Reservoir evaluation through optimally designed resistivity logging

In search of hydrocarbon, logging tools have been used over the years to provide information about underground formations. In particular, electromagnetic devices, such as galvanic and induction tools, have played a preponderant role in the determination of movable and residual hydrocarbon. A logging technology requires consideration of two major aspects: the design of the instrument and the interpretation of its measurements. In dealing with tool design, the designer searches for measurements that provide optimal resolution. In dealing with interpretation (inversion), formation parameters must be derived from the acquired data.; A new philosophy for design and interpretation is proposed based on a quantitative measure of resolution. It involves all components characterizing the logging technology: the acquisition scheme, the data, the model of data noise, the measuring device, the geological objects, as well as the interpretation technique. This philosophy allows for deriving a design methodology that leads to optimal tool resolution. In addition, it provides an upper limit to the accuracy of the interpretation results which can be studied up front without actually performing it.; The processes of design and interpretation requires of algorithms that link both the data and the model spaces. For this purpose, the spectral decomposition analysis (SDA) has been developed and used as a universal technique throughout the dissertation. Based on the SDA several algorithms and their related software have been developed and used to study the resolution, design, and inversion of logging measurements.; The developed techniques have been applied to the analysis, optimization, and interpretation of multi-sensor logging devices. An optimal resolution design principle has been applied to the optimization of an array of induction coils. The resolution of two direct current arrays, focused and differential, has been studied. The proposed inversion technique has also been applied to both arrays. Inversion results prove the superiority of the differential array. A number of inversion examples applied to synthetic and field data are presented that validate the inversion technique.