We will show that microwaves reflected from and transmitted through a porous media have a fractal dimension correlated to that of the porosity. The fractal signature of the scattered microves correlates well with some physical and mechanical properties of porous media. A mathematical model relating the ground penetrating radar record to the mass fractal dimension of the soil structure is also developed.

Plenary Lecture 2:

The Role of Global Optimisation in Oil-Reservoir Production Forecast

Prof. Susana Gómez Gómez
IIMAS. UNAM.

To be able to forecast the production of a reservoir (water and oil), it is necessary to simulate the flux, which implies the characterization of the porous media of the site under study. Using historical data on the pressure and saturation, this problem of coefficient identification, can be solved as an ill- posed inverse continuous least-squares optimisation problem. The optimisation of this inverse problem, may have many local optima with good match to the data, which produce alternative scenarios of production. These alternative solutions also provide a way to deal with the uncertainty of the modelling process. Also, due to the non-continuity of the inverse operator, it is necessary to use regularization methods to get stable solutions in the realistic case of historical data with measurement errors. Our aim here, is the generation of alternative global optimisation methods that obtain the optimal solutions with good match to the data in a stable way, and in reasonable computer time, to produce efficient decision making tools.
We will present here the Parallel Tunneling Global Optimisation method, that performs multiple Levenberg-Marquard type local searches, to produce local optimal solutions with good match. Also, an alternative method to regularize and the need to efficiently scale the problem, will be discussed. The speed and robustness of the method will be shown when tested on synthetic and real reservoirs.

Special Session: Ill-Posed and Inverse Problems: Methods, Algorithms, Computing Software, Applications

Approximation of Cauchy problems for elliptic equations using the method of lines

By Mathias Charton, Hans-Juergen Reinhardt [495-146]

Choice of the regularization parameter in ill-posed problems with rough estimate of the noise level of data

By Uno Hämarik, Toomas Raus [495-171]

Solution of direct and inverse problems for Laplace type equations by GR-method

By Alexandre Grebennikov [495-315]

Session: Probability and Statistical Methods

Borland Pascal Tools for Bootstrapping Dependent Data

By A. Mouiha [495-157]

Spatial correlations in SIR epidemic models

By Henryk Fuks, Ryan Duchesne, Anna T. Lawniczak [495-202]

Blind source separation using wold decomposition and second order statistics

By Masoud Reza Aghabozorgi [495-228]

An alternative approach to modulo-multiplication for Finite Fields using the Itoh-Tsujii Algorithm

Numerical analysis of 3D boundary inverse conductivity problems for anisotropic media

Mathematical modeling and computer simulation of the Ia monosynaptic reflex fluctuations

Efficient Solutions to a Class of Generalized Time-Dependent Combinatorial Optimization Problems

By Luis H. García I., Jose F. Solis V.,Ramón Soto C., Omar J. Santos S. [495-320]

Mathematical simulation of concomitant nitride layers produces by diffusion processes

Session: Differential and Integral Equations and Applications

Traveling waves in a one-dimensional global model of synaptic activity in the cerebral cortex

Modified Theories of Laminar Flow Around a Rigid Cylinder and Flow Outside and Inside a Liquid Cylinder in Uniform and Counterflow Gaseous Jets

Chebyshev Functions and their use for two-dimensional electrostatic problems in elliptic coordinates

Certification of directional derivatives computed by automatic differentiation

Distributional LK transform, Distributional Impulsive Signals and System Response

A Study of the Periodical Oscillations for a Time Series Using the Fourier Transform

Piecewise polynomial approximations for weakly singular integral equations with discontinuous coefficients

Discrete Graphic Markov Model selection by a Genetic Algorithm: empirical comparison of two Fitting Convex Functions

Numerical Algorithm for Solving a Stationary Transport Equation
By Nikos Mastorakis, Olga Martin [495-234]