Azimuthal AVO In TTI Media

In coalfield and oilfield seismic exploration,AVO is an important tool used to predict and identify coal seam and oil reservoir.The difference of the AVO method between coal seam and oil reservoir is that the impedance contrast between coal seam and its surrounding rock is smaller compared with that between oil reservior and its surrounding rock,which always breaks the relationship between incidence angle and transmission angle,enhances the error between approximation and exactness and finally limits AVO's application in coalfiled exploration;at the same time,due to that the existence of fissures makes the targeted strata anisotropic,we usually research on the fissures in coal seam and oil reservoir with Horizontal transversely isotropic or Vertical transversely isotropic media rather than Tilt transversely isotropic media whose AVO coefficients fall in between,which could affect AVO intercept,gradient and curvature,so it could result in an intolerable error for the application of AVO attributes in identifying geophysical features of reservoirs;when the aspect ratio of fissures is large enough,it will cause energy loss with respect to the friction between the solid skeleton and the fracture fluid,which is called frequency dependence in anelastic media,so we need to analyze frequency dependant features.Aimed at the deficiencies of AVO analysis,at first we assume that incidence P-wave impinges the horizontal interface from an overlying isotropic medium and an underlying tilt transverly isotropic medium with a tilt set of fissures and the interface could generate reflected longitudinal wave,reflected fast shear wave,reflected slow shear wave,transmitted longitudinal wave,transmitted fast shear wave and transmitted slow shear wave;nextly we build the sixth order Zeoppritz equation based on continuous boundary conditions of displacement and stress;finally based on the condition of weak anisotropy,we derive,simplify and build models for numerical simulations.Through the above research statement,the main innovations are as follows:First of all,according to Thomsen's anisotropic definition,weakly anisotropic approximation and the same propagation of phase and group velocities,we keep the first order items of anisotropic parameters,derive the P wave's approximate polarization,further perturbation by anisotropy on displacement and stress,and eventually solve for AVO approximation,function of Thomsen's parameters.Based on the derived azimuthal AVO approximation,build different models to generate reflection waves' curves and conclude that a vertical P wave could generate converted waves due to the tilt fissures;comparing approximation with exactness,in the isotropic plane,i.e.at 90 degrees azimuth,the error is the largest;when the ratio of longitudinal wave to shear wave velocities is 2,the fitting effects of AVO approximate and exact curves is the best;when the ratio is less than 2,the fitting effects of AVO approximate and exact curves for shear wave is more reliable than longitudinal wave;when the ratio is more than 2,the fitting effects of AVO approximate and exact curves for longitudinal wave is more reliable than shear wave;on the basis of the analysis of the difference between numerical models,the influencing factors on the error between approximation and exactness from strong to weak are respectively the relationship between incidence angle and transmission angle,the division of approximation into isotropy and anisotropy and the derivation of velocities to azimuth.Based on the updated approximate polarization in TTI media using Ruger's VTI approximate polarization,take reflection and transmission P wave coefficients as an example,solve for the updated reflection and transmission approximations and prove that the error between approximation and exactness is the largest at 45 degrees azimuth.Two different methods for solving the seismic wave polarization could result in different conclusions.Secondly,according to Schoenberg's weaknesses expressed by Chapman's thirteen parameters,rebuild the exact Zeoppritz equation and solve for the numerical solutions of reflected longitudinal wave,reflected fast shear wave and reflected slow shear wave.In the Hooke's stiffness tensor calculated by the Chapman theory,the tangential weakness is a constant for the frequency range of 0-100 Hz and the normal weakness is frequency dependent.According to the variation of quality factor with incidence angle and azimuth angle,the attenuation of fast shear wave is the largest,but the smallest for longitudinal wave.For a vertical set of fissures,whatever azimuth,the dispersion of fast shear wave could be ignored,but the largest for longitudinal wave and slow shear wave in the symmetry axis plane(a vertical plane containing the symmetry axis);the tilt fissures could enhance the dispersion obviously,but the difference between the strikes of fissures in the upper and lower media weakens the dispersions for longitudinal wave and slow shear wave and further strengthens the dispersions for fast shear wave.Overally it's difficult for seismic reflection coefficients to predict their variations with frequency,not just increase or decrease with frequency.Then,take reflection and transmission P wave coeffients as an example,simplify the Zeoppritz equation by weaknesses and solve for the P wave's azimuthal AVO approximation.When the weaknesses are plural or real,seismic wave propagates in anelastic or elastic media.Without respect to different grain sizes in the conventional seismic exploration,we prefer the Hudson theory rather than the Chapman theory to calculate the weaknesses.According to AVO approximation,AVO attributes – intercept,gradient and curvature change greatly in the frequency range of 0-20 Hz concluded from the analysis of dispersion in the frequency range of 0-100 Hz.If we make use of the values of AVO attributes to predict the physical properties,AVO intercept reaches its maximum at 90 degrees polarization angle,AVO gradient reaches its maximum at 45 degrees polarization angle and AVO curvature reaches its maximum at 0 degree polarization angle;If we make use of the change rates of AVO attributes to predict the physical properties,AVO intercept changes greatly at 0 degree polarization angle and remains stable at 70-90 degrees polarization angle,AVO curvature changes greatly at 90 degrees polarization angle and remains stable at 0-30 degrees polarization angle,and AVO gradient changes greatly at 0 and 90 degrees polarization angle.Perturbation of intercept and curvature by the tilt fractures falls in those of the vertical and horizontal fractures,while gradient goes beyond the scope and is affected greatly at 45 degrees polarization angle.Again,make use of P wave azimuthal AVO approximation in anisotropic HTI media and take two steps to invert for weaknesses in anisotropic media due to the fact that perturbation caused by anisotropy on AVO reflection coefficients is much smaller that that by the skeleton parameters: at first,ignore the effect of weaknesses in anisotropic media and invert for the skeleton parameters;then,make use of the difference of azimuthal reflection coefficients for weaknesses.The benefit of this thought is to eliminate pathological characteristics of inverse matrix.The inversion method for the skeleton parameters,such as the ratio of P wave to S wave velocities,density,and the weaknesses are both based on the Bayesian theory,whose operator is convergent and hardly reliable on the initial model's parameters,so the ratio of the tangential to the normal weaknesses could be used to distinguish the fracture filler(e.g.gas and fluid).The inverted results of P wave reflectivity,S wave reflectivity and tangential weaknesses are reliable except density and the normal weaknesses.At last,on the basis of the derived formula for a single set of fissures and Hudson's equivalent theory without the existence of mutual influence between different groups of fractures,the Hooke's equivalent stiffness tensor is the linear sum of perturbations of different fractures and also prove the velocities and polarizations are the linear function of fracture parameters in the media with many sets of different fractures,so is the azimuthal AVO approximation,which provide the theoretical support for the analysis.Judging from the derived AVO formula,we can clearly see the effects of the master and the secondary fractures on reflection coefficients.Besides the above research contents,we supplement the formula of the stiffness tensor for the equivalent model theory in TTI media,the approximate velocities,quality factor,polarization and so on.In Chapter 3.3,we provide the formula for the converted point and find that when the visual angle is larger,the range of the projection of the converted point on the horizontal is also large;with the depth of the inclined interface increasing,the range of the projection of the converted point on the horizontal is convergent.For anelastic and elastic media,without information about the underground medium the variation of AVO curves in space can identify the fracture strike and dip.