Seismic Attenuation Models And Compensation

When seismic waves travel through the earth subsurface,the frequency-dependent absorption and dispersion caused by the anelasticity of the subsurface will inevitably degrade the quality of seismograms,decrease the resolution of migrated images,and eventually affect the reliability of seismic interpretation.Exploring the essence of seismic attenuation,establishing reasonable attenuation models,and formulating effective schemes for seismic compensation have become research hotspots in recent years.In this thesis,I systematically investigated these seismic attenuation modeling from both mechanical and mathematical viewpoints,and further developed inversion-based and imaging-based strategies for seismic attenuation compensation.Seismic attenuation can be empirically characterized either by an experimentally established frequency power law or by physically based mechanical models over a wide range of frequencies.Recently,increasing studies present a variety of fractional models that bridge the gap between these two scenarios under the assumption of continuum of relaxation mechanisms.The fractional model can be represented by classical elements with the number of units tends to infinity and exhibit frequency power-law attenuation as well,which enjoys more fundamental and physical properties than the frequency power-law characterization and holds more concise parameterization when it is compared to the classical mechanical model.This paper presented some mostly used fractional attenuation models in exploration geophysics to investigate the basic idea of these attenuation models and to figure out the connections among these different models from both mathematical and numerical viewpoints.Seismic attenuation compensation is an important processing approach for enhancing signal resolution and fidelity.However,amplitude compensation is prone to exponentially boost the high-frequency noise in seismic data.In this paper,I developed two stable compensation strategies:the least-squares inversion-based compensation scheme for post-stack seismic data and Q-compensated reverse time migration for pre-stack seismic data.Specifically,the constrained L₁ minimization serving as the convex relaxation of the literal L₀ sparsity count may not give the sparsest solution when the kernel matrix is severely ill-conditioned,in this paper,I proposed a nearly unbiased approximation of the vector sparsity,denoted as L_1-2minimization,for exact and stable seismic attenuation compensation.I analytically derived the k-space Green's functions for a constant-Q wave equation with decoupled fractional Laplacians and its compensated equation,and theoretically proved the numerical instability of seismic compensation.I further proposed an adaptive stabilization operator for the Q-compensated viscoacoustic and viscoelastic revere time migration,superior properties of time variance and Q dependence over conventional low-pass filtering-based method.This paper further presented a generalized stabilization scheme for seismic Q compensation.An explicit stabilization term in the time-space domain was formulated with an assumption that the exponent of the chosen window is a power function of the magnitude of wavenumber.Furthermore,I developed an open-source code package cu Q-RTM in a multilevel parallelism fashion?MPI+CUDA?so as to achieve high-performance computing for the proposed methods.