Fourier transforms and waves: in four lectures / Преобразование Фурье и волны: в 4-х лекциях

When earth material properties are constant in any of the cartesian variables then it is useful to Fourier transform (FT) that variable.
In seismology, the earth does not change with time (the ocean does!) so for the earth, we can generally gain by Fourier transforming the time axis thereby converting time-dependent differential equations (hard) to algebraic equations (easier) in frequency (temporal frequency).
In seismology, the earth generally changes rather strongly with depth, so we cannot usefully Fourier transform the depth axis and we are stuck with differential equations in . On the other hand, we can model a layered earth where each layer has material properties that are constant in . Then we get analytic solutions in layers and we need to patch them together. <...>