Surface wave tomography uses measured dispersion properties of surface waves to infer the spatial distribution of subsurface properties such as shear-wave velocities. These properties can be estimated vertically below any geographical location at which surface wave dispersion data are available. As the inversion is significantly non-linear, Monte Carlo methods are often used to invert dispersion curves for shear-wave velocity profiles with depth to give a probabilistic solution. Such methods provide uncertainty information but are computationally expensive. Neural network based inversion provides a more efficient way to obtain probabilistic solutions when those solutions are required beneath many geographical locations. Unlike Monte Carlo methods, once a network has been trained it can be applied rapidly to perform any number of inversions. We train a class of neural networks called mixture density networks, to invert dispersion curves for shear-wave velocity models and their non-linearised uncertainty. Mixture density networks are able to produce fully probabilistic solutions in the form of weighted sums of multivariate analytic kernels such as Gaussians, and we show that including data uncertainties in the mixture density network gives more reliable mean velocity estimates when data contains significant noise. The networks were applied to data from the Grane field in the Norwegian North sea to produce shear-wave velocity maps at several depth levels. Post-training we obtained probabilistic velocity profiles with depth beneath 26,772 locations to produce a 3D velocity model in 21 seconds on a standard desktop computer. This method is therefore ideally suited for rapid, repeated 3D subsurface imaging and monitoring.

中文翻译：

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来自表面波色散数据的 Grane 油田（北海）的概率神经网络层析成像

表面波层析成像使用测量的表面波色散特性来推断地下特性的空间分布，例如剪切波速度。这些特性可以在任何可以获得表面波色散数据的地理位置下方进行垂直估计。由于反演明显是非线性的，蒙特卡罗方法通常用于反演具有深度的横波速度剖面的频散曲线，以给出概率解。这种方法提供了不确定性信息，但计算成本很高。当在许多地理位置下需要概率解时，基于神经网络的反演提供了一种更有效的方法来获得概率解。与蒙特卡罗方法不同，一旦网络经过训练，就可以快速应用以执行任意数量的反演。我们训练了一类称为混合密度网络的神经网络，以反转剪切波速度模型的频散曲线及其非线性不确定性。混合密度网络能够以多变量分析核（如高斯）的加权和的形式生成完全概率解，我们表明，当数据包含显着噪声时，在混合密度网络中包含数据不确定性可提供更可靠的平均速度估计。这些网络应用于来自挪威北海 Grane 油田的数据，以生成多个深度级别的剪切波速度图。训练后，我们获得了深度低于 26,772 个位置的概率速度剖面，以在 21 秒内在标准台式计算机上生成 3D 速度模型。因此，这种方法非常适合快速、