Response Of Earth Research Articles

Retrieval of reflections from seismic background‐noise measurements

The retrieval of the earth's reflection response from cross‐correlations of seismic noise recordings can provide valuable information, which may otherwise not be available due to limited spatial distribution of seismic sources. We cross‐correlated ten hours of seismic background‐noise data acquired in a desert area. The cross‐correlation results show several coherent events, which align very well with reflections from an active survey at the same location. Therefore, we interpret these coherent events as reflections. Retrieving seismic reflections from background‐noise measurements has a wide range of applications in regional seismology, frontier exploration and long‐term monitoring of processes in the earth's subsurface.

Mantle lateral variations and elastogravitational deformations - I. Numerical modelling

The Earth response (deformation and gravity) to tides or to surface loads is traditionally computed assuming radial symmetry in stratified earth models, at the hydrostatic equilibrium. The present study aims at providing a new earth elastogravitational deformation model which accounts for the whole complexity of a more realistic earth. The model is based on a dynamically consistent equilibrium state which includes lateral variations in density and elastic parameters, and interface topographies. The deviation from the hydrostatic equilibrium has been taken into account as a first-order perturbation. We use a finite element method (spectral element method) and solve numerically the gravitoelasticity equations. As a validation application, we investigate the deformation of the Earth to surface loads. We first evaluate the classical loading Love numbers with a relative precision of about 0.3 per cent for PREM earth model. Then we assume an ellipsoidal homogeneous incom-pressible earth with hydrostatic pre-stresses. We investigate the impact of ellipticity on loading Love numbers analytically and numerically. We validate and discuss our numerical model. At periods greater than 1 hr, the solid earth is mainly deformed by luni-solar tides and by surface loads induced by different external fluid layers (ocean, atmosphere, continental hydrology, ice volumes). This work is devoted to the analytical and numerical development to compute the response of the Earth to such forcing. The body tides have been investigated since the 19th century. In 1862, Lord Kelvin (Sir William Thomson) made the first calculation of the elastic deformation of a homogeneous incompressible earth under the action of the tidal gravitational potential (Thomson 1862). Some years later, Love (1911) studied a compressible homogeneous earth model and showed that the tidal effects could be represented by a set of dimensionless numbers, the so-called Love numbers. Takeuchi (1950) obtained a first estimation of the Love numbers by a numerical integration of the equations using a reference earth model deduced from seismology. These results have been later extended (Smith 1974; Wahr 1981) to an ellipsoidal, rotating Earth with hydrostatic pre-stresses and a liquid core, and finally the effects of mantle anelasticity have been included (Wahr & Bergen 1986; Dehant 1987). In addition to tidal forces, mass changes in the atmosphere cause deformation and mass redistribution inside the planet. The Earth's response to such forcing involves both local and global surface motions and variations in the gravity field, which may be observed in geodetic experiments. These hydrological, atmospheric or oceanic effects on the Earth's gravity field are usually modelled for a spherical Earth with hydrostatic pre-stress (e.g. Farrell 1972; Wahr et al. 1998), generally identified to the preliminary reference earth model (PREM) developed by Dziewonski & Anderson (1981). However, the internal structure of the Earth is more complex than in a spherical non-rotating elastic isotropic (SNREI) earth model like PREM. Seismology and fluid dynamic studies show that the mantle presents heterogeneous structure induced by a thermochemical convection (Davaille 1999; Gu et al. 2001; Forte & Mitrovica 2001) and a bias from hydrostatic state. Large lateral heterogeneities have taken place on a million year timescale (Courtillot et al. 2003), like the two supposed superplumes under the Pacific and South Africa superswells, or like descending slabs. These aspects of the mantle structure are classically not taken into account in the deformation models. The elastogravitational deformations are presently observed with very high accuracy. The accuracy of superconducting gravimeter and of positioning techniques (GPS, VLBI) has seen a large improvement in the last decade. Moreover, the global gravity field will be of interest in the next 10 yr with the launch of the missions GRACE (in 2002) and GOCE (in 2007), which are dedicated to gravimetry and gradiometry 1060

On the origin of the tropical Atlantic decadal oscillation based on the analysis of the ICOADS

AbstractFrom an analysis of the International Comprehensive Ocean–Atmosphere Data Set, we were able to confirm salient features of the tropical Atlantic decadal oscillation illustrated in previous works. These features include antisymmetric behaviour of surface air pressure and sea surface temperature with two centres of action residing in the tropical North and South Atlantic Oceans. In addition to the recognized features of the oscillation, we found a new aspect: the principal mechanism regulating the oscillation differs between the north and south centres of action. Decadal components of the relative humidity time series show a maximum value of lag cross‐correlation at a lag of −2 years. Such a temporal evolution was irrespective of the centres of action and the reference time series. The two reference series employed are the sunspot numbers and the southerlies over the western equatorial Atlantic. Associated with this, statistically significant phase shifts between the decadal components of variables exist, especially in the tropical North Atlantic Ocean. For the decadal oscillation, relative humidity change was dominated by specific humidity change over the tropical North Atlantic and by air temperature change over the tropical South Atlantic. For the frequency band of the solar cycle, the variation of relative humidity seemed to amplify the Earth's response to the sun's radiation changes that had previously been considered too small to affect the Earth's climate. By incorporating our new findings with the known features of the oscillation, we can suggest that the variability of solar radiation may be crucial as an originator, or at least as a regulator, of the oscillation in combination with the climate distribution of clouds and water vapour over the tropical Atlantic. Copyright © 2006 Royal Meteorological Society.

Reanalysis of ancient eclipse, astronomic and geodetic data: A possible route to resolving the enigma of global sea-level rise

Predictions of the Earth's response to the ice age appear to simultaneously reconcile a set of astronomical, geodetic and ancient eclipse observations related to changes in rotation, thus ruling out ice melting as a major contributor to 20th century sea-level rise. We demonstrate that the reconciliation disappears when an improved theory of rotational stability is applied. Furthermore, our reanalysis of longer satellite records renders previous estimates of the secular change in rotation rate suspect. The updated ice-age predictions and observations permit an anomalous 20th century ice flux of ∼1 mm/yr equivalent sea-level rise. Thus, the full suite of Earth rotation observations are consistent with a connection between climatic warming and recent melting of ice reservoirs.

Seasonal fluctuations in the mass of the Amazon River system and Earth's elastic response

A GPS station in Manaus, near the center of the Amazon basin, manifests an annual cycle of vertical displacement with a peak‐to‐peak amplitude of 50–75 mm. This is by far the largest crustal oscillation observed to date, and nearly 2–3 times larger than the amplitude predicted for this region. Vertical ground displacement is strongly anti‐correlated with the local stage height of the Amazon river, with no detectable time lag between the two time series. This suggests that we are observing, for the first time, a purely elastic response to changes in the weight of a flowing river system. We use a simple hydrological model to relate stage height to the regional pattern of flooding, and argue that the elastic oscillations observed in Manaus are dominated by changes in water loading developed within ∼200 km of the GPS station.

Evidence of power-law flow in the Mojave desert mantle.

Studies of the Earth's response to large earthquakes can be viewed as large rock deformation experiments in which sudden stress changes induce viscous flow in the lower crust and upper mantle that lead to observable postseismic surface deformation. Laboratory experiments suggest that viscous flow of deforming hot lithospheric rocks is characterized by a power law in which strain rate is proportional to stress raised to a power, n (refs 2, 3). Most geodynamic models of flow in the lower crust and upper mantle, however, resort to newtonian (linear) stress-strain rate relations. Here we show that a power-law model of viscous flow in the mantle with n = 3.5 successfully explains the spatial and temporal evolution of transient surface deformation following the 1992 Landers and 1999 Hector Mine earthquakes in southern California. A power-law rheology implies that viscosity varies spatially with stress causing localization of strain, and varies temporally as stress evolves, rendering newtonian models untenable. Our findings are consistent with laboratory-derived flow law parameters for hot and wet olivine--the most abundant mineral in the upper mantle--and support the contention that, at least beneath the Mojave desert, the upper mantle is weaker than the lower crust.

Sea-level change through the last glacial cycle: geophysical, glaciological and palaeogeographic consequences

Abstract Sea-level fluctuations in recent geological time are primarily the result of climate change with its associated glacial cycles. Observations reveal a complex spatial and temporal pattern of change that contains a record of the timing of the glacial cycles, of the locations and dimensions of the past ice sheets, of the earth's response function to long-term loading and of tectonic events. By analysing data from different locations and different epochs these different contributions can be separated and comprehensive models of the change associated with the glacial cycles have been developed. These provide constraints on the depth and, to lesser degree, the spatial variation in mantle viscosity, and on the volumes of ice locked up in the individual past ice sheets. These models provide the reference for establishing rates of vertical tectonic motion and also enable the migration of coastlines to be predicted, particularly for the anthropologically important period leading out of the last ice age. To cite this article: K. Lambeck, C. R. Geoscience 336 (2004).

Temperature response of Earth to the annual solar irradiance cycle

We directly determine the sensitivity and time delay of Earth's surface temperature response to annual solar irradiance variations from 60 years of data. A two-layer energy balance model is developed to interpret the results. Explaining both the resulting low sensitivity and time delay of 1–2 months requires negative feedback.

Bow shock's geometry at the magnetospheric flanks

The database of IMP 8 bow shock crossings was used to investigate properties of the bow shock's cross section between 10 and 15 RE tailward of Earth in response to selected upstream and magnetospheric parameters. Best‐fitted ellipses were derived for each parameter subset and analyzed. We have found that for average solar wind conditions, the shock's cross section moves in the north‐south directions by 3.8 RE when the dipole tilt changes from sunward to antisunward orientations. Comparisons with results provided by global three‐dimensional MHD simulations of the magnetosphere have shown that the tilt angle effect is likely to be also important for the estimation of the dayside shock wave's position. We have found the orientation of the IMF with respect to the solar wind flow, expressed by the angle θBv, to influence the size and stability of the shock shape/position. The observed Mach number dependence agreed with previous studies and no other significant IMF‐induced asymmetries were found.

Geophysical monitoring and evaluation of coastal plain aquifers.

We use time domain electromagnetic (TDEM) soundings to monitor ground water conditions beneath the coastal plain in eastern North Carolina. The TDEM method measures the earth's response to an induced electromagnetic field. The resulting signal is converted, through a complex inversion process, to apparent resistivity values, which can be directly correlated to borehole resistivity logs. TDEM soundings are used to map the interface between fresh and salt water within coastal aquifers, and estimate depth to basement when siting new monitoring wells. Focused TDEM surveys have identified areas of salt water encroachment caused by high volumes of discharge from local supply wells. Electromagnetic sounding, when used in tandem with the state's network of monitoring wells, is an accurate and inexpensive tool for evaluating fresh water/salt water relationships on both local and regional scales within coastal plain aquifers.

Role of tropics in changing the response to Milankovich forcing some three million years ago

Throughout the Cenozoic the Earth experienced global cooling that led to the appearance of continental glaciers in high northern latitudes around 3 Ma ago. At approximately the same time, cold surface waters first appeared in regions that today have intense oceanic upwelling: the eastern equatorial Pacific and the coastal zones of southwestern Africa and California. There was furthermore a significant change in the Earth's response to Milankovich forcing: obliquity signals became large, but those associated with precession and eccentricity remained the same. The latter change in the Earth's response can be explained by hypothesizing that the global cooling during the Cenozoic affected the thermal structure of the ocean; it caused a gradual shoaling of the thermocline. Around 3 Ma the thermocline was sufficiently shallow for the winds to bring cold water from below the thermocline to the surface in certain upwelling regions. This brought into play feedbacks involving ocean‐atmosphere interactions of the type associated with El Niño and also mechanisms by which high‐latitude surface conditions can influence the depth of the tropical thermocline. Those feedbacks and mechanisms can account for the amplification of the Earth's response to periodic variations in obliquity (at a period of 41K) without altering the response to Milankovich forcing at periods of 100,000 and 23,000 years. This hypothesis is testable. If correct, then in the tropics and subtropics the response to obliquity variations is in phase with, and corresponds to, El Niño conditions when tilt is large and La Niña conditions when tilt is small.

Deformation Response of a Snrei Earth to Surface Loads and Tidal Forces

AbstractBased on the preliminary reference Earth model (PREM), we use the deformation theory for a spherically stratified and non‐rotating Earth with perfectly elastic and isotropic structural relation (SNREI Earth) to investigate the deformation characteristics under different forces exerting on the Earth. The 4th order Runge‐Kutta numerical integration technique is utilized to solve the motion equations of the Earth's displacement field. The numerical solutions for the deformation and gravitational potential perturbation within the Earth interior and on the surface under the surface loads and luni‐solar tidal force, as well as the Love numbers for surface loads and body tides are obtained. The results indicate that deformation within the solid inner core is very small. The variation of displacement at low spherical harmonic degrees (n < 10) with radius is relatively complicated within the liquid outer core. While the loading degree is larger than 10, the deformation and the gravitational potential perturbation in the core, including both the inner and outer core, are significantly little. As a result, the Earth's response is mainly expressed as the radial displacement in the elastic mantle and decreases rapidly with increasing depth. The higher the loading degree is, the more rapidly this response decreases. The frequency‐dependence of Love numbers for the surface loads and body tides is very weak for a SNREI Earth. In the computation of Love numbers for the body tides, the motion equations for a SNREI Earth are also adopted. Meanwhile, the additional pressure on the core mantle boundary (CMB) is taken into account due to the Earth's rotation and ellipticity. The final results, obtained with this approximate procedure, are in good agreement with the tidal gravity observations on the Earth surface.

Polar motions equivalent to high frequency nutations for a nonrigid Earth with anelastic mantle

The coefficients of polar motions of the rigid/nonrigid Earth in frequency bands other than the retrograde diurnal one are systematically computed using general expressions, derived here for the first time, for the prograde and retrograde torques exerted on the Earth by lunisolar potentials of arbitrary spherical harmonic type. Taken together with the already known coefficients of low frequency nutations and UT1 variations, they provide a complete characterization, with high precision, of the motions of the pole of the terrestrial reference frame in space; this is needed for high precision studies in astronomy and space geodesy. The inputs used for our computations are a table of tidal amplitudes, and values of the geopotential coefficients of degrees up to 4 and of other relevant basic Earth parameters. General relations which connect the coefficients of high frequency nutations to those of the equivalent polar motions are established and used for deducing the former. The Chandler resonance plays a significant role in low frequency polar motions. In this context, the role of mantle anelasticity and the nature of the Earth's deformational response to zero frequency forcing are given special consideration. The free core nutation (FCN) resonance of low frequency nutations is shown to affect the prograde semidiurnal nutations through the coupling produced between the nutations in the two frequency bands by triaxiality terms in the angular momenta of the whole Earth and of its fluid core. It is shown in a transparent fashion that the effect of the core triaxiality arises almost exclusively from the huge FCN-related resonance in the wobble of the core. The magnitude of the effect is found to be a few times smaller than reported in a recent paper; it is also found, unlike in that paper, that the changes in the eigenfrequencies due to trixiality are only of the second order in the triaxiality parameter. Numerical results for the polar motions of the nonrigid Earth in different frequency bands, as well as for the elliptical nutations of the rigid Earth, are tabulated and compared with available numbers from earlier works.

Self‐consistency in reference frames, geocenter definition, and surface loading of the solid Earth

Crustal motion can be described as a vector displacement field, which depends on both the physical deformation and the reference frame. Self‐consistent descriptions of surface kinematics must account for the dynamic relationship between the Earth's surface and the frame origin at some defined center of the Earth, which is governed by the Earth's response to the degree‐one spherical harmonic component of surface loads. Terrestrial reference frames are defined here as “isomorphic” if the computed surface displacements functionally accord with load Love number theory. Isomorphic frames are shown to move relative to each other along the direction of the load's center of mass. The following frames are isomorphic: center of mass of the solid Earth, center of mass of the entire Earth system, no‐net translation of the surface, no‐net horizontal translation of the surface, and no‐net vertical translation of the surface. The theory predicts different degree‐one load Love numbers and geocenter motion for specific isomorphic frames. Under a change in center of mass of surface load in any isomorphic frame, the total surface displacement field consists not only of a geocenter translation in inertial space, but must also be accompanied by surface deformation. Therefore estimation of geocenter displacement should account for this deformation. Even very long baseline interferometry (VLBI) is sensitive to geocenter displacement, as the accompanying deformation changes baseline lengths. The choice of specific isomorphic frame can facilitate scientific interpretation; the theory presented here clarifies how coordinate displacements and horizontal versus vertical motion are critically tied to this choice.

What Might GRACE Contribute to Studies of Post Glacial Rebound?

The NASA/DLR satellite gravity mission GRACE, launched in March, 2002, will map the Earth's gravity field at scales of a few hundred km and greater, every 30 days for five years. These data can be used to solve for time-variations in the gravity field with unprecedented accuracy and resolution. One of the many scientific problems that can be addressed with these time-variable gravity estimates, is post glacial rebound (PGR): the viscous adjustment of the solid Earth in response to the deglaciation of the Earth's surface following the last ice age. In this paper we examine the expected sensitivity of the GRACE measurements to the PGR signal, and explore the accuracy with which the PGR signal can be separated from other secular gravity signals. We do this by constructing synthetic GRACE data that include contributions from a PGR model as well as from a number of other geophysical processes, and then looking to see how well the PGR model can be recovered from those synthetic data. We conclude that the availability of GRACE data should result in improved estimates of the Earth's viscosity profile.

Style of density stratification in the mantle and true polar wander induced by ice loading

[1] The present-day velocity of true polar wander (TPW) and the displacement of the axis of rotation of the Earth in response to ice ages, resulting from stratified, viscoelastic Earth models, are sensitive to the nonadiabatic density gradient in the mantle. Previous studies, based on a fully nonadiabatic, or chemically stratified mantle, overestimated the present-day TPW for lower mantle viscosities in the range 1021–1022 Pa s. For a density profile in agreement with the reference seismological model, where nonadiabaticity is confined to the transition zone between 420 and 670 km, the predicted present-day TPW for viscosities on the order of 1021 Pa s is 0.65–0.9 deg/Myr, substantially lower than the 3.0 deg/Myr obtained for the chemical mantle. This decrease is due to the lack of an isostatic restoring force in the adiabatic case or to a global reduction of the buoyancy, which favors the attainment of rotational equilibrium. The correctness of this physical interpretation is demonstrated by the behavior of a fully adiabatic phase change that can be satisfactorily modeled by deleting the buoyancy restoring modes due to chemical density contrasts. This finding provides quantitative support to the procedure used in previous studies to simulate the rotational behavior of an adiabatic transition zone by simply deleting the buoyancy modes triggered by the (chemical) density contrasts at 670 km, as done by Mitrovica and Milne [1998] for present-day TPW and by Ricard and Sabadini [1990] for long-term TPW driven by mantle density anomalies. The reduction of present-day TPW induced by the Pleistocenic deglaciation, for an adiabatic mantle with nonadiabatic density gradients due to phase changes localized in the transition zone, impacts the inversion of the lower mantle viscosity. Predictions based on such a model are characterized by two best fit values in proximity of 1021 and 1022 Pa s, resembling the behavior of the time derivative of the second-degree component of the gravity field. The reduction of predicted present-day TPW due to Pleistocene deglaciation suggests that other mechanisms, such as present-day ice mass instability in Antarctica and Greenland, are presently contributing to the drift of 0.9 deg/Myr of the axis of rotation toward Newfoundland. The secular drift of the adiabatic mantle model during the continuous occurrence of ice ages is increased by 50% with respect to the chemically stratified one, showing a longer decay time after termination of the ice cycles. This mantle model confirms that ice cycles cannot be the major source of TPW for timescales of 106–107 years.

Reducing uncertainty about carbon dioxide as a climate driver.

The lack of an adequate ancient analogue for future climates means that we ultimately must use and trust climate models, evaluated against modern observation and our best geologic records of warm and cold climates of the past. Armed with an elevated confidence in the models, we will then be able to make reliable predictions of the Earth's response to our risky experiment with the climate system.

Sun-climate connections. Earth's response to a variable Sun.

Solar radiation reaching Earth is not constant but rather varies with time because of cyclical changes in the sun's activity. In their Perspective, [Lean and Rind][1] discuss the emerging evidence that this variability, albeit small, is translated into climatic variability on Earth. This issue is important because the solar variability signal must be distinguished from the anthropogenic signal to understand the human influence on climatic change. [1]: http://www.sciencemag.org/cgi/content/full/292/5515/234

The distention of the magnetosphere on May 11, 1999: High latitude Antarctic observations and comparisons with low latitude magnetic and geopotential data

We examine the Earth's ionospheric response on May 11, 1999, to an unusually tenuous solar wind, focusing on magnetometer, riometer, and optical data from high geomagnetic latitudes in Antarctica. Comparisons are also made with POLAR satellite data during a perigee pass over Antarctica, and with geomagnetic data collected at low latitudes. It is shown that the southern hemisphere was geophysically active, even though the Kp index on May 11 ranged only from 0 to 0+. Furthermore, despite the fact that the IMF and solar wind conditions favored northern hemisphere polar rain, low energy electron precipitation did occur in the southern polar cap. Geomagnetic power levels at low, cusp, and polar cap latitudes were also lower on May 11 than on surrounding days. Although this might be expected, discrete millihertz peaks in ULF power were still evident, especially at cusp latitudes.

Glacio-seismotectonics: ice sheets, crustal deformation and seismicity

The last decade has witnessed a significant growth in our understanding of the past and continuing effects of ice sheets and glaciers on contemporary crustal deformation and seismicity. This growth has been driven largely by the emergence of postglacial rebound models (PGM) constrained by new field observations that incorporate increasingly realistic rheological, mechanical, and glacial parameters. In this paper, we highlight some of these recent field-based investigations and new PGMs, and examine their implications for understanding crustal deformation and seismicity during glaciation and following deglaciation. The emerging glacial rebound models outlined in the paper support the view that both tectonic stresses and glacial rebound stresses are needed to explain the distribution and style of contemporary earthquake activity in former glaciated shields of eastern Canada and Fennoscandia. However, many of these models neglect important parameters, such as topography, lateral variations in lithospheric strength and tectonic strain built up during glaciation. In glaciated mountainous terrains, glacial erosion may directly modulate tectonic deformation by resetting the orogenic topography and thereby providing an additional compensatory uplift mechanism. Such effects are likely to be important both in tectonically active orogens and in the mountainous regions of glaciated shields. In general, the short-term response to ice fluctuations is similar to the Earth's response to fluctuations in water reservoirs with the subsequent increase or decrease in seismicity which depends on the pre-existing stress state. When the ice fluctuations occur on the spatial scale, and magnitude, of the Late Pleistocene glaciation and deglaciation, however, the viscoelastic response of the Earth (especially the mantle) causes significant changes in crustal deformation and earthquake activity that is spatially extensive and temporally complex. The regions of greatest ice thickness and the regions marginal to the Late Pleistocene ice sheets indicate the most dramatic evidence of earthquake faulting. The mantle response to these large ice mass fluctuations and the change in mass between the oceans and land caused, and continues to cause, measureable crustal deformation at hundreds of kilometres from the ice margins. For both tectonically active and cratonic regions, palaeoseismic investigations of Late Pleistocene and Holocene faults are an important tool in evaluating earthquake hazard. The predicted response of the Earth over this time, however, is very dependent on the model assumed. For most regions, far more carefully designed field observations are needed to constrain the existing rheological and ice models.