Most frequent value‐based factor analysis of direct‐push logging data

Abstract

ABSTRACTAn improved, iteratively re‐weighted factor analysis procedure is presented to interpret engineering geophysical sounding logs in shallow unsaturated sediments. We simultaneously process cone resistance, electric resistivity, and nuclear data acquired by direct‐push tools to give robust estimates of factor variables and water content in unconsolidated heterogeneous formations. The statistical procedure is based on the iterative re‐weighting of the deviations between the measured and calculated data using the most frequent value method famous for its robustness and high statistical efficiency. The iterative approach improves the result of factor analysis for not normally distributed data and extremely noisy measurements. By detecting a strong regression relation between one of the extracted factors and the fractional volume of water, we establish an independent method for water content estimation along the penetration hole. We verify the estimated values of water volume by using a highly over‐determined, quality‐checked interval inversion procedure. The multidimensional extension of the statistical method allows the estimation of water content distribution along both the vertical and the horizontal coordinates. Numerical tests using engineering geophysical sounding data measured in a Hungarian loessy–sandy formation demonstrate the feasibility of the most frequent value‐based factor analysis, which can be efficiently used for a more reliable hydrogeophysical characterisation of the unsaturated zone.