Seismic Reflection Travel Time Tomography Studies, Theory And Application

Velocity model building is an important technique in seismic exploration. Migrationvelocity analysis and tomography are two important manners among others. From thepoint-view of theory, the accuracy of tomography is higher, but tomography is restrictedby many factors in application, the difficulties of tomography don't lie with theories andmethods, but lie with the skills of implementation.Considering the difficulties in the theories and applications of the tomography, andthe ambiguities between the velocity and the reflection depth, the idea of using theresults of migration velocity analysis as the initial model of the tomography isestablished, so that the tomography inversion can have a good start.In this paper, the development status in quo of migration velocity analysis andtomography are introduced briefly, then the problems existed in tomography areexpounded, and the two velocity model building methods are compared. The migrationvelocity analysis is required less, the constant velocities in layers are fine, but thereflection depths of interfaces are necessary. Due to the iterative and alternatingcharacteristic of migration velocity analysis, Kirchhoff migration method suitable forlocal areas and the strategy of analyzing velocity along the reflector are adopted.On tomography, Several aspects are introduced: the solver of tomography equationsystem, regularization and normalization. The solution process of tomography equationsystem has two stages: the direct solution and the iterative solution. The direct solutionis only suitable for matrix with small dimensions, and the iterative solution includesART methods and projection methods. ART method emerges in the early age oftomography development at that moment the memory and storage space of computer arelimit. Projection methods are the most used methods currently, mainly includes Lanczosmethod, conjugate gradient method, least square conjugate gradient and least square QRfactor decomposition method. It is very important using regularization to constrain theunderdetermined and the null space components in tomography inversion.Regularization usually has two manners: using the over-determined components toconstrain the under-determined and the null space components; and using the priorinformation to constrain the under-determined and the null space components. In thispaper, the fashion of regularization is classified into two classes: the addition style andthe multiplication style. The addition style usually pads the regularization equationsystem after the primal equation system; the multiplication style usually multiples theregularization equation system with the primal equation system. Except the action rangeand action style of regularization, the matrix expression and compression storage ofregularization are also introduced in this paper. In addition, the effects of variousregularization patterns are also analyzed. Normalization is another important problem inseismic tomography. In tomography, the data and the model have different physicaldimensions, and even elements of data and model parameter have different physical dimensions in multi-parameter tomography. The modules of different column vectors ofthe Frechet matrix are very different, which results in poor condition of tomography, sowe must normalize all the data and model parameters to nondimensional mount beforetomography.About the ambiguity between velocity and reflection depth in reflectiontomography, research results of many geophysicists are integrated and the followingconclusions are obtained: In essence, the ambiguity between velocity and reflectiondepth is caused b y s mall offset, t he ambiguity can b e mitigated by t he existences o flarge offsets. The ambiguity between velocity and reflection depth is influenced by thefollowing factors:(1) the ratio between the offset and the depth, the larger the ratio, theweaker the ambiguity;(2) the pick error, the smaller the pick error, the weaker theambiguity;(3) the dip of the reflector, the smaller the reflection dip, the weaker theambiguity;(4) the ratio between perturbation wavelength and characteristic wavelength,when the ratio is greater than 1, velocity perturbation dominates, when the ratio issmaller than 1, the depth perturbation dominates, when the ratio is equal to 1, theambiguity occurs. The characteristic wavelength depends on the thickness of anomalyand the distance between the anomaly and the reflector.In this paper, the tomography system based on the rectangle cell parameteration isestablished. In modeling based on rectangle cell, Langan ray tracing is adopted, whichhas three merits:(1) The three-parameters expression style of the velocity in one cell,considers the limits of ray theory——velocity must be smooth, thus the method has somesmooth effects in essence;(2)L angan ray tracing has perfect analytic expression, andaccuracy and efficiency can be guaranteed;(3) when the model vector is chosen asslowness vector difference, the data vector is chosen as the time difference, the length ofray in cell is the Frechet derivative which denotes the sensitivity of the data due to themodel perturbation. Considering the storage and computation pressure caused byrectangle cell parameteration, line-indexed compression storage is designed in this paper,and the various computation skills are also designed so that various projection iterationmethods suitable for primal tomography matrix are also suitable for compressed matrix.Various regularization matrixes are also stored and take part in tomography computationin compression style. The compression storage and solution of primal matrix andregularization matrix are very effective, large amount of computation time and storagecan be saved.In current tomography, rectangle cell parameteration is the most adopted, butrectangle cell parameteration is not optimistic in many aspects: To finely expresssubsurface medium, the rectangle cell parameteration need large mount of cells, whichresults in huge matrix dimensions (even worse when considers regularization), thesparseness of matrix expenses large mount of computation time and storage space,although the line-indexed compression storage method and solution of compressedstorage equation system are designed so that large amount computation time and storagemount can be saved, the iterative and interactive characteristic of tomography still makes large amount of computation time and storage space as the limiting factors inrectangle cell tomography system. In addition, the uniform rectangle cell is not flexible,the same size of cell must be adopted both in complex structures areas and in simplestructures areas, thus the number of cell is very large, which results in morecomputation time, more computation mount and more storage space in modeling andresults in the worse condition and the larger difficulties in tomography. Moreover,rectangle cell parameteration has shortcomings in expressing the reflection interfaces,the velocity change above and under the interface can only expressed in saw-teethfashion, thus increase the difficulties and inducts the errors when treating interfaces.Aiming at the several adverse factors introduced by rectangle cell parameteration, thetomography system based on triangle cell parameteration is established. Triangle cellparameteration is not only flexible, but also has some regularization effects in essence.Compared with rectangle cell parameteration, the triangle cell parameteration has meritsin computation time, computation mount and storage mount. And the results obtainedby the two parameteration styles are comparative.