We employ a standard ultrasonic (100 KHz to 1000 KHz) pulse transmission technique to measure ultrasonic velocities. The geometry of the system is shown in Figure 1. The sample is placed in an impermeable neoprene sleeve (jacket). The jacket is a little large than the sample allowing the fitting of sealing endcaps to both sample faces. Three piezoelectric transducers (P, S1 and S2) are housed within each end cap along with an integrated circuit containing a unique serial number. The neoprene jacket is fastened to each encap using a hose clamp. The assembly is then sealed from any externally applied fluid pressure. Holes within each endcap route pore fluid to and from the sample. Pore pressures can be controlled independent of confining pressures.
The three piezoelectric crystals generate compressional (P) and polarized shear waves (S1 and S2). The shear waves are orthogonally polarized. A matched set of transducers acts as a receiver array. Transducer delay calibrations are stored in a computer along with the unique serial number for each transducer pair. Transducers are activated such that five waveforms are digitally recorded at each programmed pressure point. The five waveforms are: (1) P-wave; (2) S-wave (S1 transmits and S1 receives); (3) S-wave (S2 transmits and S2 receives); (4) S-wave (S1 transmits and S2 receives) ; and (5) S-wave (S2 transmits and S1 receives). If a material is isotropic, then there should be no signal recorded on the cross coupled transmitter-receiver pairs. Signal is a positive indication of anisotropy.
The velocities are calculated from a knowledge of the sample length and the travel times for the respective wave. The travel times are revived from an analysis of a waveform. The analysis is usually straightforward for the P-wave because there is generally good signal to noise ratio. This not true for the S-wave as 1) signals are generally weaker and (2) the some coda remains from the P-wave during the arrival of the S-wave. So travel times are fundamentally dependent upon "signal" or waveform quality. Figures below show typical waveforms for P- and S-wave as a function of increasing confining pressure .The red dashed line indicates the arrival of energy and corresponds to a travel time after removing the transducer delay.
The S-wave is shown below:
In each of the figures above pressure increases from bottom to top. Note the time scales in the two figures are different.
The velocity of course is simply the sample length divided by the corresponding travel time:
Vp, Vs = Length/Travel_time. The units are ft/sec, m/sec, km/sec, etc. The inverse of velocity, "interval transit time" is commonly used in well log environments and has units of usec/ft, usec/m, etc.
When velocity is measured as a function of pressure, the response is more often than not described by a nonlinear curve. The nonlinearity reflects the degree to which the pore space is non spherical. The complications of pore space escape precise definition but can be idealized with simple objects such as spherical pores and highly ellipsoidal crack like features. These elliptical features have a strong pressure dependence which is reflected in the velocity pressure dependence. In the figure below, one can see the characteristic nonlinear velocity-pressure dependence. The change in frame compressibility or its inverse, incompressibility or Bulk modulus, can be calculated from the compressional and shear wave velocities. Note too in this figure that the two orthogonal shear velocities, Vs1 and Vs2, show identical responses indicating that the sample is isotropic.
Pressure (pore, confining and axial), temperature and saturation can be varied while the velocities are being measured, thus allowing the characterization of dependence upon these independent variable. These testing capabilities are critical to the calibration and interpretation of seismic time-lapse studies, AVO and attribute analysis, reservoir characterization and modeling, evaluation of seismic stratigraphy, etc.
Measurement of velocity on cores cut at different orientations can reveal elastic anisotropy. Rocks with strong mineral fabric or aligned fractures display different velocities in different orientations, elastic anisotropy. Anisotropic elastic constants can be determined from a properly sampled suite of velocity measurements and a density.