Surface-wave inversion is a non-linear and ill-conditioned problem usually solved through deterministic or global optimization approaches. Here, we present an alternative method based on machine learning. Under the assumption of a local one-dimensional model, we train a residual neural network to predict the non-linear mapping between the full dispersion image and the model space, parameterized in terms of shear wave velocity and layer thicknesses. On the one hand, compared to standard convolutional neural networks, the residual network prevents the vanishing gradient problem when training a deep network. On the other hand, the use of the full dispersion image avoids the time-consuming and often ambiguous picking procedure and allows considering higher modes in the inversion framework. One key aspect of any machine learning inversion strategy is the definition of an appropriate training set. In this case, the models forming the training and validation examples are uniformly drawn from previously defined ranges that cover a wide range of possible near-surface layered Vs models. The reflectivity method constitutes the forward modelling operator that converts the model parameters into the observed shot gathers. The inversion also includes a Monte Carlo simulation strategy that propagates onto the model space the uncertainties related to noise in the data and the modelling error introduced by the network approximation. We first discuss synthetic inversions to assess the applicability of the proposed method and to analyse the effect of erroneous model parameterizations. The inversion results are also benchmarked with those provided by a more standard approach in which the particle swarm optimization algorithm inverts the fundamental mode only. Then, we discuss a field data application. Our tests confirm that the residual neural network inversion provides accurate model estimations and reliable uncertainty appraisals. One of the main benefits of the proposed approach is that once the network is trained it provides the near-surface shear wave velocity profile in near real-time.

中文翻译：

---

一种混合残差神经网络-蒙特卡罗方法来反演表面波色散数据

表面波反演是一个非线性和病态问题，通常通过确定性或全局优化方法来解决。在这里，我们提出了一种基于机器学习的替代方法。在局部一维模型的假设下，我们训练一个残差神经网络来预测全色散图像和模型空间之间的非线性映射，根据剪切波速度和层厚度参数化。一方面，与标准卷积神经网络相比，残差网络在训练深度网络时防止了梯度消失问题。另一方面，全色散图像的使用避免了耗时且通常不明确的拾取过程，并允许在反演框架中考虑更高的模式。任何机器学习反转策略的一个关键方面是定义适当的训练集。在这种情况下，形成训练和验证示例的模型统一从先前定义的范围中抽取，这些范围涵盖了广泛的可能的近地表分层对比楷模。反射率方法构成了正向建模算子，它将模型参数转换为观察到的炮点道集。反演还包括蒙特卡罗模拟策略，该策略将与数据中噪声相关的不确定性和网络近似引入的建模误差传播到模型空间。我们首先讨论合成反演以评估所提出方法的适用性并分析错误模型参数化的影响。反演结果也以更标准的方法提供的结果为基准，其中粒子群优化算法仅反演基本模式。然后，我们讨论现场数据应用。我们的测试证实残差神经网络反演提供了准确的模型估计和可靠的不确定性评估。