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实现非线性折射波旅行时层析的几个重要问题已得到了验证,它们是折射波旅行时和射线路径计算的精度,折射波旅行时曲线的物理特性和折射波旅行时误差的特性。由此,我们开发了一种带有优化节点分布的最短路径射线追踪方法,它能精确地计算任何速度模型中折射波旅行时和射线路径。我们发现地震折射法中由短和长射线引起的构造多解性会大大影响反演结果。因此,我们提出了这样一种非线性反演方法,它明显地减小了平均慢度(旅行时与相应射线长度的比率)和视慢度(旅行时对距离的导数)的闭合差。结果,既改善了分辨率也提高了收敛速度。为规范化反演问题,我们使用了Tikhonov方法来避免解病态的反演问题,折射旅行时误差以共炮点误差和相对旅行时梯度误差来表征,共炮点误差即来自同一炮记录的偏差为一常数,而后者与旅行时曲线的真实梯度相比具有零均值。因此,我们使用非线性蒙特卡罗方法来量度我们的层析解的不定性,并计算了与两种不同类型的随机数据向量和一个随机模型向量有关的后验模型协方差。非线性不定性分析表明,层析解的分辨率也许与射线路径不对应。我们把这种层析技术用于马萨诸塞州波士顿市附近的一个煤矿的浅层速度构造成像,结果与后来的钻井结果一致
Several key issues in the travel-time tomography of nonlinear refracted waves have been validated. They are the accuracy of refracted wave travel and ray path computation, the physical properties of refracted wave travel curves, and the error characteristics of refracted wave travel. As a result, we have developed a shortest-path ray tracing method with optimized node distribution that accurately calculates the traveltimes and ray paths of refracted waves in any velocity model. We find that the structural multi-solvability caused by short and long rays in seismic refraction methods can greatly affect the inversion results. Therefore, we propose a nonlinear inversion method that significantly reduces the closing difference between the average slowness (the ratio of travel to the corresponding ray length) and the apparent slowness (the derivative of distance when traveling). As a result, both the resolution and the convergence speed are improved. In order to normalize the inversion problem, we use the Tikhonov method to avoid the ill-posed inversion problem. The error of refraction trip is characterized by a common shot error and a relative gradient error of travel time. The error of shot point is the deviation from the record of the same shot A constant, and the latter has a zero mean compared to the true gradient of the travel time curve. Therefore, we use the non-linear Monte Carlo method to measure the uncertainty of our chromatograms and calculate the covariance of the posterior models with two different types of random data vectors and a random model vector. Nonlinear uncertainty analysis shows that the resolution of the chromatographic solution may not correspond to the ray path. We applied this technique to shallow-speed tectonic imaging at a coal mine near Boston, Massachusetts, and the result was consistent with subsequent drilling results