Determination of Shear Wave Velocities in "Slow" Formations

Direct determination of formation shear wave travel time is impossible in "slow" formations where the shear wave velocity is lower than the borehole fluid (mud) velocity. However, the Stoneley waves in these formations are very sensitive to changes in formation shear wave properties and can be used to indirectly determine the formation shear velocity, In addition, the P wave packet is highly dependent on the Poisson's ratio and thus can be used to estimate the shear velocity once the P wave velocity is known. These phenomena are demonstrated with both numerical and field examples.Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortiu

Full Waveform Acoustic Logging - From Theory To Applications

This report contains results from the third year of the Full Waveform Acoustic Logging Consortium and rock physics studies at M.J.T. This year marks the completion of the first phase of the project which has been directed primarily to the understanding of the basic theoretical aspects of acoustic waves in a borehole. With such a background we are ready to emphasize applications as well as to undertake special problems which require new and different theoretical approaches. As examples of the latter, we can mention uncentered tools, vertical fractures around boreholes, thinly bedded formations and anisotropy. The third year studies fall into four general areas: theoretical aspects of wave propagation in the borehole, applications to the characterization of formations, integrated log analysis and physical properties of sedimentary rocks relevant to logging. There are fifteen papers in this report which discuss individual topics in detail. In this introduction we summarize the major points and also list the potential applications of full waveform acoustic logs and future directions of our research

Propagation Of Flexural Waves In An Azimuthally Anisotropic Borehole Model

Flexural waves generated by a dipole source have been studied theoretically and used to estimate the shear parameters of a formation. The basic principles and main properties of flexural waves propagating in a borehole are reviewed in this paper. A mono/dipole transducer made of a PZT piezoelectric tube is used for laboratory experiments in borehole models. The radiation pattern of the dipole source is measured in a water tank. In order to simulate the hard and soft formations, measurements are performed in borehole models made of aluminum and lucite, respectively. Experimental results are in good agreement with the theoretical dispersion characteristics. Measurements are also performed with the transducers in an azimuthally anisotropic borehole model made of Phenolite XX-324. Both fast and slow flexural waves with different velocities are generated by a dipole source in the model. The flexural waves are related to the fast or slow shear waves in the anisotropic material. Experimental results show that the flexural wave splits into a fast and a slow component in an azimuthally anisotropic borehole; therefore, dipole acoustic well logging could be an effective means for estimating a formation's anisotropy.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumUnited States. Dept. of Energy (Grant DE-FG0286ER13636

Borehole Wave Propagation In Isotropic And Anisotropic Media III: Anisotropic Formation

In this paper we extend the 3-D finite difference method to simulate wave propagations in an anisotropic medium. The scheme is tested in the homogeneous medium. The finite difference results agree excellently with the analytic solutions of a point force source in the transversely isotropic medium. The finite difference synthetics are compared with ultrasonic lab measurements in a scaled borehole drilled along the X axis in an orthorhombic phenolite solid. Both monopole and dipole logs agree well. The 3-D time domain finite difference method is applied to the fluid-filled borehole wave propagation problems in the anisotropic formation. The following results are obtained: 1. In a borehole drilled along the Z axis in a phenolite formation, the monopole log shows the P wave travelling with velocity v[subscript zz]. There are no shear-pseudo-Rayleigh wave arrivals. The dipole log is dominated by the single slow flexural mode. 2. In a borehole drilled along the Y axis in a phenolite formation, the monopole log shows the P wave travelling with velocity v[subscript yy]. There are shear-pseudo-Rayleigh wave arrivals shown on the monopole seismograms between the P and Stoneley waves due to the shear wave anisotropy. The anisotropy also causes the shear wave splitting in the dipole log. The two shear wave arrivals correspond to the fast and the slow flexural modes. 3. The disagreement between the shear wave velocity from the Stoneley wave inversion and the direct shear wave log velocity from field data is beyond the errors in the measurements. It is shown that the formation permeability is not the cause of the discrepancy. From the estimated "shear/pseudo-Rayleigh" phase velocities in the array full waveform log and the 3-D finite difference synthetics in the anisotropic formation, the discrepancy can be explained as shear wave anisotropy.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumERL/nCUBE Geophysical Center for Parallel Processin

Polarization Of Flexural Waves In An Anisotropic Borehole Model

Two modes of flexural waves can be generated by a dipole source in an anisotropic borehole. Their velocities are related to those of the fast and slow shear waves in the formation. The particle motions and the polarization diagrams of the fast and slow flexural waves are measured in borehole models made of phenolite materials with transverse isotropy or orthorhombic anisotropy. The experimental results show that the particle motion of the fast flexural wave is linear and in the same direction as that of the fast shear wave in the formation. The polarization direction of the fast flexural wave coincides with that of the fast shear wave and is independent ofthe direction of the dipole source. The particle motion of the slow flexural wave is nonlinear and elliptic. Its polarization direction and variation are dependent on the anisotropic material and the source direction. This means that the slow flexural wave is a more complicated wave mode rather than the simple mode where the particle motion generated by a dipole source is in the direction of the slow shear wave. The polarization characteristics of the fast flexural wave can be applied to determine the principal axis of an anisotropic formation by in-line and cross-line logging data.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumUnited States. Dept. of Energy (Contract DE-FG02-86ER13636

Stoneley Wave Propagation In Heterogeneous Permeable Porous Formations

The propagation of borehole Stoneley waves is strongly correlated with permeability of the formation. Previous studies primarily focused on the situation where the permeability is homogeneously distributed in the formation. In many in-situ situations, however, the permeability distribution of the formation is heterogeneous, due to effects such as a damaged zone around the borehole, random variation of the formation permeability, and layering, etc. This study investigates the effects of formation permeability heterogeneity on Stoneley wave propagation. Using the theory of dynamic permeability and a finite difference technique in cylindrical coordinates, dynamic pore fluid flow in an arbitrarily heterogeneous porous medium surrounding the borehole is modeled. The effects of the flow on the borehole Stoneley waves are calculated. The calculations were performed on various types of permeability heterogeneities. For a formation having random permeability variation with various heterogeneity scale lengths (smaller than the scale of the borehole), the Stoneley wave attenuation and dispersion are only slightly higher than those calculated with a constant permeability (mean value of the random distributions). For a formation with permeability linearly increasing or decreasing away from the borehole, the Stoneley wave behaviors are also similar to those calculated with a constant permeability. Significant effects are found for a damaged zone case where the zone has much higher permeability than the virgin formation. The attenuation exhibits a peak and the Stoneley wave velocity is significantly decreased in the frequency range from 0 to 3 kHz. These features, if measured from the data, can be used as a diagnostic of the borehole condition.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumUnited States. Dept. of Energy (Grant DE-FG02-86ER13636

Borehole Wave Propagation In Isotropic And Anisotropic Media I: Finite Difference Method

In this paper we developed a 3-D finite difference method to simulate wave propagations in an isotropic medium. The wave equation is formulated into the first-order hyperbolic equations by using velocity and stress and then discretizing it on a staggered grid. The 3-D time domain finite difference scheme is second order accurate in time and fourth order accurate in space. The grid dispersion and anisotropy are analyzed and the stable condition of the scheme is obtained. Higdon's absorbing boundary condition is discussed and generalized to the anisotropic medium. The scheme can provide realistic 3-D wave propagation simulation by the use of a parallel computer. The scheme is tested in the homogeneous medium. The finite difference results agree excellently with the analytic solutions of a point explosion source in the acoustic medium and a point force source in the elastic medium. The finite difference method accurately models not only the far field P and S waves, but also the near field term. It demonstrates that the second-order Higdon's absorbing boundary condition works very well in an acoustic and elastic medium.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumERL/nCUBE Geophysical Center for Parallel Processin

Stoneley Wave Propagation Across Borehole Permeability Heterogeneities

An important application of borehole acoustic logging is the determination of formation permeability using Stoneley waves. Heterogeneous permeable structures, such as fractures, sand-shale sequences, etc., are commonly encountered in acoustic logging. The purpose of this study is to investigate the effects of the permeability heterogeneities on the borehole Stoneley wave propagation. We have studied the effects of formation permeability heterogeneities on the Stoneley wave propagation when the heterogeneity changes in radial and azimuthal directions (Zhao et al, 1993). To further study the problem of acoustic logging in heterogeneous porous formations, we study the case where the formation permeability varies in the borehole axial and radial directions. This is a very important problem because vertical heterogeneity variations are commonly encountered in acoustic logging applications. Using the finite difference approach, such heterogeneities as random heterogeneous permeability variations, multiple fracture zones, permeable (sand) - non-permeable (shale) sequences, can be readily modeled, and the results are presented. Our numerical simulation results show that the continuous permeability variations in the formation have only minimal effects on the Stoneley wave propagation. Whereas the discontinuous variation (e.g., permeable sand and non-permeable shale sequences) can have significant effeces on the Stoneley wave propagation. However, when the Stoneley wavelength is considerably large compared to the scale of heterogeneity variations, the Stoneley wave is sensitive only to the overall fluid transmissivity of the formation heterogeneity, To demonstrate the effects of heterogeneity on the Stoneley wave propagation. an experimental data set (Winkler et aI., 1989) has been modeled using a randomly layered permeability model. The heterogeneous permeability model results agree with the data very well, while the data disagree with the results from homogeneous permeability models. The numerical technique for calculating Stoneley wave propagation across permeability heterogeneities has been applied to interpret the acoustic logging data across a heeerogeneous fraceure zone (paillet. 1984). The modeling technique, in conjunction with a variable permeability model, successfully explains the non-symmetric patterns of the Stoneley wave attenuation and reileceion at the top and bottom of the fracture zone, while it is difficult to explain these patterns using a homogeneous permeable zone model. The technique developed in this study can be used as an effective means for characterizing permeability heterogeneities using borehole Stoneley waves.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumUnited States. Dept. of Energy (Grant DE-FG02-86ERI3636

Source Characterization Of Microearthquakes Induced By Hydraulic Fracturing With Empirical Green's Function

In this paper, we retrieved relative source time functions (RSTF) and estimated the source parameters for microearthquakes (M= -1.9 to -2.6) induced by hydraulic injection at Fenton Hill, New Mexico, using an empirical Green's function (EGF) method. Seismic waveform of a small event in seismic doublets or multiplets (Gelle and Meuller, 1980), defined as co-located events with similar focal mechanisms, within a hydraulic fracture zone, is treated as the EGF and is deconvolved from that of a larger event in the doublets or multiplets to retrieve the relative source time function. Time domain analysis of the RSTFs reveals the source complexity of the induced microearthquakes. The azimuthal variation of the RSTF indicates that the rupture propagates to the northwest, which is consistent with the growth direction of the hydraulic fracture zone determined by Li and Cheng (1995) with a seismicity temporal-spatial distribution pattern. The source duration of the induced events ranges from 2 to 8 ms and the source radii are estimated to be 4 to 12 meters. Values of stress drops are from 1 to 19 bars. Significant variation of the stress drops may reflect the heterogeneity of the stress field in the hydraulic fracture zone and its vicinity and indicate that the stress field heterogeneity extends down to a few meters.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumUnited States. Dept. of Energy (Contract DE-FG02-86ER13636

Experimental Study Of The Flexural Waves In The Fractured Or Cased Borehole Model

The ultrasonic logging is performed with dipole transducers in aluminum and lucite borehole models to study the propagation of the flexural waves in a fractured or cased borehole. The experimental results show that the flexural wave is much more sensitive to a horizontal fracture than to a vertical one. The propagation of flexural waves in a borehole with an inclined fracture is related to both the polarization of the flexural wave and the direction of the fracture. The experimental results show that a very strong low-frequency flexural wave can be generated by a dipole source in a cased borehole and it propagates with the shear wave velocity of the formation. High-frequency waves generated by a dipole source propagate with the compressional wave and flexural wave velocities of the casing. Dipole acoustic well logging could be an effective means for determining horizontal and declined fractures and measuring the formation shear wave velocity in a cased borehole.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumUnited States. Dept. of Energy (Grant DE-FG02-86ER13636