Full-waveform inversion problems are usually formulated as optimization problems, where the forward-wave propagation operator $f$ maps the subsurface velocity structures to seismic signals. The existing computational methods for solving full-waveform inversion are not only computationally expensive, but also yields low-resolution results because of the ill-posedness and cycle skipping issues of full-waveform inversion. To resolve those issues, we employ machine-learning techniques to solve the full-waveform inversion. Specifically, we focus on applying the convolutional neural network~(CNN) to directly derive the inversion operator $f^{-1}$ so that the velocity structure can be obtained without knowing the forward operator $f$. We build a convolutional neural network with an encoder-decoder structure to model the correspondence from seismic data to subsurface velocity structures. Furthermore, we employ the conditional random field~(CRF) on top of the CNN to generate structural predictions by modeling the interactions between different locations on the velocity model. Our numerical examples using synthetic seismic reflection data show that the propose CNN-CRF model significantly improve the accuracy of the velocity inversion while the computational time is reduced.

中文翻译：

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InversionNet：一种高效准确的数据驱动全波形反演

全波形反演问题通常被表述为优化问题，其中前向波传播算子 $f$ 将地下速度结构映射到地震信号。现有的求解全波形反演的计算方法不仅计算量大，而且由于全波形反演的不适定性和跳周期问题，产生的结果分辨率低。为了解决这些问题，我们采用机器学习技术来解决全波形反演。具体来说，我们专注于应用卷积神经网络~(CNN)直接推导反演算子$f^{-1}$，这样就可以在不知道前向算子$f$的情况下获得速度结构。我们构建了一个具有编码器-解码器结构的卷积神经网络，以模拟从地震数据到地下速度结构的对应关系。此外，我们在 CNN 之上使用条件随机场~（CRF），通过对速度模型上不同位置之间的相互作用进行建模来生成结构预测。我们使用合成地震反射数据的数值例子表明，所提出的 CNN-CRF 模型显着提高了速度反演的准确性，同时减少了计算时间。