Angle-Domain Imaging Method Of Relative Impedance Perturbation

Imaging method of geological bodies using seismic data includes three levels: the first level is the imaging of the geological body’s boundary location information(structural imaging); the second level is the imaging of the boundary parameters(e.g.,reflectivity); the third level is the imaging of the physical parameters(e.g.,velocity,density,and porosity)successively.With the application of wide-azimuth,broadband,high-density data acquisition methods and the continuous development of various inversion methods,people hope that the migration imaging methods can make full use of the waveform information of the seismic data to obtain high-precision and high-resolution imaging results,which can be used for lithology analysis,inversion and other related work.Further,it can promote the transformation of the migration imaging methods from the first stage to the second and third stages.The impedance is an important physical parameter connecting geology and reflection seismic data.It can be directly compared with geology and logging information so that it has a special position in seismic data processing.The current migration imaging method is still mainly based on the structural imaging.For the method of calculating impedance using conventional migration imaging,one is that based on the conventional reflectivity-related structural migration imaging results,the wave impedance imaging is obtained by integrating the reflectivity.The other is that the eatimation of the impedance is obtained by modifing the conventional migration imaging formula to the impedance imaging formula.Thus,the current impedance imaging methods using the conventional migration imaging lack a forward expression of seismic data based on the impedance variation and impedance migration imaging method based on this forward expression.It is likely to cause insufficient use of seismic data’s waveform information and it is also not conducive to the development of fine imaging of seismic exploration.Therefore,in order to solve the above problems and taking into account the current development needs of seismic migration imaging,this paper aims to construct a pre-stack seismic migration imaging method based on the relative impedance perturbation forward equation of the reflected wave by studing the relationship between underground acoustic wave and elastic wave impedance and seismic data.First,this paper starts with the acoustic waves,and then gradually expands to elastic waves.And the imaging methods research of the acoustic and elastic wave impedance relative perturbation is carried out in depth domain and angle domain successively.The specific implementation methods can be expressed as follows:1)As for the acoustic wave,the perturbation method is firstly applied to the wave equation under a given smooth background model to obtain a wave equation suitable for the perturbed wavefield generated by the inhomogeneous body.According to the relationship between the seismic wavelength and the size of the inhomogeneous bodies,the seismic data can be divided into the scattered data and the reflected data.In order to study the variation of the impedance,we only focus on the reflected waves in this paper.It assumes that the relationship between the size of the inhomogeneous body and the seismic wavelength satisfies the condition for generating the reflected waves.Then the corresponding perturbation wave equation is transformed into the reflected wave perturbation equation.In terms of the primary wave approximation and high frequency approximation,the linear forward expression of the reflected wave based on the relative impedance perturbation is obtained.Finally based on this forward equation,the least squares solution is obtained by solving the linear inverse problem,and the adjoint matrix and the source-receiver bidirectional illumination are used to approximate the generalized inverse matrix,thereby obtaining the approximate solution of the relative impedance perturbation.The imaging method can image the relative impedance perturbation directly,and the obtained imaging result reflects the variation of the relative impedance perturbation between formations.Due to the directional characteristic of the reflected waves,the relative impedance perturbation is an expression related to the angle.The wavefield is further converted into the angle domain,and then we can carry out in-depth research related to lithology and physical parameters So according to the relationship between the relative impedance perturbation and the reflected angle,the extracted angle domain common image gathers(ADCIGs)can be used to estimate the relative impedance perturbation and the relative velocity perturbation,respectively.2)Elastic wave seismic exploration can describe the relevant information of the underground medium in more detail.So on the basis of the acoustic wave impedance imaging method,we further conduct the preliminary study on the relative impedance perturbation of the elastic waves.Similarly,we derived the reflected wave equation of elastic waves based on the relative impedance perturbation,and then solve the linear equation to obtain the estimation of the relative impedance perturbation of the elastic waves.Based on the analysis of this theory,if the wavefield can not be converted to the angle domain,the relative impedance perturbation can be obtained by this imaging method directly; If the wavefield is converted to the angle domain,we can further estimated the relative perturbation of P wave velocity,S wave velocity and the density following the relationship of the relative impedance perturbation and the angle.Finally,The impedance relative perturbation imaging method proposed in this paper constructs a forward equation based on the relative impedance perturbation.And on this basis,we can obtain the approximate solution of the relative impedance perturbation by means of the linear inversion.The imaging method in this paper can make full use of the waveform information of the seismic data to obtain the migration imaging result reflecting the variation of the underground lithology and physical property parameters.And it also provides the basic data for lithology and physical parameter analysis and inversion.Thereby,this method proposed in this paper promotes the transformation of the migration imaging method from structural imaging to lithology and physical property imaging.The numerical experiments prove the effectiveness of the proposed reflected waves imaging method based on the relative impedance perturbation in this paper.