| The velocity of seismic waves through the medium is an important physical quantity in seismic exploration, as well as the core basis of processing and interpretation the seismic data. Velocity is indispensable for time-depth conversion, structural imaging, lithology identification, and crack detection of seismic data. It can be said that velocity is of great importance among all the links of processing and interpretation the seismic data. Early seismic exploration is based on the assumption of horizontal layer medium. In addition, the signal-to-noise ratio related to seismic data is relatively low at that time. Therefore, CMP stacking method is proposed to raise the ratio and realize the purpose of structuring imaging. In order to make the CMP stacking available, the stacking velocity which is related to the NMO velocity is needed. NMO velocity is then related to the RMS velocity based on which the average velocity and interval velocity can be figured out. Thus it can be seen that NMO velocity, the basis of velocity analysis and modeling, plays an important role and is an essential flow in processing and interpretation the seismic data.NMO velocity is closely related to gathers. Generally speaking, different gathers possess different analytical expressions for the time-distance relationship and NMO velocity. Theoretically, NMO velocity can be figured out through the ratio between the travel time when the time-distance first-order derivative is zero and the offset second-order derivative. NMO velocity, generally speaking, is defined at the locations of zero offset. If the time-distance first-order derivative is not zero at this location, that is, the time-distance based on the zero-offset is not symmetrical, e.g. CSG and PS converted waves CMP gather, then the NMO velocity at this location does not exist. The CRP gather of isotropic medium to P wave on the three-dimensional dipping interface is in accordance with the reciprocity principle, therefore, the time-distance based on the zero-offset is symmetrical, and the time-distance first-order derivative in the locations of zero offset must be zero, and we can select NMO velocity in such circumstance. Although The CRP gather of isotropic medium to PS wave on the three-dimensional dipping interface is not in accordance with the reciprocity principle of shot point and detection point, and the time-distance based on the zero-offset is unsymmetrical, we can still select NMO velocity in the above circumstance, because as for this kind of gather, the first-order derivative of travel time to offset is zero. In the anisotropic medium, if the anisotropic symmetry axis runs parallel or vertical to the normal of the three-dimensional dipping interface, then first-order derivative of travel time of the similar reflection wave and the reflected converted wave at the locations of zero offset to the offset distance is zero. At this time, we can adopt the same NMO velocity.There have been numerous researches on 3D3C seismic exploration both at home and abroad. This kind of exploration has been applied in some sectors of coal and oil production. In connection with the 3D3C seismic exploration, this paper mainly takes into consideration the following three aspects: structural form, adopted gather, and medium assumption.In regard to the structural form, 3D3C seismic exploration many faces some complicated structural issues including the three-dimensional dipping interface. In this paper, the focus is mainly put on a single three-dimensional dipping interface. The complicated curved interface is treated as equivalence to the tangent plane of each point of this complicated curved interface. Meanwhile, the concept of RMS velocity is introduced and multilayer medium is regarded as equivalence to the monolayer medium so as to reduce the complexity of these problems.As for the gather, in terms of three-dimensional dipping interface, different gathers possess different time-distance relationships, and if there is NMO velocity, then they also possess different NMO velocities. Meanwhile, each gather has its own advantages and disadvantages. The selection of gather depends on the perspective of considering the issues. This paper, mainly from the perspective of the reflection point and the converted point, adopts the CRP gather and CCP gather. Adopting these two gathers involves the extraction of gathers, which needs prepared corresponding structures and velocity models. How to complete the extraction of the CRP gather and CCP gather becomes the key point. Traditional CMP gather does not depend on the medium velocity or interface shape, and it can take the interface shape resulted form CMP stacking as the initial model. On this basis, analysis of velocity will be conducted by use of the gathers which have been extracted so as to obtain a much more accurate model. And then extraction of the CRP gather and CCP gather will be repeated until the real profile of stacked CRP gather and CCP gather. From this we can see that the procedure of forming a CRP and CCP gather can be regarded as an interactive procedure. Specially, if the modeling method mentioned in Chapter two is adopted, the P wave and PS converted wave can be processed separately, and thus practical difficulties in comparing the horizons of the P wave and PS converted wave will be straitened out.As for medium assumption, isotropic medium is the foundation of researches of anisotropic medium. This paper firstly discusses the exact solution of time-distance relation between P waves and PS converted waves when common conversion point gathers are adopted on the three-dimensional dipping interface under the circumstance of isotropic medium and its approximate solution under the circumstance of non-distant offset and the corresponding NMO velocity. Besides, as for researches on anisotropic medium, despite the spatial orientation of symmetry axis of anisotropic medium and the degree of strength of anisotropic medium, domestic and foreign researches on anisotropic medium overall think that P wave is based on CMP gathers, and most converted waves is supposed on level interface. The content of this paper's researches is put forward on the basis that on the three-dimensional titled interface, similar waves have common reflection points and converted waves have common conversion points, which is greatly different with prior researches. Isotropic medium is much more complex than anisotropic medium, so it is necessary to make proper hypotheses for corresponding researches. There are two basic hypotheses in this paper: firstly, considering weak anisotropic ATI medium to ignore differences between phase propagation path and group propagation path and avoid complexity of other low symmetric anisotropic medium. Secondly, on the premise of continuum hypothesis of weak anisotropic medium, we assume that the propagation paths of isotropic medium and of anisotropic medium are the same, in this way we can separate the issue of velocity of anisotropic medium from propagation and common reflection points of anisotropic medium or gathers of common converted points so that we can conduct better discussion of time distance relation and NMO velocity under the circumstance of anisotropic medium to probe into inversion problems of anisotropic medium's parameters. In order to make it simple, anisotropic medium studied in this paper takes two modals that are usual on geology into consideration: (1) the symmetry axis of anisotropic medium is perpendicular to three-dimensional dipping interface; (2) the symmetry axis of anisotropic medium is parallel to three-dimensional dipping interface.1. Basis of Topic, Research Ideas and Methods and InnovationBasis of topic: Yao Chen (2005) puts forward new extraction methods of CRP groups and CCP groups of isotropic medium on three-dimensional dipping interface, and on this basis, he raises analytical expression of corresponding time-distance of the two groups; Yao Chen (2006) gives analytical expression of phase velocity of any anisotropic medium; domestic and foreign researches are about either common reflection points or common converted points, and they don't discuss the influence of anisotropic medium on the NMO velocity of these two gathers under the circumstance of three-dimensional dipping interface.Research Ideas: analytical solutions of travel time and offset of CRP gathers and CCP gathers of anisotropic medium on three-dimensional interface are all functions of ray parameter p. Under the circumstance of non-distant offset, we regard travel time as function of offset, conduct Taylor expansion of travel time and choose the quadratic term of offset, and then get the square of approximate travel time and delete the term higher than quadratic. Because travel time and offset are all functions of ray parameter p, so by using the derivation rule of parametric equations, we can get first-order derivative and second-order derivative of time travel to offset and finally obtain the hyperbolic approximate analytic expression of travel time. According to physical definition of NMO velocity, we can obtain the analytical expression of these two groups'NMO velocity of isotropic medium on three-dimensional dipping interface. According to mathematic definition of NMO velocity, we can directly get NMO velocity's analytical expression through derivation. Relevant theoretical derivation focuses on CCP groups and treats CRP groups as special exceptional cases of CCP groups. The derivation of anisotropic medium is comparatively complex. Its basic thought is treating anisotropic medium as the result that a disturbance is attached to isotropic medium. Therefore, the above results of anisotropic medium are still valid, and what needs to be dealt with is just the disturbance. According to analytical expression of the phase velocity of any anisotropic medium, we can get its velocity disturbance, which is a function about anisotropic medium dip angle and azimuth of anisotropic medium's symmetry axis as well as dip angle and azimuth of propagation direction. The NMO velocity of CCP groups of anisotropic medium on three-dimensional dipping interface can be obtained through the derivative of disturbance to offset, which can be obtained through derivation of a series of intermediate variables.Research Methods: the method of analysis is adopted.Innovation: this is the first research of NMO velocity of CRP groups and CCP groups of anisotropic medium on three-dimensional dipping interface based on real common reflection points and common reverted points and it gives specific analytical expression of NMO velocity. It is first to give analytical expression of NMO velocity of these two groups under the circumstance that anisotropic medium is on three-dimensional dipping interface, and discuss the influence of azimuthal effect of both anisotropic medium and three-dimensional dipping interface on characteristics of NMO velocity of real CRP groups and CCP groups.2.The brief introduction of each chapter of the paper as well as the relative resultsChapter one is the introduction, which concisely introduces the significance of NMO velocity in the processing and illustrating of the entire earthquake data, the concept of NMO velocity, the constitution of the utilized CRP Gather and CCP Gather, as well as the domestic and overseas current researching conditions of NMO velocity.No matter the isotropic medium or the anisotropic medium it is, the relative researches of NMO velocity of P wave are based on CMP Gather. When the interface tilts, its reflective spots scatter which will affect the accuracy of the calculation of the velocity, as well as is disadvantageous to further commit the lithologic interpretation and AVO analysis. Whereas for the processing of the PS wave, we have already recognized that we should take advantage of the CCP Gather, due to the complexities of the problem, we usually produce the approximation for the constitution of the Gather. In addition to the Isotropic closed offset of the horizontal interface, the research of the NMO velocity of PS wave is scarcely to see. According to the problems of the scattering of the reflective spots of CMP Gather of P wave and the requirements of CCP Gather of PS wave, interestedly, we utilize the CRP Gather and CCP Gather for the processing of the 3D3C earthquake data. For the problem of three-dimensional dipping interface, the ways are much more complex, thus the relative researches are much more challenging. Comprehensively taking the above problems into account, no matter the CRP Gather or the CCP Gather, whether they own the hyperbolic travel time curve or the approximate hyperbolic travel time curve and the relative NMO velocity is remained unknown in the domestic and overseas researches. Theoretically, offering the necessary explanation is constructive. Chapter two is about the structure morphology and the velocity model of the common reflective spots of the isotropic medium and the extraction of the common breaking gather that are referred to. According to the time-distance relationship approximate analysis expression of the PS converted wave of CMP Gather, by utilizing the PS wave data, theoretically offers the estimation method of the five independent parameters, such as the dip angle, tendency, and depth, velocity of longitudinal wave and velocity of transverse waves of three-dimensional dipping interface that used to describe time-distance relationships. Moreover, via the approach of theory stimulating the data, the feasibility of this method is proved, and the main results are as follows:(1) There exists the minimal arrival time in the case that the apparent dip of CMP Gather of PS converted wave is in the medium and small angles and their values are negative in the three-dimensional dipping interface. The minimal arrival time is less than the self-excitation time of 0-offset, whereas it is not evident in the variation of azimuth. The location of the minimal arrival time deviant from the 0-offset and it is evident in the variation of azimuth. It is related with the depth of the interface, the apparent dip, the rate of the velocity of longitudinal wave and velocity of transverse waves. It has nothing to do with the velocity of longitudinal wave and velocity of transverse waves. It is very sensitive to the absolute value of the apparent dip. (2) The approximate time-distance relationship is hyperbolic, when x / h < 1, it can best fit the accurate time-distance relationship. The error of fitting is relative to the depth of the interface, the apparent dip, the velocity of longitudinal wave and velocity of transverse waves as well as the offset distance. In normal condition, the larger rate of the offset distance and the velocity of longitudinal wave and velocity of transverse waves, the bigger error of fitting is. For the same offset distance, the larger the depth, the smaller the error of fitting is. For the identical rate of the velocity of longitudinal wave and velocity of transverse waves, the larger of the velocity of longitudinal wave and velocity of transverse waves, the smaller the error of fitting is. When the apparent dip is positive, namely, the error of fitting is small for the up dip blasting and the down dip receiving. When the apparent dip is negative, namely, the error of fitting is comparatively large for the up dip blasting and the down dip receiving.(3) Theoretically, taking advantage of the parameterized approximate time-distance relationship, via the two PS converted wave data of the measuring positions, the five independent parameters, which are the dip angle of the interface, tendency, depth, the velocity of longitudinal wave and velocity of transverse waves respectively that are used to describe CMP Gather of PS converted waves of the three-dimensional dipping interface completely and solely. The practical difficulties in comparing the horizons of the P wave and PS converted wave will be straitened out.In Chapter 3 and Chapter 4, the analytical expressions for time-distance features and relevant NMO velocity of the P wave CPR gather in the isotropic medium as well as the PS converted wave CCP gather are analyzed. Results and recognitions are as follows:(1)P wave CPR gather and PS converted wave CCP gather of the three-dimensional dipping interface possess a simple approximate hyperbolic time-distance relationship just as P wave CMP gather. When the ratio of offset to depth is less than 2 for P wave, or the ratio of offset to depth is less than 1 for PS wave, a relatively higher fitting accuracy can be achieved.(2) Different gathers have different time-distance relationships and NMO velocities. The analytical expressions for NMO velocities of P wave CPR gather and PS converted wave CCP gather differ from that of CMP gather mainly in that the former responds differently to the apparent dip towards the interface. With regard to P wave, the NMO velocity of CPR gather is slower than that of the medium, which decreases with the increasing interface apparent dip. On the contrary, the NMO velocity of CMP gather is larger than that of the medium, which increases with the increasing interface apparent dip.(3) The NMO velocity of P wave CPR gather and PS converted wave CCP gather features ellipse shape with the changing surveying line direction. The larger the dip angle, the more obvious the feature of the ellipse is. The long axis of NMO velocity ellipse is along with the interface direction, and the minor axis is along with the interface tendency. The ratio between the long and minor axis is 1 + sin 2δ, even if it is a high dip angle, the maximum ratio between long and minor axis would be 1.4.Chapter 5 discusses the analytic relations between NMO velocity of similar reflected wave and that of reflected converted wave in conditions when anisotropic asymmetry axis and the normal three-dimensional dipping interface are mutually parallel and vertical to each other. The conclusions are as follows:(1)Whether anisotropic asymmetry axis and the normal three-dimensional dipping interface are in parallel or vertical relations, the first-order derivative of travel time to offset distance is zero, so even the anisotropic offset distance is not so long, the time-distance relationship still possesses the approximate solution of hyperbolic form at non-distant offset..(2)Under both anisotropic medium conditions, the NMO velocity curves of both similar reflected wave and reflection converted wave are ellipse. When anisotropic asymmetry axis and the normal of three-dimensional dipping interface are in parallel relation, the long and minor axis direction of NMO velocity ellipse is the same with that in isotropic conditions, that is to say the long axis is along with the interface direction, and the minor axis is along with the interface tendency. The length of long and minor axis has nothing to do with the dip angle of the interface, but only concerns with anisotropic parameters, that is to say the stronger the anisotropy, the longer the long axis. The length of minor axis depends on the strength of anisotropy and the dip angle of dipping interface. When the anisotropy is more powerful, the minor axis becomes much longer. When the interface dip is larger, the minor axis is much shorter, and the ellipse features become more obvious. When anisotropic asymmetry axis and three-dimensional dipping interface normal are in vertical relation, the long and minor axis direction of NMO velocity ellipse differs with that of the isotropy. The offset angle of the two relates with interface dip, tendency and the spatial orientation of anisotropic symmetry axis.At last, Chapter 6 summarizes the basic conclusion and existing shortages of this paper, and proposes further work assumption.In terms of isotropic medium, when the ratio between offset distance and depth of P wave CPR gather and time travel of PS converted wave CCP gather is less than 2 or less than 1, the accuracy is relatively high. In dynamic correction process, the ratio between offset distance and depth of P wave and PS converted wave is 1.6 and 0.8 respectively. Aiming at the above problems, we can further develop the approximate solution to time-distance relationship with long offset distance.In terms of anisotropic medium, we only discuss about the two special spatial orientations of anisotropic asymmetry axis, while other spatial orientations of anisotropic asymmetry axis also need further study.
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