Method Of Wave Equation Reflection Tomography In The Acoustic Media

In the exploration seismology,the background velocity is the key factor that decides the propagation of seismic wave.It also is the basis for further inversion of higher velocity components.For transmitted wave and refracted wave,with a larger incidence angle aperture,they can be used to recover the long wavelength components of velocity model.But the reflections,due to the narrow range of reflection angle aperture,typically be used to recover short wavelength components.Faced with the phenomenon,this article study the derivation method of reflected wave path,the construction of objective functions in reflection tomography and the improvements for FWI.Finally we achieve the low wavenumber components inversion of velocity model using reflection wave information.The ‘wave paths' can accurately describe the propagation of seismic waves in the Earth media.Compared with the traditional ray paths,‘wave paths' can avoid the phenomena that ray paths will focus on high velocity region and diverge on slow areas.Wave equation tomography is proposed on the basis of wave paths.The geometry of reflected wave paths proposed in this paper yields the characteristic double banana-shape due to constructive interference of the wave fields within the Fresnel-zone around the central ray.We backproject the data residuals along the reflections path,and achieve the wave equation reflection tomography.We will choose the corresponding objective functions depending on different initial velocity model.Since the amplitude information of simulated seismic wave is uncertain,the waveform inversion founded on the traditional least squares error function is severely restricted.However,various forms of wave equations follow a common eikonal equation,the travel-time information will not be affected.So we should focus more on travel-time information in waveform inversion.Because of the large difference between initial velocity model and the true velocity model,we select the inversion based on travel-time information,reducing its dependency on wave equation.Only when the initial velocity is not large deviating from the true velocity model,the waveform inversion can be taken.We simulate the reflected wave field by migration/demigration operator in this paper.Then we construct the reflected wave paths and establish the gradient formula of wave equation reflection tomography.Finally we compare the inversion effect with different objective functions in inversion.On this basis,we achieve the wave equation reflection travel-time inversion.In the wave equation reflection travel-time inversion,we combine the idea of Ma Yong and Luo Yi to improve the form of adjoint source.Simultaneously dynamic image warping method is used for the time lag calculation between reflections.Then we achieve the low wavenumber components inversion of the velocity model using reflections travel-time information.In wave equation reflection waveform inversion,we achieve the complex model test,and improve the FWI results.Model tests demonstrate its better stability and application potentiality.