomography and a model of subducted slabs, along with the resulting dynamic topography predicted for an Earth model with a low-viscosity asthenosphere (ca. 10²⁰ Pa s) overlying a moderate viscosity (ca. 10^(22.5) Pa s) lower mantle. This viscosity stratification would lead to rapid mixing in the asthenosphere, with little mixing in the lower mantle. Chemically stratified models can also explain the geoid, but they predict hundreds of kilometres of dynamic topography at the 670 km discontinuity, a prediction currently unsupported by observation. A low-viscosity or chemically distinct D" layer tends to decouple CMB topography from convective circulation in the overlying mantle. Dynamic topography at the surface should result in long-term changes in eustatic sea level.https://authors.library.caltech.edu/records/5f6n9-beq92Short-term earthquake hazard assessment for the San Andreas Fault in southern California
https://resolver.caltech.edu/CaltechAUTHORS:20141029-154001569
Authors: Jones, Lucile M.; Sieh, Kerry; Agnew, Duncan; Allen, Clarence; Bilham, Roger; Ghilarducci, Mark; Hager, Bradford; Hauksson, Egill; Hudnut, Kenneth; Jackson, David D.; Sylvester, Arthur; Aki, Keiti; Wyatt, Frank
Year: 1991
The southernmost 200 km of the San Andreas fault in California, from Cajon Pass
southeast to Bombay Beach on the Salton Sea (Figure 1), has not produced a major earthquake
within the historic record. Both geodetic evidence of continuing strain accumulation (Savage et al,
1986) and the occurrence of recent prehistoric large earthquakes (Sieh, 1986; Sieh and Williams,
1990), however, lead us to conclude that this fault segment will eventually produce great
earthquakes that pose one of the greatest hazards to southern California. An estimated 1.0-1.5
million people now live adjacent to the San Andreas fault within the projected zone of severe
shaking for such an earthquake. A magnitude 7.5 to 8.0 earthquake on this segment would also
cause widespread damage to San Bernardino, Imperial, Riverside, Orange, and Los Angeles
counties, which together have over 12 million inhabitants. For these reasons, the Southern San
Andreas Fault Working Group was formed in 1989 to recommend how the scientific community
might best respond to anomalous geophysical activity along the fault, increase our understanding
of regional seismotectonics, and offer timely scientific advice to state and local governments.https://authors.library.caltech.edu/records/r74hf-x7r36Plains Tectonism on Venus: The Deformation Belts of Lavinia Planitia
https://resolver.caltech.edu/CaltechAUTHORS:20140312-112008370
Authors: Squyres, Steven W.; Jankowski, David G.; Simons, Mark; Solomon, Sean C.; Hager, Bradford H.; McGill, George E.
Year: 1992
DOI: 10.1029/92JE00481
High-resolution radar images from the Magellan spacecraft have revealed the first details of the morphology of the Lavinia Planitia region of Venus. A number of geologic units can be distinguished, including volcanic plains units with a range of ages. Transecting these plains over much of the Lavinia region are two types of generally orthogonal features that we interpret to be compressional wrinkle ridges and extensional grooves. The dominant tectonic features of Lavinia are broad elevated belts of intense deformation that transect the plains with complex geometry. They are many tens to a few hundred kilometers wide, as much as 1000 km long, and elevated hundreds of meters above the surrounding plains. Two classes of deformation belts are seen in the Lavinia region. "Ridge belts" are composed of parallel ridges, each a few hundred meters in elevation, that we interpret to be folds. Typical fold spacings are 5–10 km. "Fracture belts" are dominated instead by intense faulting, with faults in some instances paired to form narrow grabens. There is also some evidence for modest amounts of horizontal shear distributed across both ridge and fracture belts. Crosscutting relationships among the belts show there to be a range in belt ages. In western Lavinia in particular, many ridge and fracture belts appear to bear a relationship to the much smaller wrinkle ridges and grooves on the surrounding plains: Ridge morphology tends to dominate belts that lie more nearly parallel to local plains wrinkle ridges, and fracture morphology tends to dominate belts that lie more nearly parallel to local plains grooves. We use simple models to explore the formation of ridge and fracture belts. We show that convective motions in the mantle can couple to the crust to cause horizontal stresses of a magnitude sufficient to induce the formation of deformation belts like those observed in Lavinia. We also use the small-scale wavelengths of deformation observed within individual ridge belts to place an approximate lower limit on the venusian thermal gradient in the Lavinia region at the time of deformation.https://authors.library.caltech.edu/records/bkf1g-3z419Topographic Core-Mantle Coupling and Fluctuations in the Earth's Rotation
https://resolver.caltech.edu/CaltechAUTHORS:20121016-145941398
Authors: Hide, R.; Clayton, R. W.; Hager, B. H.; Spieth, M. A.; Voorhdes, C. V.
Year: 1993
DOI: 10.1029/GM076p0107
Astronomically-determined irregular fluctuations in the Earth's rotation vector on decadal time scales can be used to estimate the fluctuating torque on the lower surface of the Earth's mantle produced by magnetohydrodynamic flow in the underlying liquid metallic core. A method has been proposed for testing the hypothesis that the torque is due primarily to fluctuating dynamic pressure forces acting on irregular topographic features of the core-mantle boundary and also on the equatorial bulge. The method exploits (a) geostrophically-constrained models of fluid motions in the upper reaches of the core based on geomagnetic secular variation data, and (b) patterns of the topography of the CMB based on the mantle flow models constrained by data from seismic tomography, determinations of long wave-length anomalies of the Earth's gravitational field and other geophysical and geodetic data. According to the present study, the magnitude of the axial component of the torque implied by determinations of irregular changes in the length of the day is compatible with models of the Earth's deep interior characterized by the presence of irregular CMB topography of effective "height" no more than about 0.5 km (about 6% of the equatorial bulge) and strong horizontal variations in the properties of the D″ layer at the base of the mantle. The investigation is now being extended to cover a wider range of epochs and also the case of polar motion on decadal time scales produced by fluctuations in the equatorial components of the torque.https://authors.library.caltech.edu/records/k00cv-6cf89Global Variations in the Geoid/Topography Admittance of Venus
https://resolver.caltech.edu/CaltechAUTHORS:20130605-143623453
Authors: Simons, Mark; Hager, Bradford H.; Solomon, Sean C.
Year: 1994
DOI: 10.1126/science.264.5160.798
Global representations of geoid height and topography are used to map variations in the geoid/topography ratio (admittance) of Venus. The admittance values are permissive of two mutually exclusive models for convection-driven topography. In the first, compressive highland plateaus are expressions of present mantle downwelling, broad volcanic rises are expressions of mantle upwelling, and lowlands overlie regions with no substantial vertical motion in the mantle. In the second, compressive highland plateaus are remnants of an earlier regime of high crustal strain, and most other long-wavelength topographic variations arise from normal convective tractions at the base of the lithosphere.https://authors.library.caltech.edu/records/p796e-tvd04Co-Seismic Displacements of the 1994 Northridge, California, Earthquake
https://resolver.caltech.edu/CaltechAUTHORS:20140805-154226754
Authors: Hudnut, K. W.; Shen, Z.; Murray, M.; McClusky, S.; King, R.; Herring, T.; Hager, B. H.; Feng, Y.; Fang, P.; Donnellan, A.; Bock, Y.
Year: 1996
The 17 January 1994 Northridge, California, earthquake significantly deformed the Earth's crust in the epicentral region. Displacements of 66 survey stations determined from Global Positioning System (GPS) observations collected before and after the earthquake show that individual stations were uplifted by up to 417 ± 5 mm and displaced horizontally by up to 216 ± 3 mm. Using these displacements, we estimate parameters of a uniform-slip model. Fault geometry and slip are estimated independent of seismological information, using Monte Carlo optimization techniques that minimize the model residuals. The plane that best fits the geodetic data lies 1 to 2 km above the plane indicated by aftershock seismicity. Modeling for distributed slip on a coplanar, yet larger model fault indicates that a high-slip patch occurred up-dip and northwest of the mainshock hypocenter and that less than 1 m of slip occurred in the uppermost 5 km of the crust. This finding is consistent with the lack of clear surface rupture and with the notion that the intersection with the fault that ruptured in 1971 formed the up-dip terminus of slip in the Northridge earthquake. Displacements predicted by either of these simple models explain most of the variance in the data within 50 km of the epicenter. On average, however, the scatter of the residuals is twice the data uncertainties, and in some areas, there is significant systematic misfit to either model. The co-seismic contributions of aftershocks are insufficient to explain this mismatch, indicating that the source geometry is more complicated than a single rectangular plane.https://authors.library.caltech.edu/records/43w2e-vwv80Localization of gravity and topography: constraints on the tectonics and mantle dynamics of Venus
https://resolver.caltech.edu/CaltechAUTHORS:20130710-142207254
Authors: Simons, Mark; Solomon, Sean C.; Hager, Bradford H.
Year: 1997
DOI: 10.1111/j.1365-246X.1997.tb00593.x
We develop a method for spatio-spectral localization of harmonic data on a sphere and use it to interpret recent high-resolution global estimates of the gravity and topography of Venus in the context of geodynamical models. Our approach applies equally to the simple spatial windowing of harmonic data and to variable-length-scale analyses, which are analogous to a wavelet transform in the Cartesian domain. Using the variable-length-scale approach, we calculate the localized RMS amplitudes of gravity and topography, as well as the spectral admittance between the two fields, as functions of position and wavelength. The observed admittances over 10 per cent of the surface of Venus (highland plateaus and tessera regions) are consistent with isostatic compensation of topography by variations in crustal thickness, while admittances over the remaining 90 per cent of the surface (rises, plains and lowlands) indicate that long-wavelength topography is dominantly the result of vertical convective tractions at the base of the lithosphere. The global average crustal thickness is less than 30 km, but can reach values as large as 40 km beneath tesserae and highland plateaus. We also note that an Earth-like radial viscosity structure cannot be rejected by the gravity and topography data and that, without a mechanical model of the lithosphere, admittance values cannot constrain the thickness of the thermal boundary layer of Venus. Modelling the lithosphere as a thin elastic plate indicates that at the time of formation of relief in highland plateaus and tesserae, the effective elastic plate thickness, T_e, was less than 20 km. Estimates of T_e at highland rises are consistently less than 30 km. Our inability to find regions with T_e > 30 km is inconsistent with predictions made by a class of catastrophic resurfacing models.https://authors.library.caltech.edu/records/x026c-jmj15Localization of the gravity field and the signature of glacial rebound
https://resolver.caltech.edu/CaltechAUTHORS:20130610-102157743
Authors: Simons, Mark; Hager, Bradford H.
Year: 1997
DOI: 10.1038/37339
The negative free-air gravity anomaly centred on Hudson Bay, Canada, shows a remarkable correlation with the location of the Laurentide ice sheet, suggesting that this gravity anomaly is the result of incomplete post-glacial rebound. This region, however, is also underlain by higher-than-average mantle seismic velocities, suggesting that the gravity low might result instead from dynamic topography associated with convective downwellings. Here we analyse the global gravity field as a simultaneous function of geographic location and spectral content. We find that the Hudson Bay gravity low is unique, with anomalously high amplitude in the spectral band where the power from the Laurentide ice load is greatest and the relaxation times predicted for viable models of viscous relaxation are longest. We estimate that about half of the Hudson Bay gravity anomaly is the result of incomplete post-glacial rebound, and derive a mantle viscosity model that explains both this gravity signature and the characteristic uplift rates for the central Laurentide and Fennoscandian regions. This model has a jump in viscosity at 670 km depth, comparable to that in dynamic models of the geoid highs over subducted slabs, but lacks a low-viscosity asthenosphere, consistent with a higher viscosity in the upper mantle beneath shields than in oceanic regions.https://authors.library.caltech.edu/records/1xfmj-ywq45Mantle convection with strong subduction zones
https://resolver.caltech.edu/CaltechAUTHORS:20170420-082811114
Authors: Conrad, Clinton P.; Hager, Bradford H.
Year: 2001
DOI: 10.1046/j.1365-246x.2001.00321.x
Because mantle viscosity is temperature‐dependent, cold subducting lithosphere should be strong, which implies that the rapid, localized deformation associated with subduction should strongly resist plate motions. Due to computational constraints, the deformation of a subducting plate cannot be accurately resolved in mantle‐scale convection models, so its effect on convection is difficult to investigate. We have developed a new method for implementing subduction that parametrizes the deformation of the oceanic lithosphere within a small region of a finite element grid. By imposing velocity boundary conditions in the vicinity of the subduction zone, we enforce a geometry for subduction, producing a slab with a realistic thermal structure. To make the model dynamically consistent, we specify a rate for subduction that balances the energy budget for convection, which includes an expression for the energy needed to deform the oceanic lithosphere as it subducts. This expression is determined here from a local model of bending for a strong viscous lithosphere. By implementing subduction in this way, we have demonstrated convection with plates and slabs that resemble those observed on Earth, but in which up to 40 per cent of the mantle's total convective resistance is associated with deformation occurring within the subduction zone. This additional resistance slows plate velocities by nearly a factor of two compared to models with a weak slab. For sufficiently strong lithosphere, the bending deformation slows surface plates sufficiently that they no longer actively participate in global‐scale convection, which occurs instead beneath a 'sluggish lid'. By introducing a low‐viscosity asthenosphere beneath the oceanic plate, we demonstrate that small‐scale convection at the base of oceanic lithosphere may limit plate thickness, and thus the resistance to bending, and cause plate velocities to depend on the strength of the bending lithosphere rather than on the viscosity of the underlying mantle. For a cooling Earth, the effective lithosphere viscosity should be nearly constant, but the mantle viscosity should increase with time. Thus, subduction‐resisted convection should produce nearly constant plate velocities and heat flow over time, which has implications for the Earth's thermal evolution. We estimate that this style of convection should apply if the effective viscosity of the bending lithosphere is greater than about 10^(23) Pa s, but only if some mechanism, such as small‐scale convection, prevents the bending resistance from stopping plates altogether. Such a mechanism could be fundamental to plate tectonics and Earth's thermal history.https://authors.library.caltech.edu/records/chcap-q5k90Interseismic strain accumulation: Spin-up, cycle invariance, and irregular rupture sequences
https://resolver.caltech.edu/CaltechAUTHORS:HETggg06
Authors: Hetland, E. A.; Hager, B. H.
Year: 2006
DOI: 10.1029/2005GC001087
Using models of infinite length strike-slip faults in an elastic layer above linear viscoelastic regions, we investigate interseismic deformation. In the models we investigate, interseismic strain accumulation on mature faults is the result of the cumulative effects of all previous ruptures and is independent of the fault loading conditions. The time for a fault to spin-up to a mature state depends on the rheologies and the fault loading conditions. After the model has spun-up, the temporal variation of shear stresses is determined by the fault slip rate and model rheologies. The change in stress during spin-up depends on the slip rate, rheologies, and fault loading conditions but is independent of the magnitude of the initial stress. Over enough cycles such that the cumulative deformation is block-like, the average mature interseismic velocities are equal to the interseismic velocities of an elastic model with the same geometry and distribution of shear moduli. In a model that has spun-up with the fault rupturing periodically, the cumulative deformation is block-like at the end of each seismic cycle, and the interseismic deformation is cycle-invariant (i.e., the same in all cycles). When the fault ruptures nonperiodically, the fault spins up to a mature state that is the same as if the fault had ruptured periodically with the mean slip rate. When the fault slip rate within each cycle varies, the interseismic deformation evolves toward the cycle-invariant deformation determined by the most recent fault slip rate. Around a fault whose slip rate has been faster (slower) than average, interseismic velocities are larger (smaller) than the cycle-invariant velocities and increase (decrease) from cycle to cycle.https://authors.library.caltech.edu/records/88x58-pk518The effects of rheological layering on post-seismic deformation
https://resolver.caltech.edu/CaltechAUTHORS:HETgji06
Authors: Hetland, E. A.; Hager, B. H.
Year: 2006
DOI: 10.1111/j.1365-246X.2006.02974.x
We examine the effects of rheological layering on post-seismic deformation using models of an elastic layer over a viscoelastic layer and a viscoelastic half-space. We extend a general linear viscoelastic theory we have previously proposed to models with two layers over a half-space, although we only consider univiscous Maxwell and biviscous Burgers rheologies. In layered viscoelastic models, there are multiple mechanical timescales of post-seismic deformation; however, not all of these timescales arise as distinct phases of post-seismic relaxation observed at the surface. The surface displacements in layered models with only univiscous, Maxwell viscoelastic rheologies always exhibit one exponential-like phase of relaxation. Layered models containing biviscous rheologies may produce multiple phases of relaxation, where the distinctness of the phases depends on the geometry and the contrast in strengths between the layers. Post-seismic displacements in models with biviscous rheologies can often be described by logarithmic functions.https://authors.library.caltech.edu/records/rwj4j-74p64The Effects of Fault Roughness on the Earthquake Nucleation Process
https://resolver.caltech.edu/CaltechAUTHORS:20180314-111622058
Authors: Tal, Yuval; Hager, Bradford H.; Ampuero, Jean Paul
Year: 2018
DOI: 10.1002/2017JB014746
We study numerically the effects of fault roughness on the nucleation process during earthquake sequences. The faults are governed by a rate and state friction law. The roughness introduces local barriers that complicate the nucleation process and result in asymmetric expansion of the rupture, nonmonotonic increase in the slip rates on the fault, and the generation of multiple slip pulses. These complexities are reflected as irregular fluctuations in the moment rate. There is a large difference between first slip events in the sequences and later events. In the first events, for roughness amplitude b_r ≤ 0.002, there is a large increase in the nucleation length with increasing br. For larger values of b_r, slip is mostly aseismic. For the later events there is a trade-off between the effects of the finite fault length and the fault roughness. For b_r ≤ 0.002, the finite length is a more dominant factor and the nucleation length barely changes with br. For larger values of b_r, the roughness plays a larger role and the nucleation length increases significantly with b_r. Using an energy balance approach, where the roughness is accounted for in the fault stiffness, we derive an approximate solution for the nucleation length on rough faults. The solution agrees well with the main trends observed in the simulations for the later events and provides an estimate of the frictional and roughness properties under which faults experience a transition between seismic and aseismic slip.https://authors.library.caltech.edu/records/9mj84-7wa78