http://hdl.handle.net/2122/288 Search the Channel search http://www.earth-prints.org/simple-search http://hdl.handle.net/2122/3979 Title: Source ambiguity from an estimation of the scaling exponent of potential field power spectra <br/> <br/>Authors: Quarta, T.; Dipartimento di Scienza dei Materiali, via per Arnesano, 73100 Lecce, Italy; Fedi, M.; Dipartimento di Geofisica e Vulcanologia, L.go S. Marcellino 10, 80138 Napoli, Italy; De Santis, A.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia <br/> <br/>Abstract: An analysis of the field scaling power spectrum yields useful information about the source distribution, but it is uncertain whether deterministic, random, fractal or mixed approaches have to be used for the interpretation. To this end, the scaling properties of potential field spectra are analysed for a number of different source models of geological interest. Besides the models of Naidu (purely random sources) and Spector and Grant (gross block statistical ensembles) we consider other types of density and magnetization distributions with spectral exponents in the fractal range, such as a single homogeneous body with a random white source distribution. Spectral slopes in the fractal range are obtained. We also study the effects of important natural sources, such as salt domes and sedimentary basins, representing them with simple Gaussians or combinations of Gaussian signals. The same spectral slopes as for gravity signals generated by 3-D fractal source distributions are found for them. Hence the power law decay of the field is not a characteristic only of fractal source models. If a 3-D fractal source distribution is assumed a priori, a way of verifying the goodness of the model is to examine the whitened field at source level. The probability that the whitened field derives from a random white population is estimated for synthetic and real anomalies by applying the usual statistical tests. Fri, 29 Oct 1999 22:58:59 GMT http://hdl.handle.net/2122/3978 Title: A discussion of the uniqueness of a Laplacian potential when given only partial field information on a sphere <br/> <br/>Authors: Lowes, F. J.; Physics Department, University of Newcastle, Newcastle upon Tyne NE1 7RU, UK; De Santis, A.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia; Duka, B.; Faculty of Natural Sciences, Department of Physics, University of Tirana, Tirana, Albania <br/> <br/>Abstract: For a vector field defined by a scalar potential outside a surface enclosing all the sources, it is well known that the potential is defined uniquely if either the potential itself, or its derivative normal to the surface, is known everywhere on the surface. For a spherical surface, the normal derivative is the radial component of the field; the horizontal (vector) component of the field also gives uniqueness (except for any monopole contribution). This paper discusses the way other partial information of the field on the spherical surface can give a unique, or almost unique, knowledge of the external potential/field, bringing together and correcting previous work. For convenience the results are given in the context of the geomagnetic field B. This is often expressed in terms of its local Cartesian components (X, Y, Z), equivalent to (-Bθ, BΦ, -Br); it can also be expressed in terms of Z and the vector horizontal component H = (X, Y). Alternatively, local "spherical polar" components (F, I, D) are used, where F = |B|, the inclination I is the angle in the vertical plane downward from H to B, and the declination D is the angle in the horizontal plane eastward from north to H. Knowledge of X over the sphere gives a complete knowledge of the potential, apart from that of any monopole (which is zero in geomagnetism), and Y gives the potential except for any axially symmetric part (which can be provided by a knowledge of X along a meridian, or of H along any path from pole to pole). In terms of (F, I, D) the situation is more complicated; either F or the total angle (I, D) needs to be known throughout a finite volume; for the latter, this paper shows how, in principle, the actual potential can be determined (except for an unknown scaling factor). Similarly D on the sphere also needs a knowledge of |H| on a line from (magnetic) pole to pole. We also discuss how these various properties affect the determination, by surface integration, of the Gauss coefficients of the field representation in terms of spherical harmonics. Sat, 29 Oct 1994 22:58:59 GMT http://hdl.handle.net/2122/3977 Title: A simple approach to the transformation of spherical harmonic models under coordinate system rotation <br/> <br/>Authors: De Santis, A.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia; Torta, J. M.; Observatori de l'Ebre, CSIC, 43520 Roquetes, (Tarragona), Spain; Falcone, C.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma1, Roma, Italia <br/> <br/>Abstract: The transformation of a set of spherical harmonic coefficients characterizing a model of the geomagnetic field, or a general function defined on a sphere, subject to a rotation of the coordinate system, is given by the direct relations between the coefficients and then by using a numerical approach. The parameters for a pair of such rotations (from one set to another, and vice versa) are given, along with a few examples of their application. The method is particularly useful for the comparison of geophysical characteristics derived from models developed under different coordinate systems. It offers a practical solution to the problem, which can be implemented without difficulty. Sun, 29 Oct 1995 22:58:59 GMT http://hdl.handle.net/2122/3976 Title: Translated origin spherical cap harmonic analysis <br/> <br/>Authors: De Santis, A.; Istituto Nazionale di Geofisica, Roma, Italia <br/> <br/>Abstract: The method of spherical cap harmonic analysis (SCHA), due to Haines (1985) is appropriate for regional geomagnetic field modelling as it includes the required potential field constraints and, for a given number of model parameters, describes shorter wavelength features than a global spherical harmonic model. If the origin of the coordinate system is moved from the centre of the Earth towards the surface then the Earth's surface is no longer equidistant from the origin. At the Earth's surface the minimum wavelength described by a SCH model in the new coordinate system is smaller at the centre of the region than at the edge. This method of translated origin spherical cap harmonic analysis (TOSCA) has been applied to regional field modelling for Italy. The method is able to take advantage of the dense distribution of data at the centre of region and the model effectively smooths towards the periphery. The performance of the TOSCA model is discussed in relation to a model derived using conventional SCHA. Mon, 29 Oct 1990 22:58:59 GMT