Abstract：The paper used the Fourier transform algo-rithm to implement the parallel algorithm of 3-Dprestack sonic model，obtained 3-D synthetic seis-mographs and applied the ray theory analysis toprove the algorithm.The algorithm allows the ve-locity to change both in vertical and in lateral di-rections.The largest difficulty of calculating 3-Dprestack model is a large amount of memory andcomputational efforts,the main advantages are thatcalculating parts of main bodies are carried out byFFT，the vectorization technique and the relation-ship between complex sequence of Fourier trans-form and real sequence of Fourier transform aresuccessfully used for 2-D and 3-D FFT so that theprogram can be optimized，the computational effi-ciency can be improved and the memory can besaved.The theoretic analysis and real data testshowed that adequately adjusting special and tem-poral sampling intervals and dominant frequencyand length of source wavelet can reduce the disper-sion resulted from the difference approaching thedifferential that can get better simulation results.Using information-transmitting-parallel program-ming environment and parallel program of micro-computer cluster operation can greatly increase thecomputational efficiency and reduce the computa-tional times;meanwhile，combination of snap shotplotting wavefield with velocity sections can betterobserve wave-spreading process.The syntheticseismographs of model testing showed the feasibili-ty and effectiveness of the algorithm.
