| The object of this paper is porous, cranny and crack 3D two-phase orthotropic medium which are filled with fluid. Firstly, we have had carried out the detailed review on the theory of porous medium and anisotropic medium and the technical Status of related seismic numerical modeling.Based on the above theory, we derived the 3D elastic kinetic equation and elastic wave propagating equation in two-phase BISQ medium according to Dvorkin (1993) and Yang Dinghui's studies. In view of the staggered grid high-order finite-difference method which had the numerous merits is quite popularly at present. We derived the forward numerical solution of staggered-grid finite difference method. Unifying predecessor's researches, we have given out the stable condition and boundary condition and studied systematically the source factor's influence to wavefield simulation in the staggered grid finite-difference method. Through 16 kinds of isotropic medium models'research, we found out:The source add on the stress item, and the source function is sphere cavity source, S wave appeared in the wave field snapshot , it is not tally with classical theory's conclusion, and the numerical frequency dispersion is very serious too. When the source function change to explosive point source, only the P-wave appeared in the wave field snapshot,this is tally with classical theory's conclusion, but on the three orthogonal planes(the YoZ plane of X component,the XoZ plane of Y component and the XoY plane of Z component) appeared the numerical frequency dispersion (noise) seriously. When the source is single direction source of the above two source functions respectively, the wave fields are tally with classical theory's conclusion, but exist obvious numerical frequency dispersion on the shapshots. On the other hand, the source add on the velocity item, there all exists S wave in the wave field snapshots when the source using cavity source and explosive point source respectively, it is not tally with classical theory's conclusion, but the numerical frequency dispersion disappear when using the explosive point source (although the S-wave wavefront is is not very circular in certain planes). and the situation of the numerical frequency dispersion is not improved at all when using the cavity source. The simulations of using single direction source still exists obvious numerical frequency dispersion. In summary, The author concluded that the most appropriate type of source is explosive point source added on the velocity when we adopted the staggered grid finite-difference method to simulate elastic wave propagation. Under this kind of condition, although the S-wave wavefront is asymmetrical in certain planes, numerical dispersion (noise) is smallest, which is the most advantaged to explain to the complex wave field. On the meantime, the author consider that regarding anisotropic medium elastic wave numerical simulation, no matter the source function being used ,it can excitated the P wave and the S wave simultaneously in the wave field.On the basis of these researches, First, based on BISQ mechanism, we simulated 3D-3C elastic wavefield of 3D two-phase orthotropic medium and analysed wavefield snapshots of different times,surface seismic records and VSP records. As a comparison, we have also presented the other two-phase medium wavefield snapshots: two-phase transversely isotropic medium,two-phase azimuth anisotropy medium. We analyzed the characters of wavefield. According to the above studies, we got the following conclusions: (1) There are four kinds of waves in two-phase anisotropy media, namely, fast quasi-P wave, slow quasi-P wave, fast quasi-S wave, and slow quasi-S wave. (2) For the viscous media, because the slow qP-wave have a strong attenuation property, we can not see clearly from the solid phase wavefield, but for the ideal non-viscous media, the clear slow qP-wave shown can be seen in both fluid and solid phase snapshots and records. (3) Assuming the anisotropy of solid-fluid coupling density and permeability, the propagation of slow qP-wave show anisotropy characteristic. The change of solid-fluid coupling density is more obvious to the influence of slow P-wave's propagation velocity. (4) In two phase anisotropy media, the wave field is much more complex due to the reflection, transmission, conversion and shear wave splitting on the interface. (5) From the two kinds of three-layers VSP records, we can see that seismic wavefield is more complex in two-phase medium. Fast qP wave propagation not only has the transmission, and reflection, but also has the conversion (convert to qSV wave and slow qP wave). The qS wave can converted to slow qP wave too. The reflection wave of slow qP-wave is quite weak, and also has not seen its conversion. Dispersion situation is quite serious on Y components of fluid-phase wavefield and Z components. The corresponding dispersion situation of solid-phase is quite slight. We analyzed the reason that slow P-wave velocity is low (less than 100/s) and does not satisfy the stable condition. This may be solved by decreasing the space and time domain sample interval(spatial sampling interval around 1m). However, because of the limitation of computer hardware at present, we can only be given such a result. (6) From the surface records we can see that X,Y component is quite sensitive to the S wave, the amplitude of reflection S-wave is more strong and P-wave is relatively quite weak. However, Z component is just right opposite. This is also evidence of our present exploration, especially the proof of P-wave exploration. For three-layers two-phase medium we may observe the slow p-wave's direct wave and reflection on fluid-phase wavefield. But for the three-layers model with single-phase and two-phase interface, the slow p-wave's direct wave and reflection cannot be seen even if on the fluid-phase wavefield.Researching dispersion and attenuation of seismic wave have vital significance for predicting the existing and distribution of fluid in media and studying the pore construction. We deduced the Christoffel equation of 3D two phase media according to the elastic wave propagation equation based on the BISQ mechanism. By solving the Christoffel equation, we got the formulas of phase velocity, the inverse quality factor(Q-1)and the absorption coefficient of different waves, which thus has established relations between the two and solid media parameters,fluid permeability,porosity,glutinousness,frequency,fluid character ejection flow length,wave propagation direction. According to the derived formulas, we has calculated each kind of wave phase velocity and inverse quality factor(Q-1) in the well logging frequency band (100-2000Hz),and has studied the impact of solid flow parameters on the seismic wave dispersion and attenuation. This is important for oil parameter inversion using well log data. Because the massive predecessors study are aimed at high frequency situation(above ten thousand MHz),reflected the medium high frequency wave character, but high frequency characteristic of porous medium including fluid can not necessarily reflect the low frequency character. Through the researches, we can get the following conclusions: (1) In the well log frequency band,.the phase velocity of fast qP-wave, slow qP-wave, qSV-wave increases along with the frequency increasing, but has little influence on qSH-wave. The inverse quality factor(Q-1) of fast qP-wave, qSV-wave qSH-wave increases along with the frequency increasing gratwoly the slow qP-wave just right opposite (2) Porosity mainly affects on phase velocity to seismic wave dispersion and attenuation. Along with porosity increasing, phase velocity of the four waves is reducing gratwoly. However, slow P-wave's reduce is quite small. But if the porosity were gratwoly reduced, the speed of slow qP-wave was increased gratwoly, when porosity were less than 10-8, slow P-wave would completely vanish. The wavefield of solid-phase and fluid-phase are almost the same, which is equal to the result of the theory of pure elastic. (3)Permeability mainly impacts dispersion and attenuation of the qP-wave and qSV, but has little influence on qSH-wave. (4) The viscosity also has the varying degree influence to four kinds of wave's phase velocity and attenuation. To compare with slow qP-wave, the change of other three kinds of waves is small. (5)The direction of wave propagation has great influence on wave attenuation and dispersion. Fast qP-wave has the strongest attenuation value in the axis of symmetry direction. This direction was usually considered as the direction of bearing permeability. The situation of slow qP-wave and fast qP-wave is opposite. (6) The dispersion and attenuation of seismic wave have anisotropic character,which were caused by the anisotropy of solid frame together with solid-fluid coupling anisotropy.
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