运用Hartley变换模拟地震波在正交各向异性介质中的传播

在地震传播理论中,地震波场的正演数值模拟一直是研究的热点。而在正演数值模拟方法的研究中,计算精度和计算效率是评价此方法的有效性及优越性的二个关键问题。伪谱法在计算精度与计算效率方面优越性十分明显,常用的有Fourier变换法和Hartley变换法;虽然Hartley变换法在求取导数时较Fourier变换法复杂,但由于Fourier变换法的计算同时涉及复数的实部与虚部,在计算速度和占用内存方面不如Hartley变换法。这里详细地阐述了利用Hartley变换求解正交各向异性介质波动方程的数值方法,并模拟了多种正交各向异性介质模型,对比分析了地震波在各向同性介质与正交各向异性介质中的传播差异。结论表明,该方法能正确、高效、直观地反应地震波在正交各向异性介质中的传播规律。

Using hartley transform method to simulate seismic wave propagation in the ORA media

In seismic propagation theory,the forward modeling of the seismic wave fields always is the hot spot.And in the forward modeling methods,the computation precision and the efficiency are two pivotal questions to evaluate the validity and superiority of the method.By the pseudo spectrum method,the superiority about its computing precision and efficiency is very clearly.The pseudo spectrum methods commonly include Fourier method and Hartley method.Although to seek the derivative by Hartley transform method is more sophisticated than that by Fourier transform method,in the computing,the former only compute the real number,and the latter compute the real part and imaginary part of complex number at the same time.Therefore,Hartley transform method can not only compute faster but also occupies less memory than Fourier transform method.In this paper,authors expands the numerical technique by Hartley transform to solve the wave propagation equation in the ORA medium in detail,simulates several ORA models,and contrasts the wave propagation differences between the isotropy media and the ORA media. The results proves that the methods can be rightly,high efficiency and directly testy the wave propagation regulation in the ORA media.