A space-time perturbation of any physical field that can be described by expressions (1) and (2) is called a nonstationary wave
Now consider the so-called stationary waves, changing in time as the harmonic functions. The nonstationary and stationary waves are connected under the time-frequency Fourier transform:
The wave motions correspond to some components of the more general form of motion described by equations of dynamics. That is why the substantiation of wave propagation theory can be obtained as the consequences of these exact equations. The main consequences are Fermat's principle, the law of energy flux conservation, and the reflection/transmission law. These laws are valid at the wave fronts only. However, they can give the initial approximation for different methods of perturbation theory or asymptotic expansions in the neighborhood of wave fronts (or for the high-frequency asymptotic description
Figures & Tables
This book is devoted to one important aspect of development of physical foundations of the seismic method — the theory of edge diffraction phenomena. Thoese phenomena occur when conditions of the regular wave reflection/transmission change sharply. Though these phenomena drew the attention of many scientist for many decades, their real influence on the resolution ability of the seismic method was truly understood rather recently due to interpretation of seismic data in block structures. Clearly, to develop seismic method for investigation of such structures without developing the theory of edge diffraction phenomena is impossible. The latter is the aim of this book.
The seismic method is based on the fundamental laws of continuum mechanics. These laws describe the behavior of wavefields on the microscopic level, i.e., in the form of differential equations of motion. Integrating these equations under some initial conditions or boundary conditions, makes possible acquisition of all necessary information on the wavefield in the given situation. However, the working base of the seismic method consists of not only the differential equations of motion themselves but of some general and simple enough consequences of their solutions, which are formulated in the form of physical principles and l aws. The latter include the concepts of wave, Fermat’s principle, the law of conservation of the energy flux, and the reflection/transmission laws. Essentially these laws and principles must form a system of concepts sufficient for the solution of some class of typical interpretation problems. In fact, these principles and laws form the physical fo ndation of the seismic method.