Franklin G. Horowitz

Time-dependent, irreversible entropy production and geodynamics

We present an application of entropy production as an abstraction tool for complex processes in geodynamics. Geodynamic theories are generally based on the principle of maximum dissipation being equivalent to the maximum entropy production. This represents a restriction of the second law of thermodynamics to its upper bound. In this paper, starting from the equation of motion, the first law of thermodynamics and decomposition of the entropy into reversible and irreversible terms,1 we come up with an entropy balance equation in an integral form. We propose that the extrema of this equation give upper and lower bounds that can be used to constrain geodynamics solutions. This procedure represents an extension of the classical limit analysis theory of continuum mechanics, which considers only stress and strain rates. The new approach, however, extends the analysis to temperature-dependent problems where thermal feedbacks can play a significant role. We apply the proposed procedure to a simple convective/conductive heat transfer problem such as in a planetary system. The results show that it is not necessary to have a detailed knowledge of the material parameters inside the planet to derive upper and lower bounds for self-driven heat transfer processes. The analysis can be refined by considering precise dissipation processes such as plasticity and viscous creep.

Improved edge detection in potential field maps and graphical estimation of depth-to-the-top

Summary We present an algorithm that improves the detection of minor anomalies and patterns in potential field maps. Its use in conjunction with standard edge detection algorithms provides a tool for visual estimation of depth-to-the-source in gravity and magnetic maps.

A Fast, Spatial Domain Technique for Terrain Corrections in Gravity Field Modelling

A fast computation of terrain corrections requires (1) a quick forward algorithm, and (2) a strategy for organising the data in a computer program. In this paper we present some new ideas on (1). The discussion of (2) is very brief. The proposed method is a space domain method, similar to prism integration, but quicker and more flexible. We show that the method works both in the flat-Earth geometry and in the spherical Earth geometry. The “elementary body” of the mass density model is an infinitely thin, horizontal and homogenous rectangular lamina.

Earthworms; "multiscale" edges in the EGM96 global gravity field

Summary We perform edge detection on the EGM96 global geodetic gravity field. The technique is in accord with our wavelet based multiscale edge analysis, which is valid for a flatearth approximation. For the spherical earth, it is not clear that the technique yields a formal wavelet transform. However, spherical results appear as interpretable as the flat-earth results at short scales. In Australia, we find general agreement with the flat-earth results, and note a correlation between results from seismic tomography and our present work.

Fast, Spatial Domain Potential Field Modeling

In this contribution we propose an alternative method to the traditional spatial domain technique of prism integration in potential field modeling. The advantages and disadvantages of prism integration as compared to e.g. Fourier methods or wavelet methods are well known. Our aim is to improve the main disadvantages of the space domain methods in order to make them an attractive alternative to FFT based techniques. Our long-range goal is to enhance the flexibility in the complexity of source distribution that can be handled, as well as to significantly improve the computational speed. However, these goals must be achieved without compromising the accuracy of the computed potential field signal. The first numerical experiments reported here were successful in all respects.

Application of wavelet theory to the analysis of gravity data.

Summary. The fundamental equations of potential field theory have an interesting interpretation when regarded as a particular case of a multiscale wavelet transform. This allows the implementation of algorithms for image processing and inversion in a parameterisation that is geologically natural and meaningful.