A novel method for wave phenomena investigation

To study wave phenomena, the precise analytical expressions are used for particular solutions of the wave equations and the results of modeling the measurements of the available instruments (seismograms, ultrasonic sensors, etc.). The theory of the construction of analytical processes is usually built on the expansion in a Fourier series. Methods for modeling wave phenomena can be divided into two classes: methods of full-wave modeling, which allows to solve boundary-value problems of the elastic and acoustic wave equation in the time domain, and ray tracing methods. When using full-wave simulation, all types of scattering are present, however, due to the huge amount (hundreds of TB on the hard disk) of the calculated data. Interpretation of the results of computational experiments is significantly complicated. Also for dividing waves into longitudinal (P-wave) and transverse (S-wave), the Pointing vector is used. However, this technique does not work well in the case of multiple interference, and for surface waves, moreover, it does not allow the researcher to form a complete understanding of wave dynamics and makes it difficult to search for wave phenomena that were not previously used in practice. Using ray tracing method not all types of scattering are present, but only those that were laid during its development. Moreover, such features of wave dynamics as the central decrease in the amplitude of the transverse waves may be missing if they, again, were not laid by the developers. The approach, developed within this paper and called Wave Logica, to analyze spatial dynamic wave fields calculated by full-wave computer simulation describes the dynamics of wave propagation and the structure of wave fronts in more detail than the classical approach, which implies the explicit selection of particular analytical solutions of the wave equation, and more precisely than the geometric approximation and the ray tracing method. Accordingly, this approach allows to more accurately identify wave patterns that can later be used in the development of equipment for seismic exploration, ultrasound and non-destructive testing.