A poincaré model for the earth's fluid core

Abstract

The superconducting-gravimeter data of Melchior and Ducarme (1986) has been interpreted as internal motion in the Earth's core by Aldridge and Lumb (1987) using a Poincaré model. Several low-order modes with periods of 13–16 hours have been tentatively identified in the core which is taken to be an incompressible, homogeneous fluid within a rigid, rotating container. The identification is based on asymptotic values of the frequencies which change slowly with time while the modes decay with an e-folding time of about 280 days. The slow change in frequency with time implies a small temporal variation in the rotation rate of the core. This mean flow is a nonlinear effect often observed in laboratory experiments designed to excite Poincaré modes. Interaction among modes during free ringdown is also observed in those experiments and apparently in the data of Melchior et al. (1988) as well. Laboratory work thus provides the link to extend the Poincaré model to include viscous and nonlinear effects in order to interpret the gravimetric observations as core modes.     

Mixed layer depth front and subduction of low potential vorticity water under seasonal forcings in an idealized OGCM

The mixed layer depth (MLD) front and subduction under seasonal variability are investigated using an idealized ocean general circulation model (OGCM) with simple seasonal forcings. A sharp MLD front develops and subduction occurs at the front from late winter to early spring. The position of the MLD front agrees with the curve where \({\rm D}T_{\rm s}/{\rm D}t = \partial T_{\rm s} /\partial t + {\user2{u}}_{\rm g} \cdot \nabla T_{\rm s} = 0\) is satisfied (t is time, \({\user2{u}}_{\rm g}\) is the upper-ocean geostrophic velocity, \(T_{\rm s}\) is the sea surface temperature (SST), and \(\nabla\) is the horizontal gradient operator), indicating that thick mixed-layer water is subducted there parallel to the SST contour. This is a generalization of the past result that the MLD front coincides with the curve \({\user2{u}}_{\rm g} \cdot \nabla T_{\rm s} = 0\) when the forcing is steady. Irreversible subduction at the MLD front is limited to about 1 month, where the beginning of the irreversible subduction period agrees with the first coincidence of the MLD front and \({\rm D}T_{\rm s}/{\rm D}t =0\) in late winter, and the end of the period roughly corresponds to the disappearance of the MLD front in early spring. Subduction volume at the MLD front during this period is similar to that during 1 year in the steady-forcing model. Since the cooling of the deep mixed-layer water occurs only in winter and SST can not fully catch up with the seasonally varying reference temperature of restoring, the cooling rate of SST is reduced and the zonal gradient of the SST in the northwestern subtropical gyre is a little altered in the seasonal-forcing case. These effects result in slightly lower densities of subducted water and the eastward shift of the MLD front.     

Improvement of the geoid in local areas by satellite gradiometry

Summary Satellite gradiometry is studied as a means to improve the geoid in local areas from a limited data coverage. Least-squares collocation is used for this purpose because it allows to combine heterogeneous data in a consistent way and to estimate the integrated effect of the attenuated spectrum. In this way accuracy studies can be performed in a general and reliable manner. It is shown that only three second-order gradients contribute significantly to the estimation of the geoidal undulations and that it is sufficient to have gradiometer data in a 5°×5° area around the estimation point. The accuracy of the geoid determination is strongly dependent on the degree and order of the reference field used. An accuracy of about ±1 m can be achieved with a reference field of (12, 12). There is an optimal satellite altitude for each reference field and this altitude may be higher than 300 km for a field of low degree and order. The influence of measuring errors is discussed and it is shown that only gradiometer data with accuracies better than ±0.05 E will give a significant improvement of the geoid. Finally, some results on the combination of satellite gradiometry and terrestrial gravity measurements are given. The proposed method seems to be well suited for local geoid determinations down to the meter range. It is especially interesting for unsurveyed and difficult areas because no terrestrial measurements are necessary. Furthermore, it has the practical advantage that only a local data coverage is needed.     

Was the M<Subscript>w</Subscript> 7.5 1952 Kern County,California, earthquake induced (or triggered)?

Several recent studies have presented evidence that significant induced earthquakes occurred in a number of oil-producing regions during the early and mid-twentieth century related to either production or wastewater injection. We consider whether the 21 July 1952 M_w 7.5 Kern County earthquake might have been induced by production in the Wheeler Ridge oil field. The mainshock, which was not preceded by any significant foreshocks, occurred 98 days after the initial production of oil in Eocene strata at depths reaching 3 km, within ~1 km of the White Wolf fault (WWF). Based on this spatial and temporal proximity, we explore a potential causal relationship between the earthquake and oil production. While production would have normally be expected to have reduced pore pressure, inhibiting failure on the WWF, we present an analytical model based on industry stratigraphic data and best estimates of parameters whereby an impermeable splay fault adjacent to the main WWF could plausibly have blocked direct pore pressure effects, allowing the poroelastic stress change associated with production to destabilize the WWF, promoting initial failure. This proof-of-concept model can also account for the 98-day delay between the onset of production and the earthquake. While the earthquake clearly released stored tectonic stress, any initial perturbation on or near a major fault system can trigger a larger rupture. Our proposed mechanism provides an explanation for why significant earthquakes are not commonly induced by production in proximity to major faults.     

Effect of spatial resolution on regionalization of hydrological model parameters

Lack of availability of historical data series is one of the major hindrances in hydrological modelling. Regionalization of hydrological model parameters is one of the solutions to obtain the parameters for ungauged basins. Recently, lots of methodologies have been developed. They can be categorized as model calibration then fitting regression between model parameters and catchments characteristics, using some kind of transfer function. The aim of this study was to compare different regionalization methods as well as to look how the spatial resolution affects regionalization. In this study, a modified Lipschitz and monotony condition was used for regionalization. To identify the effect of the model resolution, the parameters of a distributed and semi‐distributed version of the Hydrologiska Byråns Vattenbalansavdelning (HBV) model were regionalized. The study was conducted at the upper Neckar catchment of southwest Germany. It has been found that the combination of Lipschitz and monotony condition has performed reasonably. It has been seen that the distributed model structure has outperformed the semi‐distributed model structure. It shows under present data conditions that higher model resolution can describe processes of ungauged basins reasonably. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of Photoelectric Occultations and Development of a Digital Model of the Lunar Libration Zone

Astronomy Reports - One of the priority tasks of modern astronomy is the observation and study of transient celestial processes, which also concerns photoelectric observations of lunar occultations...     

Planetons: An example of large amplitude solitary waves

Abstract

The term ‘‘solitary wave'’ is usually used to denote a steadily propagating permanent form solution of a nonlinear wave equation, with the permanency arising from a balance between steepening and dispersive tendencies. It is known that large-scale thermal anomalies in the ocean are subject to a steepening mechanism driven by the beta effect, while at the smaller deformation scale, such phenomena are highly dispersive. It is shown here that the evolution of a physical system subject to both effects is governed by the ‘‘frontal semi-geostrophic equation'’ (FSGE), which is valid for large amplitude thermocline disturbances. Solitary wave solutions of the FSGE (here named planetons) are calculated and their properties are described with a view towards examining the behavior of finite amplitude solitary waves. In contrast, most known solitary wave solutions belong to weakly nonlinear wave equations (e.g., the Korteweg—deVries (KdV) equation).

The FSGE is shown to reduce to the KdV equation at small amplitudes. Classical sech² solitons thus represent a limiting class of solutions to the FSGE. The primary new effect on planetons at finite amplitudes is nonlinear dispersion. It is argued that due to this effect the propagation rates of finite amplitude planetons differ significantly from the ‘‘weak planeton'', or KdV, dispersion relation. Planeton structure is found to be simple and reminiscent of KdV solitons. Numerical evidence is presented which suggests that collisions between finite amplitude solitary waves are weakly inelastic, indicating the loss of true soliton behavior of the FSGE at moderate amplitudes. Lastly, the sensitivity of solitary waves to the existence of a nontrivial far field is demonstrated and the role of this analysis in the interpretation of lab experiments and the evolution of the thermocline is discussed.