Chuen Hon Cheng

Elastic wave propagation in a fluid‐filled borehole and synthetic acoustic logs

The propagation and dispersion characteristics of guided waves in a fluid‐filled borehole are studied using dispersion curves and modeling full‐wave acoustic logs by synthetic microseismograms. The dispersion characteristics of the pseudo‐Rayleigh (reflected) and Stoneley waves in a borehole with and without a tool in the center are compared. Effects of different tool properties are calculated. The effect of a rigid tool is to make the effective borehole radius smaller. As an approximation, dispersion characteristics of the guided waves in a borehole with a tool can be calculated as a purely fluid‐filled borehole with a smaller effective radius. Theoretical waveforms (microseismograms) of elastic waves propagating in a borehole are calculated using a discrete wavenumber integration. With an appropriate choice of parameters, our results look similar to the acoustic waveforms recorded in a limestone and a shale formation. Several factors affect the shape of an acoustic log microseismogram. The effective rad...

A numerical investigation of head waves and leaky modes in fluid‐filled boreholes

Although synthetic borehole seismograms can be computed for a wide range of borehole conditions, the physical nature of shear and compressional head waves in fluid‐filled boreholes is poorly understood. This paper presents a series of numerical experiments designed to explain the physical mechanisms controlling head‐wave propagation in boreholes. These calculations demonstrate the existence of compressional normal modes equivalent to shear normal modes, or pseudo‐Rayleigh waves, with sequential cutoff frequencies spaced between the cutoff frequencies for the shear normal modes. Major contributions to head‐wave spectra occur in discrete peaks at frequencies just below mode cutoff for both compressional and shear modes. This result is confirmed by calculations with synthetic waveforms at frequencies corresponding to mode cutoff, and by branch‐cut integrals designed to yield independent spectra for the compressional mode. For soft formations where shear velocity falls below acoustic velocity in the borehole ...

Shear wave logging in semi‐infinite saturated porous formations

Recent theoretical and experimental studies have demonstrated the interest of using nonaxisymmetric sources, such as dipole and quadrupole, to record shear wave events in any kind of formation (fast or slow). Nonaxisymmetric sources excite surface waves whose Airy phase is predominant in the records at intermediate frequencies (≂3 to 6 kHz). They are referred to as the flexural and screw modes, respectively, for the dipole and the quadrupole sources. Their dispersion and attenuation are studied in a fluid‐filled borehole embedded in a homogeneous saturated porous formation. The two‐phase medium is modeled using Biot’s theory modified in accordance with the homogenization theory. Calculation of synthetic full waveform logs is also performed using the discrete wavenumber method. Whatever the formation, the most reliable information that can be extracted from low‐frequency parts of the wavetrains is the formation shear wave velocity and attenuation. It is of great interest in the inversion of Stoneley wave v...

Error analysis of phase screen method in 3‐D

The purpose of the research presented in this paper is to do an error analysis of the phase screen method for forward and inverse wave propagation calculations in 3D heterogeneous acoustic media. The differential operator formalism approach is used, which provides new insight into the phase screen method. Under the assumptions that backscattering and commutator term of operators R and Q are negligible, we derive a partial differential equation and its solution corresponding to the phase screen method. The errors introduced in these derivations are also obtained. For a one-step (δz) phase screen calculation, the leading error term is in the first order of k0Δz and proportional to the error from splitting the square-root operator Q. The propagation angle should be less than 40 degrees to control the error from the splitting operator Q under 5%.

Wave Propagation in a Borehole

In full waveform acoustic logging, a pressure source generates various types of elastic waves propagating down the borehole. These waves, because their wavelengths are of the order of the borehole radius, are guided waves. Depending on the velocity of propagation, these guided waves are either normal modes, like the Stoneley wave, where all the energy is contained around the borehole, or leaky modes, like the P leaky mode, where some of the energy is converted into body waves and radiates away from the borehole into the formation. Both the normal and leaky modes are significantly affected by the P and especially the S wave velocity of the formation. Other physical parameters affecting their propagation are attenuation, permeability and anisotropy. With proper processing techniques in combination with inversion algorithms, we can obtain estimates of the S wave velocity even in soft marine sediments where no refracted S wave arrival exists on the full waveform logs.

Stoneley-wave propagation in a fluid-filled borehole with a vertical fracture : Geophysics V56, N4, April 1991, P447–460

The propagation of Stoneley waves in a fluid-filled borehole with a vertical fracture is investigated both theoretically and experimentally. The borehole propagation excites fluid motion in the fracture and the resulting fluid flow at the fracture opening perturbs the fluid-solid interface boundary condition at the borehole wall. By developing a boundary condition perturbation technique for the borehole situation, we have studied the effect of this change in the boundary condition on the Stoneley propagation. Cases of both hard and soft formations have been investigated. It has been shown that the fracture has minimal effects on the Stoneley velocity except in the very low frequency range in which the Stoneley velocity drastically decreases with decreasing frequency. Significant Stoneley wave attenuation is produced because of the energy dissipation into the fracture. In general, the effects of the fracture are more important in the low frequency range than at higher frequencies. The quantitative behavior of these effects depends not only on fracture aperture and borehole radius, but also on the acoustic properties of the formation and fluid. Ultrasonic experiments have been performed to measure Stoneley propagation in laboratory fracture borehole models. Aluminum and lucite were used to simulate a hard and a soft formation, respectively. Array data for wave propagation were obtained and were processed using Pronys method to give velocity and attenuation of Stoneley waves as a function of frequency. In both hard and soft formation cases, the experimental results were found to agree well with the theoretical predictions. The important result of this study is that, we have found a quantitative relationship between the Stoneley propagation and the fracture character in conjunction with formation and fluid properties. This relationship can be used to provide a method for estimating the characteristics of a vertical fracture by means of Stoneley wave measurements. 64 Tang et al.