Inductive Source Design for Inductive Fracture Detection

Traditional inductive logging uses sources whose focussing input waveform does not change with borehole position. While this arrangement facilitates hardware design, the resolution which it provides varies from formation to formation, and is only accidentally optimal for any given sound position. Optimization theory provides a method for designing a distributed inductive borehole source array , which adaptively maximizes the response from an unknown inclusion in a known formation. The adaptive source waveform shaping can be hardwired or can be simulated using simpler source data. The independent information used for the adaptive focussing can be geometric in nature, such as FMS logs, or can be physical property estimates. Source optimization is particularly important when attempting to detect a subtle feature, such as a fracture in a geothermal field, using triaxial source and triaxial receiver measurements, such as has been suggested in recent literature. A few simple numerical simulations demonstrate why this is so. INTRODUCTION Tripp et al. ( 1999) demonstrate that triaxial source receiver geometry’s and anisotropic formations should be considered for optimal inductive borehole resolution of fracture systems. Unfortunately, the triaxial geometry’s and anisotropic formations offer interpretational difficulties which are not encountered in the conventional uniaxial arrays in isotropic materials. The purpose of this paper is to consider some of these problems and to present a possible means of ameliorating their influence. Moran and Gianzero ( 1979) offer an extensive investigation of multi-component logging in anisotropic material, which illustrates many of the problems which need to be overcome in a successful system. We will discuss some of their observations briefly. Although it is necessary to model the response of anisotropic materials in arbitrary geometries, much can be learned about the problems encountered in inductive fracture detection by studying the response of anisotropic whole spaces, contacts between thick anisotropic beds, or a borehole in a anisotropic whole space. Figure 1 illustrates the coordinate system and the source receiver geometry. For the present section, we assume that the source dipoles are aligned perpendicular and parallel to the bedding. Moran and Gianzero demonstrate that it is possible to develop a complex apparent conductivity (σa) f = σr + i (σx )f , where σr and (σx )f are real quantities. Figure 2 (Moran and Gianzero ) illustrates a nomograph for determining σh , λ, and hence σv from (σa) f for thick beds. Figures 3 to 7 illustrate the effects of bed boundaries and boreholes on the bed conductivity values. It is apparent from these figures that bed boundaries and boreholes can have a significant impact on the accuracy of the formation conductivity estimate.