A Comparison of Second-Order and High-Order of Finite Difference Staggered-Grid Method in 2D P-SV Wave Propagation Modelling using Graphics Processing Unit

A comparison of second order and high order (4th, 8th and 12th order) of finite difference staggered-grid method on 2D P-SV elastic wave propagation has been conducted. The comparison plot of numerical dispersion and accuracy among each order has been generated to show the stability condition. CUDA C programming language is used to apply the finite difference staggered-grid schema on GPU NVIDIA GeForce GTX-590 and to measure the duration of process time quantitatively. The code has been verified by comparing travel time of direct wave, reflection, refraction and conversion from the synthetic seismogram with analytical calculation from two layer medium using Snell's law. The program is applied to one-layer medium and complex medium (Marmousi-2 model). The time process of one shot simulation on Marmousi-2 model with 4800x2400 grid size are 1168.72s (2nd order), 1736.40s (4th order), 2816.80s (8th order) and 3778.67s (12th order). The difference of seismogram showed that the second order and high order of the finite difference on two layer model indicate that the numerical dispersion has occurred on the waveform. The result shows that the higher order of the finite difference will have less numerical dispersion compared to the low order but need longer process time.