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MT）数据反演是通过地表测量的天然电磁场推断地下介质分布的手段，广泛被用于油气、矿产资源勘测和地质调查等领域。大地电磁方法的探测深度大、测量复杂度低、操作较为简便，但其固有的数据分辨率低、病态性和多解性强等问题，限制了其对地下结构刻画的精度。为解决这一问题，通常需要反演地块的先验知识约束地下结构反演重建。",{"type":17,"tag":25,"props":61,"children":62},{},[63],{"type":23,"value":64},"作为一种高效的生成模型，变分自编码器（VAE）通过隐空间采样可以生成符合特定分布模式的图像，因此可用来灵活地向反演融入各种先验知识。在本工作中，我们基于昇思MindSpore构建了融合多物理先验知识的特征域大地电磁反演算法。该求解器采用昇思MindSpore框架实现了VAE的训练和推理，同时借助昇思MindSpore的自动微分能力，将VAE解码器构建的结构生成器无缝融入基于梯度的反演优化算法。在保证数据拟合的基础上，我们的算法可以显著降低反演的模型残差，提升反演的精度和分辨率。基于提出的算法，我们成功地处理南部非洲大地电磁实验项目（SAMTEX）的实测数据。",{"type":17,"tag":25,"props":66,"children":67},{},[68,70],{"type":23,"value":69},"**1、**",{"type":17,"tag":31,"props":71,"children":72},{},[73],{"type":23,"value":74},"大地电磁（MT）正演建模",{"type":17,"tag":25,"props":76,"children":77},{},[78],{"type":23,"value":79},"对于二维大地电磁正演建模，列出频域麦克斯韦方程",{"type":17,"tag":25,"props":81,"children":82},{},[83],{"type":17,"tag":84,"props":85,"children":87},"img",{"alt":7,"src":86},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/01/05/d7accf671a1a4c3bb342ed8946a9385d.png",[],{"type":17,"tag":25,"props":89,"children":90},{},[91],{"type":23,"value":92},"公式1",{"type":17,"tag":25,"props":94,"children":95},{},[96],{"type":23,"value":97},"考虑沿x走向均匀的二维结构，分别得到横磁（transverse 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反演要实现的效果",{"type":17,"tag":25,"props":306,"children":307},{},[308,310],{"type":23,"value":309},"**3、**",{"type":17,"tag":31,"props":311,"children":312},{},[313],{"type":23,"value":314},"实验与结论",{"type":17,"tag":25,"props":316,"children":317},{},[318],{"type":17,"tag":31,"props":319,"children":320},{},[321],{"type":23,"value":322},"3.1 算例1：仿真算例反演实验",{"type":17,"tag":25,"props":324,"children":325},{},[326],{"type":23,"value":327},"在仿真算例中，研究区域的水平长度为10km，深度为1km，仿真生成了均匀分布的16个地表接收机的数据，包括共14个频点。假设对反演区域有如下图所示的先验知识，即通过地震等非电磁手段获取了电阻率随深度的大致分布。",{"type":17,"tag":25,"props":329,"children":330},{},[331],{"type":17,"tag":84,"props":332,"children":334},{"alt":7,"src":333},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/01/05/4fce8b423e044479a428d93ab7468a3e.png",[],{"type":17,"tag":25,"props":336,"children":337},{},[338],{"type":23,"value":339},"图2. 反演区先验知识",{"type":17,"tag":25,"props":341,"children":342},{},[343],{"type":23,"value":344},"首先，基于昇思MindSpore的卷积神经网络等模块，构建VAE的编码器、解码器和采样、计算KL散度等模块。搭建的VAE结构部分代码如下所示。可以自定义卷积核的尺寸、采用的正则化和激活函数等参数。",{"type":17,"tag":346,"props":347,"children":349},"pre",{"code":348},"class MeanModel(nn.Cell):\n    def __init__(self):\n        super().__init__()\n        self.conv1d1 = nn.Conv1d(1, 16, 3, pad_mode=\"same\")\n        self.bn1 = nn.BatchNorm1d(16)\n        self.swish1 = Swish()\n\n        self.conv1d2 = nn.Conv1d(16, 16, 3, pad_mode=\"same\")\n        self.bn2 = nn.BatchNorm1d(16)\n        self.swish2 = Swish()\n        self.maxpool1d2 = nn.MaxPool1d(2, 2)\n\n        self.conv1d3 = nn.Conv1d(16, 32, 3, pad_mode=\"same\")\n        self.bn3 = nn.BatchNorm1d(32)\n        self.swish3 = Swish()\n\n        self.conv1d4 = nn.Conv1d(32, 32, 3, pad_mode=\"same\")\n        self.bn4 = nn.BatchNorm1d(32)\n        self.swish4 = Swish()\n        self.maxpool1d4 = nn.MaxPool1d(2, 2)\n\n        self.conv1d5 = nn.Conv1d(32, 64, 3, pad_mode=\"same\")\n        self.bn5 = nn.BatchNorm1d(64)\n        self.swish5 = Swish()\n\n        self.conv1d6 = nn.Conv1d(64, 64, 3, pad_mode=\"same\")\n        self.bn6 = nn.BatchNorm1d(64)\n        self.swish6 = Swish()\n        self.maxpool1d6 = nn.MaxPool1d(2, 2)\n\n        self.flatten = nn.Flatten()\n        self.dense1 = nn.Dense(256, 16)  \n        self.dense2 = nn.Dense(256, 16)\n",[350],{"type":17,"tag":351,"props":352,"children":353},"code",{"__ignoreMap":7},[354],{"type":23,"value":348},{"type":17,"tag":25,"props":356,"children":357},{},[358],{"type":23,"value":359},"通过仿真代码融合先验知识设计训练集，在仿真训练集上完成VAE的训练。VAE训练部分代码如下所示。可以自定义训练的损失函数、优化方式、学习率等参数。",{"type":17,"tag":346,"props":361,"children":363},{"code":362},"class MSELoss(nn.Cell):\n    def construct(self, y_true, y_pred):\n        return ops.reduce_mean(ops.multiply(lw_tens, ops.square(y_true - y_pred)))\n\nnet = Model()\nloss_net = LossFuncNet(net)\nmse_loss_net = MSELoss()\noptimizer = nn.optim.Adam(params=loss_net.trainable_params(), learning_rate=initial_rate)\ntrain_cell = nn.TrainOneStepCell(loss_net, optimizer)\n",[364],{"type":17,"tag":351,"props":365,"children":366},{"__ignoreMap":7},[367],{"type":23,"value":362},{"type":17,"tag":25,"props":369,"children":370},{},[371],{"type":23,"value":372},"完成VAE训练后，基于训练得到的生成器进行特征域MT反演。反演流程中自动求微分的代码如下所示。",{"type":17,"tag":346,"props":374,"children":376},{"code":375},"for uu in range(XN_pr2-XN_pr1):\n    v = v_array[:, uu*latent_dim:(uu+1)*latent_dim]\n    v = ms.Tensor(v, ms.float32)  # (1,16)\n    rho_recon_pred_ii = decoder(v)\n    v_broadcast = ms.ops.BroadcastTo(((1,rho_recon_pred_ii.shape[-1],v.shape[-1])))(v)\n    jacb = ms.ops.Squeeze()(ms.ops.grad(decoder)(v_broadcast))\n    jacb1 = np.reshape(jacb, [ZN_pr2 - ZN_pr1, latent_dim], order='F')  # [Nmodel, N_latent_z]\n    JD[uu*(ZN_pr2-ZN_pr1):(uu+1)*(ZN_pr2-ZN_pr1), uu*latent_dim:(uu+1)*latent_dim] = jacb1\n",[377],{"type":17,"tag":351,"props":378,"children":379},{"__ignoreMap":7},[380],{"type":23,"value":375},{"type":17,"tag":25,"props":382,"children":383},{},[384],{"type":23,"value":385},"代码中采用ms.ops.grad指令实现对生成器（也即VAE解码器）自动求微分计算生成器的雅克比矩阵，并和MT正问题的雅克比矩阵相乘，计算迭代求解的梯度方向。",{"type":17,"tag":25,"props":387,"children":388},{},[389],{"type":23,"value":390},"下图展示了仿真测试中的实际电阻率分布（第一行）与传统大地电磁反演（第二行）、特征域大地电磁反演（第三行）的结果。",{"type":17,"tag":25,"props":392,"children":393},{},[394],{"type":17,"tag":84,"props":395,"children":397},{"alt":7,"src":396},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/01/05/c37623452bd04782bb3e4c51b921e583.png",[],{"type":17,"tag":25,"props":399,"children":400},{},[401],{"type":23,"value":402},"图3. 仿真测试结果",{"type":17,"tag":25,"props":404,"children":405},{},[406],{"type":23,"value":407},"可以看出基于VAE的特征域MT反演成功地向反演中融入了关于异常体分布的先验知识。对于两组算例，传统反演和特征域的反演重建结果的数据残差接近，传统反演的模型残差分别为0.023和0.024，特征域反演的模型残差分别为0.0056和0.0054，模型残差仅为传统反演的1/4。",{"type":17,"tag":25,"props":409,"children":410},{},[411],{"type":17,"tag":31,"props":412,"children":413},{},[414],{"type":23,"value":415},"3.2 算例2：SAMTEX实测MT数据集反演实验",{"type":17,"tag":25,"props":417,"children":418},{},[419],{"type":23,"value":420},"在昇思MindSpore框架下，针对南部非洲大地电磁实验的开源数据集（SAMTEX），测试了基于变分自编码器的特征域MT反演算法。反演测区位于南部非洲西海岸附近，长度约为750km，深度选定为80km。该测区显著特征为在水平方向100km至400km之间，深度20km以浅的区域存在的高导结构。由于低频电磁波在导体结构中的衰减，MT方法对高导结构下部区域的敏感度很低，因此无先验知识约束的传统MT反演难以准确重建高导地层的下边界位置。",{"type":17,"tag":25,"props":422,"children":423},{},[424],{"type":23,"value":425},"借助昇思MindSpore框架搭建的特征域大地电磁反演算法。引入先验知识，即高导结构的厚度约为15km。基于先验知识，仿真生成训练集。完成VAE的训练并进行特征域大地电磁反演，重建结果如下所示",{"type":17,"tag":25,"props":427,"children":428},{},[429],{"type":17,"tag":84,"props":430,"children":432},{"alt":7,"src":431},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/01/05/b6032d4a0ef84553a292f6bd70e3d3e6.png",[],{"type":17,"tag":25,"props":434,"children":435},{},[436],{"type":23,"value":437},"图4. 大地电磁反演重建结果",{"type":17,"tag":25,"props":439,"children":440},{},[441],{"type":23,"value":442},"其中上图为传统MT反演的重建结果，下图为昇思MindSpore框架下实现的特征域MT反演的重建结果。特征域MT反演对高导地层的下边界重建较为清晰准确，较好地将地层厚度的先验知识融入了反演。实测实验进一步证明了提出的基于VAE的特征域MT反演可有效提升大地电磁反演的精度和分辨率。",{"type":17,"tag":25,"props":444,"children":445},{},[446,448],{"type":23,"value":447},"**4、**",{"type":17,"tag":31,"props":449,"children":450},{},[451],{"type":23,"value":452},"总结与展望",{"type":17,"tag":25,"props":454,"children":455},{},[456],{"type":23,"value":457},"我们推出了基于昇思MindSpore Elec的变分自编码器大地电磁特征域反演求解器，借助昇思MindSpore的神经网络算子及自动求微分框架，实现将研究地块的多物理先验知识融入反演算法中，提升大地电磁反演的精度和分辨率。利用在昇思MindSpore平台上实现的算法成功实现了南部非洲大地电磁实测数据的处理。我们希望能够有更多的企业、科研院所参与进来，共同打造和维护昇思MindSpore Elec套件。",{"type":17,"tag":459,"props":460,"children":462},"h2",{"id":461},"参考文献",[463],{"type":17,"tag":31,"props":464,"children":465},{},[466],{"type":23,"value":461},{"type":17,"tag":25,"props":468,"children":469},{},[470],{"type":23,"value":471},"[1] H. Zhou, et al., Feature-based magnetotelluric inversion by variational autoencoder using a subdomain encoding scheme [J], Geophysics, 2023.",{"type":17,"tag":25,"props":473,"children":474},{},[475],{"type":23,"value":476},"[2] H. Zhou, et al., An Intelligent MT Data Inversion Method With Seismic Attribute Enhancement [J], IEEE Transactions on Geoscience and Remote Sensing, 2023.",{"type":17,"tag":25,"props":478,"children":479},{},[480],{"type":23,"value":481},"[3] T. Habashy, et al., A general framework for constraint minimization for the inversion of electromagnetic measurements, Progress In Electromagnetics Research [J], 2004.",{"type":17,"tag":25,"props":483,"children":484},{},[485],{"type":23,"value":486},"[4] T. 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