1. A method for simulating and displaying wave propagation using reflection seismology in a geographical area of interest, the method comprising: converting signals associated with marine seismic soundwaves into digital electronic form, and storing the same as single precision floating numbers in an array of size N; converting the real array of size N into a complex array of size N/2; determining a first derivative of the following elastic wave equation— ρ ( x ) ∂ 2 u i ∂ t 2 - ∂ ∂ x j C ijkl ∂ ∂ x l u k = f i using the following equation— Z k ′ =  ( N 4 + N 4 sin 2 π k N - k ) Z k + N 4 cos 2 π k N Z k † * wherein said determination of the first derivative includes the determination of a fast fourier transform using an FFT vectorization scheme; using the calculated derivatives of the elastic wave equation to determine wavefield propagation underground; and processing the calculated derivatives into data that can be used to display the determined wavefields so that underground geographical features in the underground geographical area of interest can be determined.