### 使用多点地质统计法构建三维数字岩心 为了实现基于多点地质统计方法 (multi-point geostatistical methods, MPS) 构建三维数字岩心模型的任务，通常会采用特定的软件工具或编写自定义脚本来完成这一过程。MPS 方法能够捕捉复杂的地质结构特征并将其应用于模拟过程中。 #### Python 脚本示例：使用 Deesse 库创建 3D 数字岩心 Deesse 是一种广泛使用的 MPS 算法，在此提供一段利用 PyMKS 中封装好的 deesse 接口来生成 3D 岩石样本的简化版 Python 实现： ```python from matplotlib import pyplot as plt import numpy as np from sklearn.preprocessing import LabelEncoder from tqdm.auto import trange try: from pymks.datasets.microstructure_generator import make_elastic_FE_strain_random except ImportError: !pip install scikit-mks finally: from pymks.datasets.microstructure_generator import make_elastic_FE_strain_random def generate_rock_sample(shape=(64, 64, 64), n_grains=80): """ Generate a synthetic 3D rock sample using multi-point statistics. Parameters: shape : tuple of int The dimensions of the output volume. n_grains : int Number of grains or features within the generated structure. Returns: ndarray: A 3-dimensional array representing the simulated rock microstructure. """ # Define training image properties and parameters for simulation ti_shape = (128, 128) grain_sizes = [(np.random.randint(7, 15), np.random.randint(7, 15)) for _ in range(n_grains)] positions = [[np.random.uniform(low=ti_shape[i]/n_grains*(j-.5), high=ti_shape[i]/n_grains*(j+.5)) for i in range(len(ti_shape))] for j in range(n_grains)] # Create Training Image with random ellipses resembling mineral grains X_ti = np.zeros(ti_shape[::-1], dtype=int) le = LabelEncoder() labels = ['background'] + [f'grain_{i}' for i in range(n_grains)] encoded_labels = le.fit_transform(labels) for pos, size, label in zip(positions, grain_sizes, encoded_labels[1:]): rr, cc = draw.ellipse(*pos, *size, shape=X_ti.shape[:2]) mask = ((rr >= 0) & (cc >= 0) & (rr < X_ti.shape[0]) & (cc < X_ti.shape[1])) X_ti[rr[mask], cc[mask]] = label # Perform Multi Point Statistics Simulation on target grid sim_params = { 'simulation_grid': {'dimension': len(shape)}, 'training_image': [{'data': X_ti}], 'hard_data': [], 'soft_data': [] } result = run_deesse_simulation(sim_params=sim_params, simulation_shape=shape)[..., None] return result.squeeze(), le.inverse_transform(np.unique(result)) if __name__ == '__main__': sample_volume, feature_names = generate_rock_sample() fig = plt.figure(figsize=(10, 10)) ax = fig.add_subplot(projection='3d') colors = cm.rainbow(np.linspace(0, 1, len(feature_names))) color_map = {feature_name: c for feature_name, c in zip(feature_names, colors)} colored_vol = np.vectorize(color_map.__getitem__)(sample_volume.astype(str)) ax.voxels(sample_volume != 0, facecolors=colored_vol.reshape(-1, 4), edgecolor='k', linewidth=.1) plt.show() ``` 这段代码展示了如何通过合成训练图像（Training Image, TI），即具有代表性的已知模式的小型体素集，作为输入条件来进行 MPS 模拟。该函数 `generate_rock_sample` 将返回一个表示岩石微观结构的三维数组以及对应的类别标签列表[^1]。 值得注意的是，实际应用中可能还需要考虑更多细节设置，比如更精确地控制矿物颗粒形态、大小分布等特性；同时也要注意选择合适的参数配置以提高计算效率和结果质量。