While useful for representing the average degree and direction of molecular orientation, the second moment tensor analysis
obscures some information readily apparent in the 2D scattering patterns.
It is noteworthy that using moment tensor analysis
it is possible get the orientation and displacement vector of the crack.
Huang, Tensor Analysis
and Its Applications, Chinese Scientific Press, 2004 (Chinese).
McConnell, Application of Tensor Analysis
, Dover Publications, New York (1957).
(1991), "Simplified Moment Tensor Analysis
and Unified Decomposition of AE Source," J.
The text is for senior undergraduate and graduate students and scientists who are interested in quantitative seismology and are familiar with linear algebra, differential and integral calculus, vector calculus, tensor analysis
, and ordinary and partial differential equations.
Topics include special relativity in the formalism of Minkowski's four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis
, Einstein's field equation, and cosmology.
The contravariant metric tensor for the gravitational field, obtained using the Quotient Theorem of tensor analysis
 is given as
Source Characterization: Many methods are practiced here, including combined AE parameters, attenuation-corrected signal amplitude, signal frequency, waveform analysis and moment tensor analysis
. Finally, possible avenues of improvement are discussed.
Topics include vector and tensor analysis
, complex-variable theory, differential equations, linear equations, determinants, group theory and algebraic equations, and matrices.
The corresponding contravariant metric tensor for this field, is then constructed trivially using the Quotient Theorem of tensor analysis
and used to compute the affine coefficients, given explicitly as
The moment tensor analysis
of AE is available for identifying crack kinematics of location, crack-type and crack orientation (Ohtsu, 2000).