论文标题
通过源扩展的完整波形反转：为什么起作用
Full Waveform Inversion by Source Extension: Why it works
论文作者
论文摘要
一个极其简单的单轨道传输示例显示了全波形反演的扩展源公式如何在没有虚假的局部最小值的情况下产生优化问题（“循环跳过”）。数据由距点源的给定距离记录的单个跟踪组成。假定速度或缓慢是均匀的，并且靶源小波被假定为准冲动或集中在零时间滞后。源是通过允许能量在时间上扩展的扩展，并通过将扩展源小波的加权均匀平方添加到数据失误中来控制扩展，以产生扩展的反转目标。可以明确计算目标函数及其梯度，并且很容易看出所有局部最小化器都必须在正确缓慢的波长之内。该推导显示了所有类似的扩展源算法的几个重要特征。例如，内部优化（可变投影方法）中具有源估计的嵌套优化至关重要。重量操作员的选择，控制扩展的自由度，至关重要：这里提出的选择是一个差异操作员，该财产对于生产客观免于自行车而言至关重要。
An extremely simple single-trace transmission example shows how an extended source formulation of full waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"). The data consist of a single trace recorded at a given distance from a point source. The velocity or slowness is presumed homogeneous, and the target source wavelet is presumed quasi-impulsive or focused at zero time lag. The source is extended by permitting energy to spread in time, and the spread is controlled by adding a weighted mean square of the extended source wavelet to the data misfit, to produce the extended inversion objective. The objective function and its gradient can be computed explicitly, and it is easily seen that all local minimizers must be within a wavelength of the correct slowness. The derivation shows several important features of all similar extended source algorithms. For example, nested optimization, with the source estimation in the inner optimization (variable projection method), is essential. The choice of the weight operator, controlling the extended source degrees of freedom, is critical: the choice presented here is a differential operator, and that property is crucial for production of an objective immune from cycle-skipping.
