Anton Zaicenco 1 and lain Weir-Jones 1
1Weir-Jones Group, Vancouver, Canada
Elastic body waves are related to di latational and shear components of the displacement field. Wavefront detection and phase characterization are better achieved with the 3C sensors, which allow use of polarization analysis. Separation of components into stationary and random is achieved with the higher statistical moments of the time-frequency distributions. Similar statistics can be used as a triggering criterion instead of conventional averaged time window ratios.
Elastic wave equation in the heterogeneous anisotropic medium
The elastic wave equation is a second-order PDE where body forces and stress gradients on the right side are related to the dynamic forces created by accelerations acting on densities. Both sides of the equation are working with the derivatives of the displacement field of the medium. The application of Toni diagram allows the investigator to understand the kinematic, constitutive and equilibrium equations.
P- and S-wave relation to the strain tensor, polarization analysis
P- and S-waves are related to divergence and curl of the displacement vector field. The strain tensor is obtained from the deformation gradient. Its diagonal terms are directly related to the divergence (P-wave), while off-diagonal terms to the curl of the displacement field (S-wave). The dilatational and deviatoric components of the displacement field result in the pola1ized particle oscillation relative to the local wave front. Eigenvalue decomposition of the cotTelation (covariance) matrix allows body wave phase detection in time and frequency domain.
Time-frequency distributions: stationary vs. random components
Oftentimes it is important to distinguish the frequencies (STFT analysis) or scales (wavelets) that are stationary or random. Random components are potentially responsible for detected wavefronts and provide an estimate of the magnitude of the seismic event.
Body wave phase detection using multiple criteria
Multiple criteria are used to detect and characterize the body waves, the most impmiant of these are: the signal energy change and polarization analysis. A method based on higher statistical moments is suggested instead of conventional ST NLT1\, which provides more reliable energy change detection. Microseismic Industry Consortium- Research Report- Volume 1 (2011) 11-1