摘要:

Using a unified approach, expressions are derived for the various pole positions and other dipole parameters for the centered and eccentric dipole models of the earth's magnetic field. The pole positions and other parameters are then calculated using the 1945–1985 International Geomagnetic Reference Field Gauss coefficients and coefficients from models of the earth's field for earlier epochs. Comparison is made between (1) the recent pole positions and those pertaining since 1600 and (2) the various theoretical pole positions and the observed dip pole position

ISSN:8755-1209    

DOI:10.1029/RG025i001p00001

年代:1987

数据来源: WILEY

摘要:

The traditional least squares method for modeling seamount magnetism is often unsatisfactory because the models fail to reproduce the observations accurately. We describe an alternative approach permitting a more complex internal structure, guaranteed to generate an external field in close agreement with the observed anomaly. Potential field inverse problems like this one are fundamentally incapable of a unique solution, and some criterion is mandatory for picking a plausible representative from the infinite‐dimensional space of models all satisfying the data. Most of the candidates are unacceptable geologically because they contain huge magnetic intensities or rapid variations of magnetization on fine scales. To avoid such undesirable attributes, we construct the simplest type of model: the one closest to a uniform solution as measured by the norm in a specially chosen Hilbert space of magnetization functions found by a procedure called seminorm minimization. Because our solution is the most nearly uniform one we can say with certainty that any other magnetization satisfying the data must be at least as complex as ours. The theory accounts for the complicated shape of seamounts, representing the body by a covering of triangular facets. We show that the special choice of Hilbert space allows the necessary volume integrals to be reduced to surface integrals over the seamount surface, and we present numerical techniques for their evaluation. Exact agreement with the magnetic data cannot be expected because of the error of approximating the shape and because the measured fields contain noise of crustal, ionospheric, and magnetospheric origin. We examine the potential size of the various error terms and find that those caused by approximation of the shape are generally much smaller than the rest. The mean magnetization is a vector that can in principle be discovered from exact knowledge of the external field of the seamount; this vector is of primary importance for paleomagnetic work. We study the question of how large the uncertainty in the mean vector may be, based on actual noise, as opposed to exact, data; the uncertainty can be limited only by further assumptions about the internal magnetization. We choose to bound the rms intensity. In an application to a young seamount in the Louisville Ridge chain we find that remarkably little nonuniformity is required to obtain excellent agreement with the observed anomaly while the uniform magnetization gives a poor fit. The paleopole position of ordinary least squares solution lies over 30° away from the geographic north, but the pole derived from our seminorm minimizing model is very near the north pole as it should be. A calculation of the sensitivity of the mean magnetization vector to the location of the magnetic observations shows that the data on the perimeter of the survey were given the greatest weight and suggests that enlargement of the survey area might further improve the reliability of the resul

ISSN:8755-1209    

DOI:10.1029/RG025i001p00017

年代:1987

数据来源: WILEY

摘要:

Long‐range acoustic propagation for ocean tomography is elegantly described by invoking a Hamiltonian formulation. Many results previously derived in an ad hoc manner emerge naturally from the use of the Hamiltonian. The cycling between the upper and lower ocean that is characteristic of oceanic sound propagation is treatable as a libration phenomenon. General perturbation methods, highly developed in astronomy and quantum mechanics, are immediately available for understanding both range independent and range dependent disturbances to a reference profile. The tomographic two‐point boundary value problem leads, in an analogy to the old Bohr quantum mechanics, to quantization of the action, although the more naturally quantized variable is the canonical angle. An adiabatic approximation merges naturally from the formalism. In the adiabatic approximation the range dependent bias problem in tomography can be fully understood and accounted for as long as the source and the receiver remain ax

ISSN:8755-1209    

DOI:10.1029/RG025i001p00041

年代:1987

数据来源: WILEY

摘要:

This synthesis links many seismic and tectonic processes at subduction zones, including great subduction earthquakes, to the sinking of subducted plate. Earthquake data and tectonic modeling for subduction zones indicate that the slab pull force is much larger than the ridge push force. Interactions between the forces that drive and resist plate motions cause spatially and temporally localized stresses that lead to characteristic earthquake activity, providing details on how subduction occurs. Compression is localized across a locked interface thrust zone, because both the ridge push and the slab pull forces are resisted there. The slab pull force increases with increasing plate age; thus because the slab pull force tends to bend subducted plate downward and decrease the force acting normal to the interface thrust zone, the characteristic maximum earthquake at a given interface thrust zone is inversely related to the age of the subducted plate. The 1960 Chile earthquake (Mw9.5), the largest earthquake to occur in historic times, began its rupture at an interface bounding oceanic plate<30 m.y. old. However, this rupture initiation was associated with the locally oldest subducting lithosphere (weakest coupling); the rupture propagated southward along an interface bounding progressively younger oceanic lithosphere, terminating near the subducting Chile Rise. Prior to a great subduction earthquake, the sinking subducted slab will cause increased tension at depths of 50–200 km, with greatest tension near the shallow zone resisting plate subduction. Plate sinking not only leads to compressional stresses at a locked interface thrust zone but may load compressional stresses at plate depths of 260–350 km, provided that the shallow sinking occurs faster than the relaxation time of the deeper mantle. This explains K. Mogi's observations ofM≥ 7 thrust earthquakes at depths of 260–350 km, immediately downdip and within 3 years prior to five great, shallow earthquakes of northern Japan. The slab pull model explains the lower layer of double seismic zones as due to tension from the deeper, sinking plate and the upper layer as due to localized in‐plate compression, as plate motion is resisted by the bounding mantle. Just downdip of the interface thrust zone, there occurs an aseismic 20°–50° dip increase of subducted plate. This slab bend reflects the summed slab pull force of deeper plate and probably is at the crustal basalt to eclogite phase change. Resistance to subduction provided by a continually developing slab bend may be an important factor in the size of slab pull force delivered to an interfac

ISSN:8755-1209    

DOI:10.1029/RG025i001p00055

年代:1987

数据来源: WILEY

摘要:

During the last 35 years, well over 100 algorithms for modeling advection processes have been described and tested. This review summarizes the development and improvements that have taken place. The nature of the errors caused by numerical approximation to the advection equation are highlighted. Then the particular devices that have been proposed to remedy these errors are discussed. The extensive literature comparing transport algorithms is reviewed. Although there is no clear cut “best” algorithm, several conclusions can be made. The judicious use of simple finite difference schemes (second‐order time differences and even‐order (>2) spatial differences) provides a minimum level of accuracy that is suitable for many atmospheric applications. More complex schemes can yield a significant improvement in accuracy, but sometimes at great computational expense. Spectral and pseudospectral techniques consistently provide the highest degree of accuracy, but expense and difficulties assuring positive mixing ratios are serious drawbacks. Schemes which consider fluid slabs bounded by grid points (volume schemes), rather than the simple specification of constituent values at the grid points, provide accurate positive definite results. The computer memory requirements of the volume schemes can be excessive. Recent attempts to maxmize accuracy while keeping cost low have lead to such useful schemes as the one proposed by P. K. Smolar

ISSN:8755-1209    

DOI:10.1029/RG025i001p00071

年代:1987

数据来源: WILEY