论文部分内容阅读
地震图的非线性反演的传统目的是获取地球模型,对于初始条件为零和给定震源,该模型能最好地预测观测地震图。最近用迭代法解决了这一问题:每次迭代就是对当前介质中的实际震源的波动方程求解;对以当前残差为震源的反向时间波动方程求解;在空间的每个点上将由此得到的两个波场求相关。我们的反演目的较全面:要获得整套的地球模型、初始条件、震源函数和预测地震图。它们最接近某些先验值并且是通过波动方程相互联系起来的。不仅能证实以前的方法,而且还使我们能以不同的方法解相同的反演问题:对于绐定的震源和实测地面位移,现在研究的是计算的和先验的初始条件间的最佳拟合是什么?这将导致完全不同的迭代法,每次迭代包括给定地面位移和牵引力的向下外推,直到一个给定的深度(底部)。将前面的场的起始时间条件作为震源,把底部的零位移和牵引力向上外推,并且在空间的每个点上求解将由此获得的两个波场的相关。除了该结果的理论意义之外,它开拓了解反演问题的数值法的途径。如果使用正向和反向时间传播的非线性反演有效的话,那么由于在深度外推中可能使用的某些手段(逐频计算(Calculation frequency byfrequency),底层以前的顶层的反演),使用向下-向上外推的这种非线性反演将给出相同的结果并且更为经济。
The traditional purpose of nonlinear inversion of seismograms is to obtain Earth models that best predict observed seismograms for initial conditions of zero and for a given source. This problem has recently been solved by iteration: in each iteration, the wave equation of the actual source in the current medium is solved; the wave equation of the inverse time with the current residual as the source is solved; at each point in space, The two wave fields obtained are correlated. Our inversion is more comprehensive: to get a complete set of earth models, initial conditions, source functions, and prediction seismograms. They are closest to some a priori values and are related to each other by wave equations. Not only can we prove the previous method, but it also enables us to solve the same inversion problem in different ways: for a given source and measured ground displacement, we now study the best fit between the calculated and a priori initial conditions This will result in an entirely different iterative method, with each iteration including a given ground displacement and a downward push of tractive force up to a given depth (bottom). Using the onset time condition of the previous field as a source, the zero displacement and traction at the bottom are extrapolated upward and the correlation of the two wavefields thus obtained is solved at each point in space. In addition to the theoretical significance of the result, it opens the way to understanding the numerical method of inversion. If non-linear inversion using forward and reverse time propagation is valid, then due to some means that may be used in depth extrapolation (Calculation frequency by frequency, inversion of the previous top level), use This non-linear inversion of the down-up extrapolation will give the same result and be more economical.