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The article presents a study which explores the relatively dry mantle transition zone revealed by geomagnetic diurnal variations. It mentions that distribution of water within the mantle transition zone (MTZ) has important implications for the material circulation and partial melting of the mantle. It discusses the development of joint inversion of geomagnetic diurnal variation for realistic source structure and one-dimensional mantle conductivity profile.

Magnetotelluric and seismic reflection surveys at Parkfield, California, show that the San Andreas fault zone is characterized by a vertical zone of low electrical resistivity. This zone is [approximately equal to]500 m wide and extends to a depth of [approximately equal to]4000 m. The low electrical resistivity is attributed to high porosity of saline fluids present in the highly fractured fault zone. The occurrence of microearthquakes and creep in the low resistivity zone is consistent with suggestions that seismicity at Parkfield is fluid driven.

In order to access the targeted ocean signal, altimeter measurements are corrected for several geophysical parameters among which the ocean tide correction is one of the most critical, but the internal tide signature at the surface are not yet corrected globally. Internal tides can have a signature of several cm at the surface with wavelengths about 50-250 km for the first mode and even smaller scales for higher order modes. The goals of the upcoming Surface Water Ocean Topography (SWOT) mission and other high- resolution ocean measurements make the correction of these small scale signals a challenge, as the separation of all tidal variability from other oceanic signals becomes mandatory. In this context, several scientific teams are working on the development of new internal tide models, taking advantage of the very long altimeter time series now available, which represent an unprecedented and valuable global ocean database. The internal tide models presented here focus on the coherent internal tide signal and they are of three types: empirical models based upon analysis of existing altimeter missions, an assimilative model, and a three-dimensional hydrodynamic model. A detailed comparison and validation of these internal tide models is proposed using existing satellite altimeter databases. The analysis focuses on the four main tidal constituents M2, K1, O1 and S2. The validation process is based on a statistical analysis of multi-mission altimetry including Jason-2 and Cryosphere Satellite-2 data, taking advantage of the long-term altimeter databases available. The results show a significant altimeter variance reduction when using internal tide corrections on all ocean regions where internal tides are generating/propagating. A complementary spectral analysis also gives some estimation of the performance of each model as a function of wavelength, and some insight into the residual non-stationary part of internal tides in the different regions of interest. [ABSTRACT FROM AUTHOR]

Krylov subspace solvers for frequency-domain electromagnetic forward modeling problems converge remarkably more slowly as the period increases. In this article, we present an efficient four-color cellblock Gauss Seidel (GS) preconditioner for finite-difference (FD) electromagnetic modeling in geophysical applications. Rather than updating the FD electromagnetic (EM) equation edge by edge, as in a traditional GS scheme, we renew six edge components attached to one node simultaneously (i.e., in cellblock manner) effectively enforcing a local divergence free condition for currents. To improve implementation efficiency, we reorder the nodes on the FD grid into four colors so that nodes in each color are uncoupled, allowing the use of highly parallel vectorized algorithms. The four-color cellblock GS preconditioner is implemented in the MATLAB code, in conjunction with a BiCGstab solver. It is compared, in terms of iteration number and computing time, with other three commonly used preconditioners [GS, symmetric successive overrelaxation (SSOR) and incomplete lower and upper triangular matrix decomposition (ILU)] on three models—two synthetic and one modified from the version of real data inversion. The comparison indicates that the proposed algorithm is extremely stable and efficient compared with the other three preconditioners tested, over a range of periods (1-1000 s). Especially at long periods, the improvement of our proposed algorithm is substantial. In addition, a parallel implementation of the cellblock GS preconditioner is straightforward due to the independence of nodes in each color. [ABSTRACT FROM AUTHOR]

The stress field in the eastern United States is commonly considered to be broadly uniform and due to homogeneous far‐field forces; however, modern and geologic stress indicators in this region show substantial heterogeneity. Using CitcomS to model stresses based on simple input density, temperature, and viscosity fields, we show that local isostasy is key in explaining the intraplate stress field in the southeastern United States. Crustal thickness variations appear to be most important in reproducing observations, although we slightly better match the observed stress field by including variable crustal viscosity informed by magnetotelluric imaging. Our results demonstrate that local gravitational body forces can substantially reorient far‐field stresses and thereby influence patterns of intraplate seismicity. We also show that variable crustal viscosity encourages a steepening of isostatic topography in the southeastern United States; this observation suggests that a sharp boundary in crustal strength may be important in explaining the apparently long‐lived Appalachian topographic escarpment. Plain Language Summary: The origin of stresses within tectonic plates, and hence the ultimate driving force of earthquakes far from plate boundaries, is a contentious topic. Historically, the geoscience community has viewed intraplate stress patterns as being simply the result of forces applied along plate edges. However, this paradigm does not explain why earthquakes far from plate boundaries cluster into discrete seismic zones, nor does it explain the diverse mechanisms of intraplate earthquakes. Here, we consider the southeastern United States, which is thousands of kilometers from any plate boundary, but which nevertheless experiences major earthquakes, such as the 2011 Virginia earthquake that shook the nation's capital. Using numerical models, we show that forces arising from variable thickness of the Earth's crust can largely explain the stress and earthquake patterns observed in this region. Another curious feature of the southeastern United States is the steep topography of the Blue Ridge Escarpment in the Appalachian Mountains; despite having been subjected to episodic erosion for over a hundred million years, the southeastern edge of the range is surprisingly sharp. With our models, we show that weak zones within the crust beneath the Appalachians may help to explain how that steep escarpment has survived over long timescales. Key Points: Stress indicators in the southeastern United States show substantial heterogeneityGravitational body forces from variable crustal thickness are important in explaining many features of observed stress patternsCrustal weak zones beneath the Appalachian Mountains may help maintain a sharp passive margin escarpment (the Blue Ridge Escarpment) [ABSTRACT FROM AUTHOR]

Although seismic velocity and electrical conductivity are both sensitive to temperature, thermal lithosphere properties are derived almost exclusively from seismic data because conductivity is often too strongly affected by minor highly conductive phases to be a reliable indicator of temperature. However, in certain circumstances, electrical observations can provide strong constraints on mantle temperatures. In the southeastern United States (SEUS), magnetotelluric (MT) data require high resistivity values (>300 Ωm) to at least 200‐km depth. As dry mantle mineral conduction laws provide an upper bound on temperature for an observed resistivity value, the only interpretation is that lithospheric temperatures (<1330 °C) persist to 200 km. However, seismic tomography shows that velocities in this region are generally slightly slow with respect to references models; this observation has led to a view of relatively thin (<150 km), eroded thermal lithosphere beneath the SEUS. We show that MT and seismic (tomography, attenuation, receiver function) results are consistent with thick (~200 km), coherent thermal lithosphere in this region. Reduced seismic velocities (relative to reference models) can be explained by considering the effect of finite grain size (anelasticity). Calculated velocity as a function of temperature is overall slower when including anelastic effects, even at reasonable grain sizes of 1 mm to 1 cm; this permits mantle temperatures that are colder than would typically be inferred. We argue for a geodynamic scenario in which the present thermal lithosphere in the SEUS formed in association with the Central Atlantic Magmatic Province and has subsequently survived intact for ~200 Ma. Plain Language Summary: Seismic and magnetotelluric imaging techniques seem to give fundamentally different views of the mantle lithosphere beneath the southeastern United States (SEUS). Whereas seismic imaging has supported a picture of relatively thin, broken‐up lithosphere in this region, magnetotelluric imaging requires a thick, coherent lithospheric block in the SEUS. Here, by considering calculations of seismic observables including effects from finite grain size, we show that results from both geophysical data sets are consistent with this latter picture. Therefore, although previous studies have argued that the modern geodynamics of the SEUS is controlled by erosion and removal of lithosphere, our analysis supports a geodynamic scenario in which this region is underlain by a coherent lithospheric block that has survived intact for the last ~200 million years. Key Points: Magnetotelluric and seismic imaging techniques appear to give contradictory views of the lithosphere in the southeastern United StatesSlow seismic velocities are consistent with high electrical resistivities in the mantle lithosphere when considering finite grain sizeMeasured attenuation and lithospheric discontinuities are also consistent with high resistivities, which demand thick thermal lithosphere [ABSTRACT FROM AUTHOR]

We discuss a regularization approach to improving numerical stability of the frequency domain Maxwell equations of electromagnetic geophysics. To enforce divergence-free conditions we add a scaled grad-div operator to the curl–curl equation for electric fields. This deflates the null space of the curl–curl operator and significantly reduces the condition number of the linear system derived for the finite difference (FD) approximation, resulting in faster and more stable iterative solution. We explicitly discuss extensions needed to solve the adjoint problems and consider two apparently different approaches to the sensitivity calculation, which we show are ultimately equivalent. To complete assessment of the new approach in practice we have implemented the modified solver in the ModEM inversion code, and compared it to more standard methods (based on solving with a divergence correction) on inversion of a real data set. This, and simpler tests of the forward solver in isolation, demonstrate that, with appropriate scaling of the added grad-div term, the regularization approach can dramatically improve the efficiency of Krylov subspace methods. Run times for the inversion test are reduced by almost a factor of three, making 3-D FD inversion significantly more practical. [ABSTRACT FROM AUTHOR]

The magnetotelluric (MT) method for imaging the electrical conductivity structure of the Earth is based on the assumption that source magnetic fields can be considered quasi-uniform, such that the spatial scale of the inducing source is much larger than the intrinsic length scale of the electromagnetic induction process (the skin depth). Here, we show using EarthScope MT data that short spatial scale source magnetic fields from geomagnetic pulsations (Pc's) can violate this fundamental assumption. Over resistive regions of the Earth, the skin depth can be comparable to the short meridional range of Pc3-4 disturbances that are generated by geomagnetic field-line resonances (FLRs). In such cases, Pc's can introduce narrow-band bias in MT transfer function estimates at FLR eigenperiods (~ 10-100 s). Although it appears unlikely that these biases will be a significant problem for data inversions, further study is necessary to understand the conditions under which they may distort inverse solutions. [ABSTRACT FROM AUTHOR]

We present a magnetotelluric (MT) study in the northeastern part of the São Francisco Craton that encompasses an Archean-Proterozoic terrain, the Serrinha Block, breached by a rift basin developed mostly in Early Cretaceous times during the opening of the South Atlantic Ocean. Even though the MT sites are regularly spaced, the profiles have different orientations from one another, making the data distribution over the area highly uneven and therefore nonideal for 3-D modeling. However, the data set is very complex, with dimensionality analysis indicating prevalence of 3-D geoelectric structure. Results from 3-D inversion are evaluated for robustness and potentiality for yielding tectonic information. At upper crustal depths, the resulting 3-D model is coherent with surface geology, whereas at mid and lower crustal depths more cryptic structures are revealed, likely of Palaeoproterozoic age. The most striking features in the model are several strong (~1 Ω·m) crustal conductors beneath the central part of the Serrinha Block, which we attribute to a Palaeoproterozoic oceanic plate subduction and arc-continent collision event involving the Rio Itapicuru Greenstone Belt and the basement of the Serrinha Block. The west-dipping geometry of these conductors provides a constraint on subduction polarity and gives support to tectonic evolutionary models proposing that the Rio Itapicuru Belt was formed in an island arc environment. [ABSTRACT FROM AUTHOR]

With advancing computational resources, 3-D inversion techniques have become feasible in recent years and are now a more widely used tool for magnetotelluric (MT) data interpretation. Galvanic distortion caused by small-scale near-surface inhomogeneities remains an obstacle for 3-D MT inversion which so far has experienced little attention. If not considered properly, the effect on 3-D inversion can be immense and result in erroneous subsurface models and interpretations. To tackle the problem we implemented inversion of the distortion-free phase tensor into the ModEM inversion package. The dimensionless phase tensor components describe only variations of the conductivity structure. When inverting these data, particular care has to be taken of the conductivity structure in the a priori model, which provides the reference frame when transferring the information from phase tensors into absolute conductivity values. Our results obtained with synthetic data show that phase tensor inversion can recover the regional conductivity structure in presence of galvanic distortion if the a priori model provides a reasonable assumption for the regional resistivity average. Joint inversion of phase tensor data and vertical magnetic transfer functions improves recovery of the absolute resistivity structure and is less dependent on the prior model. We also used phase tensor inversion for a data set of more than 250 MT sites from the central San Andreas fault, California, where a number of sites showed significant galvanic distortion. We find the regional structure of the phase tensor inversion results compatible with previously obtained models from impedance inversion. In the vicinity of distorted sites, phase tensor inversion models exhibit more homogeneous/smoother conductivity structures. [ABSTRACT FROM AUTHOR]

Long period (10-20,000 s) magnetotelluric (MT) data are being acquired across the continental USA on a quasi-regular grid of ~70 km spacing as an electromagnetic component of the National Science Foundation EarthScope/USArray Program. These data are sensitive to fluids, melts, and other orogenic indicators, and thus provide a valuable complement to other components of EarthScope. We present and interpret results of 3-D MT data inversion from 325 sites acquired from 2006-2011 to provide a regional scale view of electrical resistivity from the middle crust to nearly the mantle transition zone, covering an area from NW Washington to NW Colorado. Beneath the active extensional subprovinces in the south-central region, on average we see a resistive upper crust, and then extensive areas of low resistivity in the lower crust and uppermost mantle. Further below, much of the upper half of the upper mantle appears moderately resistive, then subsequently the lower upper mantle becomes moderately conductive. This column suggests a dynamic process of moderately hydrated and fertile deeper upper mantle upwelling during extension, intersection of that material with the damp solidus causing dehydration and melting, and upward exodus of generated mafic melts to pond and exsolve saline fluids near Moho levels. Lithosphere here is very thin. To the east and northeast, thick sections of resistive lithosphere are imaged under the Wyoming and Medicine Hat Cratons. These are punctuated with numerous electrically conductive sutures presumably containing graphitic or sulfide-bearing meta-sediments deeply underthrust and emplaced during ancient collisions. Below Cascadia, the subducting Juan de Fuca and Gorda lithosphere appears highly resistive. Suspected oceanic lithosphere relicts in the central NW part of the model domain also are resistive, including the accreted "Siletzia" terrane beneath the Coast Ranges and Columbia Embayment, and the seismically fast "slab curtain" beneath eastern Idaho interpreted by others as stranded Farallon plate. Upwelling of deep fluid or melt in the Cascade volcanic arc region manifests as conductive features at several scales. These include quasi-horizontal conductive patches under the arc and fore-arc, likely denoting fluids evolved via breakdown of hydrous minerals in the current down-going slab. In the backarc, low resistivities concentrate in "plumes" connecting into a deeper aesthenospheric layer to the east, consistent with subduction-driven upwelling of hot, hydrated or melted, aesthenospheric mantle. Low resistivities <10 Ωm deep beneath the stable cratons suggest higher levels of hydration there, and/or influence of poorly resolved structures outside the array. [ABSTRACT FROM AUTHOR]

The interaction of the dominant semidiurnal M2 internal tide with the large-scale subtidal flow is examined in an ocean model by propagating the tide through an ensemble of background fields in a domain centered on the Hawaiian Ridge. The background fields are taken from the Simple Ocean Data Assimilation (SODA) ocean analysis, at 2-month intervals from 1992 through 2001. Tides are computed with the Primitive Equation Z-coordinate Harmonic Analysis of Tides (PEZ-HAT) model by 14-day integrations using SODA initial conditions and M2 tidal forcing. Variability of the tide is found to occur primarily as the result of propagation through the nonstationary background fields, rather than via generation site variability. Generation of incoherent tidal variability is mapped and shown to occur mostly in association with waves generated at French Frigate Shoals scattering near the Musicians Seamounts to the north of the ridge. The phase-coherent internal tide loses energy at a domain-average rate of 2 mW m−2 by scattering into the nonstationary tide. Because of the interference of waves from multiple generation sites, variability of the internal tide is spatially inhomogeneous and values of the scattering rate 10 times larger occur in localized areas. It is estimated that 20% of the baroclinic tidal energy flux is lost by adiabatic scattering (refraction) within 250 km of the ridge, a value regarded as a lower bound because of the smoothed nature of the SODA fields used in this study. [ABSTRACT FROM AUTHOR]

Dickman argues that our model of the Mf ocean tide is unrealistic and that this invalidates conclusions regarding mantle anelasticity. His evidence is based on comparison with his own ocean modelling experiments and on his physical intuition regarding near-equilibrium tides. That evidence is unconvincing. Simple physical arguments alone are enough to rebut his main points. Furthermore, we test here his suggestion of increasing bottom-friction dissipation by a factor of 100 over our preferred solution, and we show that this results in unacceptable polar motion and poor agreement with independent tide-gauge data. In contrast, tests against independent data lend support to the realism of our Mf tide model and give confidence that our estimates of mantle anelasticity are reliable within stated error bounds. [ABSTRACT FROM AUTHOR]

SUMMARY We describe novel hybrid algorithms for inversion of electromagnetic geophysical data, combining the computational and storage efficiency of a conjugate gradient approach with an Occam scheme for regularization and step-length control. The basic algorithm is based on the observation that iterative solution of the symmetric (Gauss-Newton) normal equations with conjugate gradients effectively generates a sequence of sensitivities for different linear combinations of the data, allowing construction of the Jacobian for a projection of the original full data space. The Occam scheme can then be applied to this projected problem, with the tradeoff parameter chosen by assessing fit to the full data set. For EM geophysical problems with multiple transmitters (either multiple frequencies or source geometries) an extension of the basic hybrid algorithm is possible. In this case multiple forward and adjoint solutions (one each for each transmitter) are required for each step in the iterative normal equation solver, and each corresponds to the sensitivity for a separate linear combination of data. From the perspective of the hybrid approach, with conjugate gradients generating an approximation to the full Jacobian, it is advantageous to save all of the component sensitivities, and use these to solve the projected problem in a larger subspace. We illustrate the algorithms on a simple problem, 2-D magnetotelluric inversion, using synthetic data. Both the basic and modified hybrid schemes produce essentially the same result as an Occam inversion based on a full calculation of the Jacobian, and the modified scheme requires significantly fewer steps (relative to the basic hybrid scheme) to converge to an adequate solution to the normal equations. The algorithms are expected to be useful primarily for 3-D inverse problems for which the computational burden is heavily dominated by solution to the forward and adjoint problems. [ABSTRACT FROM AUTHOR]

ABSTRACT This study of the fortnightly Mf tide comprises three main topics: (1) a new determination of the fortnightly component of polar motion and length of day (LOD) from a multidecade time-series of observed space-geodetic data; (2) the use of the polar motion determination as one constraint in the development of a hydrodynamic ocean model of the Mf tide and (3) the use of these results to place new constraints on mantle anelasticity at the Mf tidal period. Our model of the Mf ocean tide assimilates more than 14 years of altimeter data from the Topex/Poseidon and Jason-1 satellites. Because the Mf altimetric signal-to-noise ratio is very small, it is critical that altimeter data not be overweighted. The polar motion data, plus tide-gauge data and independent altimeter data, give useful additional information, with only the polar motion putting constraints on tidal current velocities. The resulting ocean-tide model, plus the dominant elastic body tide, leaves a small residual in observed LOD caused by mantle anelasticity. The inferred effective tidal Q of the anelastic body tide is 90 and is in line with a ωα frequency dependence with α in the range 0.2-0.3. [ABSTRACT FROM AUTHOR]

SUMMARY The Jacobian of the non-linear mapping from model parameters to observations is a key component in all gradient-based inversion methods, including variants on Gauss-Newton and non-linear conjugate gradients. Here, we develop a general mathematical framework for Jacobian computations arising in electromagnetic (EM) geophysical inverse problems. Our analysis, which is based on the discrete formulation of the forward problem, divides computations into components (data functionals, forward and adjoint solvers, model parameter mappings), and clarifies dependencies among these elements within realistic numerical inversion codes. To be concrete, we focus much of the specific discussion on 2-D and 3-D magnetotelluric (MT) inverse problems, but our analysis is applicable to a wide range of active and passive source EM methods. The general theory developed here provides the basis for development of a modular system of computer codes for inversion of EM geophysical data, which we summarize at the end of the paper. [ABSTRACT FROM AUTHOR]

Abstract: Using synthetic data demonstrated possible advantages of interpreting single-profile MT data with a three-dimensional (3D) inversion program. Here we explore this idea further using real MT data from two profiles on the Indian subcontinent. The first profile (330km long) cuts across the Deccan Volcanic Province of Peninsular India. The second (130km long) is in the Narmada Son Lineament zone, approximately 100km further north. Using the data-space Occam inversion code of 3D inversion is carried out on each of these profiles independently, and results are compared with previously-published two-dimensional (2D) interpretations. In addition to inversion of the full impedance tensor, we consider 3D inversion of only the off-diagonal components. We also experiment with variants on the model covariance, in particular allowing for longer smoothing length scales along the geoelectric strike. Not surprisingly, the 3D inversion finds models that fit the data better than had been possible with the 2D programs. Many of the features inferred from these previous 2D interpretations are also present in the 3D inverse solutions, but the positions and amplitudes of individual conductive features are in some cases changed. The 3D models suggest substantial non-uniqueness in the single profile data. Even without explicit or special treatment, we find that the (relatively modest) near surface distortion effects in these datasets were well fit by the 3D inversion, by inserting small scale conductive and resistive features in surface layers, mostly off-profile. [Copyright &y& Elsevier]

Abstract: Non-linear tidal constituents, such as the overtide M4 or the compound tide MS4, are generated by interaction in shallow seas of the much larger astronomically forced “primary” tidal constituents (e.g., M2, S2). As such, errors in modeling these “secondary” shallow-water tides might be expected to be caused first of all by errors in modeling the primary constituents. Thus, in the context of data assimilation, observations of primary-constituent harmonic constants can indirectly constrain shallow-water constituents. Here we consider variational data assimilation for primary and secondary tidal constituents as a coupled problem, using a simple linearized perturbation theory for weak interactions of the dominant primary constituents. Variation of the resulting penalty functional leads to weakly non-linear Euler–Lagrange equations, which we show can be solved approximately with a simple two-stage scheme. In the first stage, data for the primary constituents are assimilated into the linear shallow water equations (SWE), and the resulting inverse solutions are used to compute the quadratic interactions in the non-linear SWE that constitute the forcing for the secondary constituents. In the second stage, data for the compound or overtide constituent are assimilated into the linear SWE, using a prior forced by the results of the first stage. We apply this scheme to assimilation of TOPEX/Poseidon and Jason altimetry data on the Northwest European Shelf, comparing results to a large set of shelf and coastal tide gauges. Prior solutions for M4, MS4 and MN4 computed using inverse solutions for M2, S2, and N2 dramatically improve fits to validation tide gauges relative to unconstrained forward solutions. Further assimilation of along-track harmonic constants for these shallow-water constituents reduces RMS differences to below 1cm on the shelf, approaching the accuracy of the validation tide gauge harmonic constants. [Copyright &y& Elsevier]

• We construct a continental-scale electrical resistivity model of the US. • Only subtle lateral variations in resistivity are required below 200 km depth. • The mantle at 200–275 km is nearly dry on average. • 150–300 ppm water or temperature variations of 80–120 ∘ C is required at 275–410 km. • MT data requires a conductive MTZ (∼ 10–20 Ω. m on average) beneath the continental US. Long-period magnetotelluric (MT) sites, covering much of the continental United States (US) have been collected through the EarthScope USArray MT Transportable Array (TA) project. Previous regional studies using subsets of these data suggest large-scale variations in deep (sub-lithospheric) resistivity, often of significant amplitude. Here, we present a range of three-dimensional (3D) continental-scale electrical resistivity models from 3D inversion of the MT TA data, with a focus on testing robustness and resolution of this deep structure. The main features of our initial model, obtained with no constraints, are quite similar to those from previous studies, with significant (± 1 order of magnitude) lateral variations in deep resistivity. We show that data fit, as measured by global normalized root-mean-square misfit, is not increased by replacing structures below 200 km depth with layer averages. A more careful examination of residuals leads to further refinements, with a slight improvement in data fit. These include a moderately conductive mantle transition zone (13 Ω. m), and subtle (± 1 / 4 order of magnitude) lateral variations in resistivity below 200 km. In contrast to the initial results, these variations can be explained by reasonable variations in mantle temperature and hydration. Overall, our results suggest that the asthenospheric mantle at 200–275 km is nearly dry on average and at greater depths contains 150–300 ppm water. Lateral variations may be explained by this range of water content, or by temperature variations of 80 – 120 ∘ C. Patterns of resistivity variations below 200 km are consistent with known continental structure, and suggest deep roots (∼250 km) beneath cratons, and perhaps also beneath the mid-continent rift. Reduced resistivity, likely requiring greater hydration (or higher temperatures), occurs beneath the North-central part of the continental US, the oldest part of the continent, and beneath the Yellowstone hotspot. [ABSTRACT FROM AUTHOR]

We develop a non-linear conjugate gradient inversion for global long period electromagnetic induction studies. The scheme requires computation of derivatives of the regularized penalty functional. We derive analytical and numerical expressions for these derivatives, and the associated Jacobian, and show how these can be efficiently implemented by generalizing and extending an existing finite difference forward solver. Using layered spherical harmonics to parametrize the model space, we invert a range of synthetic data sets to test the inversion, and to study vertical and horizontal resolution of currently available data sets. We conclude that the currently available long-period global geomagnetic observatory data in the period range 5–107 d can resolve large scale (300–500 km vertically, thousands of km horizontally) heterogeneities in mantle electrical conductivity reliably at depths ∼ 670–1600 km. By extending induction response to 0.2–5 d (including daily variation periods), upper-mantle structure could also be resolved. [ABSTRACT FROM AUTHOR]

The generalized inverse of a regional model is used to estimate barotropic tidal dissipation along the Hawaiian Ridge. The model, based on the linear shallow-water equations, incorporates parameterizations for the dissipation of energy via friction in the bottom boundary layer and form drag due to internal waves generated at topographic slopes. Sea surface height data from 364 orbit cycles of the Ocean Topography Experiment (TOPEX)/Poseidon satellite mission are used to perform inversions at eight diurnal and semidiurnal tidal frequencies. It is estimated that the barotropic M2 tide loses energy at a rate of 19 GW, of which 88% is lost within 250 km of the ridge, presumably via conversion to the internal or baroclinic tide. Uncertainty in the assumed model error and wave drag in the forward model suggest that M2 dissipation values from 18 to 25 GW are consistent with the altimetric observations. Other barotropic tidal constituents are estimated to lose a total of 5.7 GW. The spatial distribution of barotropic dissipation along the ridge is similar to that inferred from three-dimensional primitive equation models, and it is largely insensitive to details of assumed model and data errors. Dissipation at semidiurnal frequencies is most intense at the French Frigate Shoals with lesser, but significant, contributions at other sites. Diurnal tidal dissipation is concentrated to the east of the French Frigate Shoals, at the Gardner Pinnacles. Further work with three-dimensional models will be necessary to determine the fate of the energy that is removed from the barotropic tide. [ABSTRACT FROM AUTHOR]

We use geodetic observations of the Earth to constrain anelasticity in the Earth's mantle at periods between 12 hr and 18.6 yr. The observations include satellite laser ranging (SLR) measurements of 12 hr and 18.6 yr tides in the J2 component of the gravity field; space-based observations of tidal variations in the Earth's rotation rate; and optical and space-based measurements of the Chandler Wobble period and damping. These geophysical signals are mostly sensitive to the lower mantle. The results suggest the dissipative process could consist of a single absorption band that extends across seismic periods out at least as far as ∼20 yr. The results also require values of the anelastic parameter Q that are smaller than those required by seismic observations. We interpret this as evidence that Q in the lower mantle is frequency dependent. The frequency dependence suggested by the geodetic observations is reasonably consistent with laboratory measurements, though those measurements have only been done on rocks at upper mantle conditions. After fitting and removing the 18.6 yr tide from the SLR J2 results, we find that the 1998–2002 anomaly present in the original J2 observations is no longer a singular anomaly in the J2 residuals, but becomes one of a series of maxima in a quasi-decadal oscillation. [ABSTRACT FROM AUTHOR]

The small S1 ocean tide is caused primarily by diurnal atmospheric pressure loading. Its excitation is therefore unlike any other diurnal tide; in particular, pressure loading is maximum near the equator where the diurnal gravitational potential is zero. The global character of the S1 tide is here determined by numerical modeling and by analysis of Ocean Topography Experiment (TOPEX)/Poseidon satellite altimeter data. The two approaches yield reasonably consistent results. Amplitudes exceeding 1 cm in several regions are further confirmed by comparison with coastal tide gauges. Notwithstanding their excitation differences, S1 and other diurnal tides are found to share several common features, such as relatively large amplitudes in the Arabian Sea, the Labrador Sea, the Sea of Okhotsk, and the Gulf of Alaska. The most noticeable difference is the lack of an S1 Antarctic Kelvin wave. These similarities and differences can be explained in terms of the coherences between near-diurnal oceanic normal modes and the underlying tidal forcings. Whereas gravitational diurnal tidal forces excite primarily a 28-h Antarctic–Pacific mode, the S1 air tide excites several other near-diurnal modes, none of which has large amplitudes near Antarctica. [ABSTRACT FROM AUTHOR]

A linearized baroclinic, spectral-in-time tidal inverse model has been developed for assimilation of surface currents from coast-based high-frequency (HF) radars. Representer functions obtained as a part of the generalized inverse solution show that for superinertial flows information from the surface velocity measurements propagates to depth along wave characteristics, allowing internal tidal flows to be mapped throughout the water column. Application of the inverse model to a 38 km × 57 km domain off the mid-Oregon coast, where data from two HF radar systems are available, provides a uniquely detailed picture of spatial and temporal variability of the M[sub 2] internal tide in a coastal environment. Most baroclinic signal contained in the data comes from outside the computational domain, and so data assimilation (DA) is used to restore baroclinic currents at the open boundary (OB). Experiments with synthetic data demonstrate that the choice of the error covariance for the OB condition affects model performance. A covariance consistent with assumed dynamics is obtained by nesting, using representers computed in a larger domain. Harmonic analysis of currents from HF radars and an acoustic Doppler profiler (ADP) mooring off Oregon for May–July 1998 reveals substantial intermittence of the internal tide, both in amplitude and phase. Assimilation of the surface current measurements captures the temporal variability and improves the ADP/solution rms difference. Despite significant temporal variability, persistent features are found for the studied period; for instance, the dominant direction of baroclinic wave phase and energy propagation is always from the northwest. At the surface, baroclinic surface tidal currents (deviations from the depth-averaged current) can be 10 cm s[sup –1] , 2 times as large as the depth-averaged current. Barotropic-to-baroclinic energy conversion is generally weak within the model domain over the shelf but reaches 5 mW m[sup –2] at times over the slopes of Stonewall Bank. [ABSTRACT FROM AUTHOR]

New empirical estimates of the long-period fortnightly (Mf ) tide obtained from TOPEX/Poseidon (T/P) altimeter data confirm significant basin-scale deviations from equilibrium. Elevations in the low-latitude Pacific have reduced amplitude and lag those in the Atlantic by 30° or more. These interbasin amplitude and phase variations are robust features that are reproduced by numerical solutions of the shallow-water equations, even for a constant-depth ocean with schematic interconnected rectangular basins. A simplified analytical model for cooscillating connected basins also reproduces the principal features observed in the empirical solutions. This simple model is largely kinematic. Zonally averaged elevations within a simple closed basin would be nearly in equilibrium with the gravitational potential, except for a constant offset required to conserve mass. With connected basins these offsets are mostly eliminated by interbasin mass flux. Because of rotation, this flux occurs mostly in a narrow boundary layer across the mouth and at the western edge of each basin, and geostrophic balance in this zone supports small residual offsets (and phase shifts) between basins. The simple model predicts that this effect should decrease roughly linearly with frequency, a result that is confirmed by numerical modeling and empirical T/P estimates of the monthly (Mm) tidal constituent. This model also explains some aspects of the anomalous nonisostatic response of the ocean to atmospheric pressure forcing at periods of around 5 days. [ABSTRACT FROM AUTHOR]

A computationally efficient relocatable system for generalized inverse (GI) modeling of barotropic ocean tides is described. The GI penalty functional is minimized using a representer method, which requires repeated solution of the forward and adjoint linearized shallow water equations (SWEs). To make representer computations efficient, the SWEs are solved in the frequency domain by factoring the coefficient matrix for a finite-difference discretization of the second-order wave equation in elevation. Once this matrix is factored representers can be calculated rapidly. By retaining the first-order SWE system (defined in terms of both elevations and currents) in the definition of the discretized GI penalty functional, complete generality in the choice of dynamical error covariances is retained. This allows rational assumptions about errors in the SWE, with soft momentum balance constraints (e.g., to account for inaccurate parameterization of dissipation), but holds mass conservation constraints. While the dynamical calculations involve elevations alone, depth-averaged currents can be directly assimilated into the tidal model with this approach. The efficient representer calculation forms the basis for the Oregon State University (OSU) Tidal Inversion Software (OTIS). OTIS includes software for generating grids, prior model covariances, and boundary conditions; for time stepping the nonlinear shallow water equations to generate a first guess or prior solution; for preliminary processing of TOPEX/Poseidon altimeter data; for solution of the GI problem; and for computation of posterior error bars. Approximate GI solution methods, based on using a reduced set of representers, allow very large datasets to be inverted. OTIS regional and local GI tidal modeling (with grids containing up to 10[sup 5] nodes) require only a few hours on a common desktop workstation. Use of OTIS is illustrated by developing a new regional-scale (1/6°) model of tides in the Indonesian Seas. [ABSTRACT FROM AUTHOR]