Uncertainty reduction of interval inversion estimation results using a factor analysis approach

Abstract

This paper aims to investigate the impact of the overdetermination (data-tounknowns) ratio on the global inversion of wireline logging data. In the course of the so-called interval inversion method, geophysical data measured in a borehole over a longer depth range is jointly inverted and the depth variation of the investigated petrophysical parameters are expanded into series using Legendre polynomials as basis functions resulting in a highly overdetermined inverse problem. A metaheuristic Particle Swarm Optimization (PSO) approach is applied as a first phase of inversion for decreasing the starting model dependence of the interval inversion procedure. In the subsequent linear inversion steps, by using the measurement error of logging tools and the covariance matrix of the estimated petrophysical parameters, we can quantify the accuracy of the model parameters.The dataset used in this study consists of nuclear, resistivity and sonic logs which are inverted to compute porosity, shale volume and water saturation along the investigated interval. For increasing the data-to-unknowns ratio of the inverse problem, shale volume is estimated separately by a PSO-based factor analysis and fixed as known parameter for the interval inversion process. Since the shale volume has been described as high degree Legendre polynomial, a significant increase of the overdetermination ratio considerably decreases the uncertainty of the remaining model parameters allowing for a more reliable calculation of hydrocarbon content.

Permeability extraction from multiple well logs using particle swarm optimization based factor analysis

“…Global optimization tools like PSO, SA and genetic algorithms can be effectively combined with linearized inversion techniques to solve such an inverse problem. By the successive application of the PSO technique and the interval inversion method, not only the computer processing time of PSO inversion can be reduced, but there is a possibility to calculate the estimation errors of petrophysical properties from the Jacobi matrix generated in a given linear inversion step (Abordán and Szabó 2020;Szabó and Dobróka 2020).…”

“…Previous studies show that the first statistical factor correlates well with the shale content of various geological formations (Szabó 2011;Szabó and Dobróka 2013;Puskarczyk et al 2015;Puskarczyk 2020;Abordán and Szabó 2020). Advanced mathematical approaches have been developed to extract the shale volume from well logs as efficient as possible.…”

“…The independence of results on the random initial particle positions in PSO algorithm has been earlier investigated in the context of inverse problem solutions (Abordán and Szabó 2020). To find the regression relationship between the first factor found by the FA-PSO method and decimal logarithm of absolute permeability, we properly scale the former into the range of 0 to 1.…”

Innovative Hydrogeophysical Approaches as Aids to Assess Hungarian Groundwater Bodies

“…The porosity, watersaturation, shale content and the fractional volume of rock matrix were earlier estimated by the interval inversion method [66], which allowed not just the automated determination of volumetric parameters, but the layer-boundaries, some zone parameters (i.e., physical properties of fluid and matrix components, textural properties, such as Archie's constants and other functional constants of probe response equations) as well as the uncertainty of the estimated model parameters. An application for the cooperative use of inverse modeling and factor analysis was published [67], which showed the advantages of the joint application of these two approaches for more accurate and reliable reservoir characterization.…”

Correlation Analysis and Application of Respiratory and Lung Diseases in Pediatrics of Traditional Chinese Medicine Based on Factor Analysis Method

“…It is very important to analyze the soil quality factors and quantitatively evaluate the soil quality in karst rocky desertification areas for providing the living conditions [16]. In selecting excellent genes of plants, the relationship between complex factors and variables can also be studied by factor analysis, and finally, seeds with good fruit quality can be selected [17][18][19][20]. Using different ultraviolet spectra, factor analysis was adopted to measure some antibacterial drugs [21].…”