Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exaspirated by the fact that new simulations must be performed when the velocity structure or source location is perturbed. Here, we explore a prototype framework for learning general solutions using a recently developed machine learning paradigm called Neural Operator. A trained Neural Operator can compute a solution in negligible time for any velocity structure or source location. We develop a scheme to train Neural Operators on an ensemble of simulations performed with random velocity models and source locations. As Neural Operators are grid-free, it is possible to evaluate solutions on higher resolution velocity models than trained on, providing additional computational efficiency. We illustrate the method with the 2D acoustic wave equation and demonstrate the method's applicability to seismic tomography, using reverse mode automatic differentiation to compute gradients of the wavefield with respect to the velocity structure. The developed procedure is nearly an order of magnitude faster than using conventional numerical methods for full waveform inversion.

翻译：地震波的传播构成了地震学研究大部分方面的基础,然而,解决波方程式则是阻碍研究进展的一个主要计算负担。 这一点被以下事实所推卸:在速度结构或源位置受到扰动时,必须进行新的模拟。 在这里, 我们探索一个用于学习一般解决办法的原型框架, 使用最近开发的机器学习范式, 叫做神经操作员。 训练有素的神经操作员可以在可忽略的时间计算出任何速度结构或源位置的解决方案。 我们开发了一个计划, 以随机速度模型和源位置的模拟组合来训练神经操作员。 由于神经操作员没有电网, 有可能评估高于所培训的分辨率速度模型的解决方案, 提供额外的计算效率 。 我们用 2D 声波方程式来说明方法, 并演示方法对地震摄影的适用性, 使用反向模式自动区分来计算波场相对于速度结构的梯度。 所开发的程序比使用常规数字方法进行全波形反向反向转换的速度快得多。