ABSTRACT:

A type of anisotropy often observed in shales is vertical transverse isotropy (VTI) or polar anisotropy. This type of anisotropy can be quantified by estimating the three Thomsen parameters epsilon (e?), delta (d), and gamma (¿). Here, we describe a new algorithm applied to borehole sonic data that transforms the compressional, fast-shear, slow-shear, and Stoneley slownesses measured with respect to the borehole axes to anisotropic moduli referred to the earth anisotropy axes. The algorithm yields up to 4 anisotropic moduli of an orthorhombic or transversely-isotropic (TI) formation. We demonstrate this method on borehole sonic data recorded with a new generation crossed-dipole sonic tool in a vertical well and a horizontal well penetrating a shale formation (the Barnett shale in Texas). Analysis of both these data provides a measure of all five anisotropic moduli. These results demonstrate that this shale is a transversely-isotropic formation with mild anelliptic behavior.

1. INTRODUCTION

Anisotropy plays a key role in the processing and interpretation of seismic data. Failure to account for its presence can lead to errors in prestack depth migration, amplitude variation with offset (AVO), and hydraulic fracture monitoring. A type of anisotropy often observed in shales is vertical transverse isotropy (VTI) or polar anisotropy. This type of anisotropy can be quantified by estimating the three Thomsen parameters epsilon (e), delta (d), and gamma (¿) [1]. Methods for estimating these parameters (and in particular epsilon and delta) have utilized trial and error scanning after migrating with the well velocities, tomographic inversion using well misties as a constraint, and measuring these parameters directly from walkaway VSP, multi-offset VSP, or multi-azimuthal VSP recordings [2,3]. The latter method has been used to update anisotropic models for prestack depth migration. Although it is recognized that walkaway VSPs can provide an important calibration point for refining anisotropic models, such data is not always available. Various conditions may limit the ability to record VSPs. The logistics of performing such a survey can be a prohibitive factor as well as the cost of these surveys. This begs the question: Can sonic data provide a measurement of the formation anisotropy parameters? Here, we describe a new algorithm that transforms the compressional, fast-shear, slowshear, and Stoneley slownesses measured with respect to the borehole axes to anisotropic moduli referred to the earth anisotropy axes. The algorithm yields up to 4 anisotropic moduli of an orthorhombic or transversely-isotropic (TI) formation using a single well sonic data with known deviation from the vertical and true stratigraphic dip from an imaging tool. he impact of vertical transverse isotropy (VTI) on sonic measurements is well known. Shales typically exhibit this type of anisotropy and it is in these formations where we observe the effect on sonic measurements. Hornby examined compressional slownesses recorded in three Alaskan wells that penetrated a shale formation at different angles ranging from vertical to 60°.He observed that compressional slowness varied considerably in the shale intersected by the three wells [4]. As expected, the compressional slowness decreased as well deviation increased.

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