Paper e

Reconciling Differences in Depth of Investigation Between 2-MHz Phase Shift and Attenuation Resistivity Measurements

Tarek Habashy and Barbara Anderson

Schlumberger

Abstract

2-MHz logging while drilling tools measure the phase shift and attenuation of electromagnetic waves. The measurements are normally calibrated to resistivity and displayed as two separate resistivity logs with different depths of investigation. The phase shift is rep­resented as a shallow measurement, and the attenuation as a deep measurement. Together the two curves are used to interpret invasion and to establish true formation resistivity.

It has been shown empirically by modeling tool response in invaded formations that the phase shift measurement is consistently shallower than the attenuation measurement. However, it has also been claimed that it is counter-intuitive for the phase shift and attenuation of the same wave to have different depths of investigation.

In this paper, we first examine forward modeling results that demonstrate the dual depth of investigation  phenomenon, and then we present a theoretical analysis to study the depths of investigation of the measured phase shift and attenuation. The measured signal is formulated in terms of a convolution-type integral over the conductivity distribu­tion of the formation. The kernel of this convolution-type operator is computed beyond traditional geometrical factor theory, since higher order scattering terms are included in its derivation. This formulation substantiates by physical principles the differences in depths of investigation previously demonstrated by empirical calculations.