where 2l is the total length of the loaded section of the cylinder, [phi] is the polar angle measured from the cylinder's axis, R is the distance to the observer, [c.sub.s] = [square root of [mu]/[rho]] and [c.sub.p] = [square root of ([lambda] + 2[mu])/[rho]] are the shear and

compressional wave speeds in the medium, and [mu] and [rho] are the rock's rigidity and density, respectively.

The high-voltage electrical pulse signal of one thousand volts is generated by the ultrasonic machine, and the electric signal was converted to the ultrasonic signal by a 50 kHz center frequency

compressional wave contact transducer.

The prestored energy loading mechanism on the torsional wave was installed at the end of the incident bar, and the impact loading mechanism on the

compressional wave was installed at the end of the transmission bar.

In the research of Sarker and Batzle (2010), on the saturated samples, Mancos B shale exhibits

compressional wave anisotropy of about 9 % and shear wave of about 5 %.

The acoustic field in solids presents a complex interference pattern because the

compressional wave and the shear wave have different propagation velocities which both have effects on particle velocity, although the usual energy method is more accurate than the potential function approach in describing the physical properties of acoustic fields.

Gstalder and Raynal measured rock hardness directly from core samples and then from

compressional wave velocities as an alternative method [1].

Physically this means that the speed of the pressure wave at these points on the shell surface is equal to the speed of the

compressional wave or to the speed of the shear wave, respectively.

where [f.sub.c] is the uniaxial compressive strength, E is the elastic modulus, [V.sub.P] is the

compressional wave velocity, and [alpha], [beta], a, and b are coefficients determined by experimental results.

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is incident pulse at the fluid, x = {[x.sub.1], [x.sub.3]}, C([omega]) is scale coefficient for the incident pulse, [H.sup.(2).sub.0] (*) is Hankel's function of second kind and zero order, is circular frequency, [c.sup.F] is

compressional wave velocity in the fluid, r = r(x) is the distance from the receiver to the source (incident pulse), k is the wave number, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] with Im [eta] < 0.

Here we present complex measurements of the resulting elastic waves using AE during impact experiments to determine material parameters, the

compressional wave propagation in the target, to quantify fracturing in the target, as well as the localization of the impact.

In calibrating data sets, Gamma ray, porosity,

compressional wave velocity ([V.sub.P]), Shear wave velocity ([V.sub.S]) and density logs were displayed and analysed in the well-viewer of the RokDoc project (figure 3).

Figure 8 shows contour lines that represented boundaries between

compressional wave velocity gradients.