A novel constant fractional-order Laplacians viscoacoustic wave equation and its numerical simulation method
CHEN Hanming1,2,3, WANG Yilin4, ZHOU Hui1,2,3
1. College of Geophysics, China University of Petroleum(Beijing), Beijing 102249, China; 2. State Key Laboratory of Petroleum Resources and Prospecting, Beijing 102249, China; 3. CNPC Key Lab of Geophysical Exploration, Beijing 102249, China; 4. School of Ocean and Earth Science, Tongji University, Shanghai 200092, China
Abstract:We develop a viscoacoustic wave equation with fractional-order Laplacians,which is better than the traditional integral-order viscoacoustic equation because the new equation more accurately describes the widely used constant-Q model.The operators related to amplitude attenuation and phase change are explicitly independent of each other,which is important for the robust reverse time migration with attenuation compensation.We formulate the first-order velocity-pressure viscoacoustic wave equation with the constant fractional-order Laplacians based on the second-order displacement viscoacoustic equation with the constant fractional-order Laplacians in time domain.To better model amplitude variation,space-varying density is involved in the new equation.To avoid spurious reflections caused by the periodicity of the Fourier transform,a convolutional perfectly matched layer (CPML) is employed as the absorbing boundary for the fractional-order Laplacian viscoacoustic equation.Numerical simulations are fulfilled using staggered-mesh pseudo-spectral method.We compare the numerical solution with the analytic solution for the homogeneous medium,and we find the new equation accurately describes the constant-Q model.We also verify its feasibility for complicated media through seismic wave field simulation using the BP salt dome model.
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