Calculation Of The Ray Path、Ray Travel Time And Ray Amplitude In Absorbing Medium-The First-order Perturbation Method

Due to the absorption of formation, wavefront diffusion and scattering, seismicwave is absorbed in which energy attenuation may occur. In this case, some theoretical results including amplitude and frequency of seismic wave can be quite different from what we have observed.According to the current research, the attenuation of seismic wave can be affected by two major elements: one is related with the propagation prooerty of seismic waves. Another factor is related to the non-perfectly elastic of the formation. And the factors related with the seismic wave propagation are generally frequency- independent, while the attenuation caused by non-perfectly elastic is frequency-dependent. In general, the absorption seismic wave in underground medium make that high-frequency part of the seismic data is lost, depth information is unclear, which reducing the seismic resolution.Many theories and experiments prove that the viscoelastic medium conform with the actual formation. In the absorbing medium, all the elastic parameters become the complex-value and frequency-dependent, thus wave equations and eikonal equation and ray tracing equations derivated by wave equations turn into the differential equations with complex coefficients. In order to solve the complex ray tracing equations, this article use thefirst-order perturbation theory, the complex-value wave properties are divided into real parts and imaginary parts, the real parts are thought of as background and the imaginary parts are considered as the disturbance of the real parts, which makes the ray tracing in absorbing medium becomes more complex and needs more computing capacity than the real ray tracing. In order to improve the computational efficiency, the ray tracing in absorbing medium is combined with the wavefront construction method, with the velocity model and Q model, using the Runge-Kutta method to solve the wavefront construction ray tracing equations, which increases the ray coverage rate and improves the computings peed.Actual calculations show that in weak attenuation medium, the real ray tracing met-hod has not only the satisfactory computational efficiency, but also the wonderful precision, which is a recommended numerical simulation method for the absorbing medium ray tracing.