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 ′ = ⅈ ⁡ ( 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, ρ is a density, u is a displacement vector, c ijkl is stiffness tensor, f is a force, Z k is the fourier transform of a set of numbers, k is an index from zero to N/2−1, k† is an index given by N/2−k, and Z k ′ is a differential operator; using the calculated derivatives of the elastic wave equation to determine wavefield propagation underground; and processing the calculated derivatives into data that are used to display the determined wavefields so that underground geographical features in the underground geographical area of interest are determined.