Statistically Partitioning of Well Logs and Core Measurements to Detect and Quantify Petrophysical Properties

The subsurface is a mixture of geologic rock constituents such as sandstones, carbonates,and shales, among others. Well logs can indirectly identify these rock constituents. Mostinterpretation methods used in log analysis require some form ofa priorior previousknowledge about the physical response of rocks. This thesis developed a new methodof interpreting well log responses that uses statistical properties of the measurements toeliminate the need for a priori geologic knowledge.Well logs or core measurements, represented as a two–dimensional histogram, are mod-eled as a joint normal distribution (JND), also referred to as a two-dimensional Gaussiandistribution. Assuming that the measurements are Gaussian, enables their parametric rep-resentation. A data set with several rock populations fit the model using the superposition of multiple JNDs —one for each population. Each population is assumed to be normallydistributed, or can be transformed into a normal distribution. I use the Microsoft ExcelSolver to minimize the sum of the square errors between measurements and their predic-tions based on statistical populations. This process determines the unknown values of themean, standard deviation, correlation coefficient, and fraction for each population. I thentransform the model into log space, with the use of Bayes’ Theorem, to create a log of theprobability of occurrence for each population.This method provides a computationally efficient way to identify rock populations, withoutprevious geologic knowledge. A desktop computer, with two 2 GHz processors and threeGB RAM, can optimize 5,000 ft of well log data in less than one minute. I then use thestatistical model to quantify the probability of a geologic population. I test the model usinga combination of synthetic data with known parameters. It is found that the correlationof the populations only impacts the interpretation of highly correlated data. Applicationof the method to a variety of field data produces results consistent with standard well–loginterpretation procedures and core measurements.