Parameter N Analysis on the Rational-Talbot Algorithm for Numerical Inversion of Laplace Transform

This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions. The set of elementary functions, for which the method is tested, has exponential and oscillatory characteristics. Based on the results obtained, it was concluded that the Rational-Talbot method is e cient for the inversion of decreasing exponential functions. At the same time, to perform the inversion process effectively for trigonometric forms, the algorithm requires a greater amount of terms in the sum. For higher values of N, the technique works well. In fact, this is observed in inverting the functions transform, that combine trigonometric and polynomial factors. The method numerical results have a good precision for the treatment of decreasing exponential functions when multiplied by trigonometric functions.

Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix

We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix. The efficiency of the presented approach is demonstrated by solving some differential equations. Also, this technique is combined with the standard Laplace Homotopy Perturbation Method. The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.

InfPolyn, a Nonparametric Bayesian Characterization for Composition-Dependent Interdiffusion Coefficients

Composition-dependent interdiffusion coefficients are key parameters in many physical processes. However, finding such coefficients for a system with few components is challenging due to the underdetermination of the governing diffusion equations, the lack of data in practice, and the unknown parametric form of the interdiffusion coefficients. In this work, we propose InfPolyn, Infinite Polynomial, a novel statistical framework to characterize the component-dependent interdiffusion coefficients. Our model is a generalization of the commonly used polynomial fitting method with extended model capacity and flexibility and it is combined with the numerical inversion-based Boltzmann–Matano method for the interdiffusion coefficient estimations. We assess InfPolyn on ternary and quaternary systems with predefined polynomial, exponential, and sinusoidal interdiffusion coefficients. The experiments show that InfPolyn outperforms the competitors, the SOTA numerical inversion-based Boltzmann–Matano methods, with a large margin in terms of relative error (10x more accurate). Its performance is also consistent and stable, whereas the number of samples required remains small.

FEATURES OF JOINT INVERSION OF NON-SIMULTANEOUS SIGNALS OF THE RUSSIAN LATERAL SOUNDING AND ELECTROMAGNETIC LOGGING IN CRETACEOUS RESERVOIRS

The article presents the results of the study of the effect of the non-simultaneous measurement of electrical and electromagnetic logging signals on the determination of the parameters of the geoelectric model by joint numerical inversion. The radial profile of the electrical resistivity is calculated for different times after drilling in the program for modeling the process of mud invasion into a porous permeable formation with parameters characteristic of the BS cretaceous reservoir. For this continuous resistivity profile electric log signals are calculated for the reservoir of unlimited thickness.

GEOELECTRIC MODEL OF THE VOSTOCHNO-SURGUTSOE FIELD JURASSIC RESERVOIR ACCORDING TO GALVANIC AND ELECTROMAGNETIC LOGGING SOUNDING DATA

The article presents the results of galvanic and electromagnetic well logs joint numerical inversion. Jurassic deposits are characterized by high contrast of electrical properties, resistivity anisotropy and dielectric polarization, that complicates modeling. Applying of modern methods of joint numerical inversion makes it possible to build detailed geoelectric models corresponding to the measured data in complex geological environments.