Quality Factor Inversion And Offset Of The Visco-acoustic Wave Equation

The earth medium is not an ideal elastic medium,there is a phenomenon of absorbing attenuation during seismic waves propagating in it.Due to the acoustic wave equation does not reflect the absorption and attenuation characteristics of the media,the migration profile can't accurately reflect the changes of lithology and physical property.In view of viscoelastic media,the viscoelastic wave equation should be used in the migration process.In the wave-field continuation,compensating for attenuation of seismic energy.The absorption attenuation characteristics can be described by the quality factor,so the accuracy of the quality factor inversion is the prerequisite for viscosity acoustic equation migration.The attenuation by absorption of seismic waves is relative to frequency and travel time.The higher the frequency of seismic wave is,the longer the propagation time is,the heavier the absorbing attenuation is.When the remaining energy is reduced to the accuracy of the numerical calculation range below,it will cause instability if the migration of viscosity acoustic equation is done directly.And compensated energy is abnormal.So the stability condition is a problem that must be considered in the viscosity acoustic equation migration.For the difficult of the quality factor inversion,the absorption mechanism of viscoelastic medium,the Boltzmann superposition principle and typical models of viscoelasticity medium are studied firstly.Then,the representative quality factor inversion methods and principles in time domain,frequency domain and time frequency domain are discussed.It takes different ways to study the quality factor inversion of the numerical modeling result.It analyzes the accuracy and anti-noise capability of different inversion methods,and select the best method.In ideal conditions,the spectral inversion method has the highest accuracy,the spectral ratio method based on the S transform is the second,and the amplitude attenuation method is the worst.In noise situation,the spectrum inversion method based on S transform has the highest precision of anti-noise,the spectrum ratio is second,and the amplitude attenuation method is the worst.Based on the previous research,aimed at the instability phenomenon in acoustic wave equation migration,the new stability condition equation was derived which combined with layer-by-layer constraint theory.In the process of wave field continuation,the hierarchical structure of loop variables is changed,the depth loop variable is placed in the outer-most loop,so the stability conditions corresponding to different depths can be obtained.Firstly,it was used in the phase-shift method for migration,and then used in the split-step Fourier method for migration of the complex model forward result,the end of this paper,it was used in processing the practical data.The results show that the resolution of this method compared with the traditional method is improved,the energy of the seismic wave can be compensated and the seismic wave band can be widened in the process of wave field continuation.