4D acoustic imaging via an array of 32 sources / 32 receivers is used to monitor hydraulic fracture propagating in a 250~mm cubic specimen under a true-triaxial state of stress. We present a method based on the arrivals of diffracted waves to reconstruct the fracture geometry (and fluid front when distinct from the fracture front). Using Bayesian model selection, we rank different possible fracture geometries (radial, elliptical, tilted or not) and estimate model error. The imaging is repeated every 4 seconds and provide a quantitative measurement of the growth of these low velocity fractures. We test the proposed method on two experiments performed in two different rocks (marble and gabbro) under experimental conditions characteristic respectively of the fluid lag-viscosity (marble) and toughness (gabbro) dominated hydraulic fracture propagation regimes. In both experiments, about 150 to 200 source-receiver combinations exhibit clear diffracted wave arrivals. The results of the inversion indicate a radial geometry evolving slightly into an ellipse towards the end of the experiment when the fractures feel the specimen boundaries. The estimated modelling error with all models is of the order of the wave arrival picking error. Posterior estimates indicate an uncertainty of the order of a millimeter on the fracture front location for a given acquisition sequence. The reconstructed fracture evolution from diffracted waves is shown to be consistent with the analysis of $90^{\circ}$ incidence transmitted waves across the growing fracture.

中文翻译：

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实验室水力压裂实验中衍射波到达的裂缝前沿的延时重建*

通过 32 个源/32 个接收器的阵列的 4D 声学成像用于监测在真三轴应力状态下在 250~mm 立方试样中传播的水力裂缝。我们提出了一种基于衍射波到达的方法来重建裂缝几何形状（以及与裂缝前沿不同时的流体前沿）。使用贝叶斯模型选择，我们对不同的可能裂缝几何形状（径向、椭圆形、倾斜或不倾斜）进行排序并估计模型误差。成像每 4 秒重复一次，并提供这些低速裂缝增长的定量测量。我们在分别以流体滞后粘度（大理石）和韧性（辉长岩）主导的水力压裂扩展机制为特征的实验条件下，在两种不同的岩石（大理石和辉长岩）中进行的两个实验中测试了所提出的方法。在这两个实验中，大约 150 到 200 个源-接收器组合表现出清晰的衍射波到达。反演结果表明，当裂缝触及试样边界时，径向几何形状在实验结束时略微演变成椭圆。所有模型的估计建模误差都是波到达拾取误差的数量级。后验估计表明，对于给定的采集序列，裂缝前沿位置存在毫米级的不确定性。