We present an efficient implementation of the method for sampling spatial realisations of a 3-D random fields with given power spectrum. The method allows for a multi-scale resolution and approaches well for parallel implementations, overcoming the physical limitation of computer memory when dealing with large 3-D problems. We implement the random field generator to execute on graphical processing units (GPU) using the CUDA C programming language. We compare the memory footprint and the wall-time of our implementation to FFT-based solutions. We illustrate the efficiency of the proposed numerical method using examples of an acoustic scattering problem which can be encountered both in controlled-source and earthquake seismology. In particular, we apply our method to study the scattering of seismic waves in 3-D anisotropic random media with a particular focus on P-wave coda observations and seismic monitoring of hydrocarbon reservoirs.
