[{"data":1,"prerenderedAt":519},["ShallowReactive",2],{"content-query-LCcwf6XKx9":3},{"_path":4,"_dir":5,"_draft":6,"_partial":6,"_locale":7,"title":8,"description":9,"date":10,"cover":11,"type":12,"body":13,"_type":513,"_id":514,"_source":515,"_file":516,"_stem":517,"_extension":518},"/technology-blogs/en/2975","en",false,"","Idea Sharing: VAE Feature-based Magnetotelluric Inversion Based on MindSpore Elec, Improving the Accuracy and Resolution of Magnetotelluric Inversion","MindSpore, cooperating with Tsinghua University and Huawei Advanced Computing and Storage Laboratory, builds a feature-based MT data inversion algorithm based on a VAE","2024-02-02","https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/abfe44abf59c444496f4513e0efffd82.png","technology-blogs",{"type":14,"children":15,"toc":508},"root",[16,24,34,39,44,49,57,62,70,75,80,87,92,99,104,111,116,123,128,136,141,148,153,158,165,170,175,182,187,206,213,218,223,230,235,254,261,266,273,278,283,290,295,300,305,312,317,325,333,338,345,350,355,360,370,375,383,388,396,408,413,420,425,430,438,443,448,455,460,465,473,478,488,493,498,503],{"type":17,"tag":18,"props":19,"children":21},"element","h1",{"id":20},"idea-sharing-vae-feature-based-magnetotelluric-inversion-based-on-mindspore-elec-improving-the-accuracy-and-resolution-of-magnetotelluric-inversion",[22],{"type":23,"value":8},"text",{"type":17,"tag":25,"props":26,"children":27},"p",{},[28],{"type":17,"tag":29,"props":30,"children":31},"strong",{},[32],{"type":23,"value":33},"Background",{"type":17,"tag":25,"props":35,"children":36},{},[37],{"type":23,"value":38},"MindSpore, cooperating with Tsinghua University and Huawei Advanced Computing and Storage Laboratory, builds a feature-based magnetotelluric (MT) data inversion algorithm based on a variational autoencoder (VAE). The accuracy of complex geophysical inversion is effectively improved with embedded priori knowledge of multiphysics.",{"type":17,"tag":25,"props":40,"children":41},{},[42],{"type":23,"value":43},"MT data inversion is a means of inferring the subsurface density distribution based on the natural electromagnetic field measured on the surface. It is widely used in surveys on oil, gas, and mineral resources, or other geological surveys. The MT method features large detection depth, low measurement complexity and simple operation. However, its inherent problems such as low data resolution, ill-posedness, and non-uniqueness limit the accuracy of subsurface structure characterization. To address this challenge, it is usually necessary to invert the priori knowledge of geophysical blocks to constrain the inversion and reconstruction of the subsurface structures.",{"type":17,"tag":25,"props":45,"children":46},{},[47],{"type":23,"value":48},"As an efficient generative model, a VAE can generate images that conform to a specific distribution pattern through latent space sampling, so it can be used to flexibly integrate various priori knowledge into inversion. In our work, based on MindSpore, we construct a feature-based MT inversion algorithm integrating priori knowledge of multiphysics. Our solver uses the MindSpore framework to implement VAE training and inference. With the help of automatic differentiation on MindSpore, the structure generator constructed by the VAE decoder is seamlessly integrated into the gradient-based inversion optimization algorithm. On the basis of data fitting, our algorithm can significantly reduce the model residuals of inversion and improve the accuracy and resolution of inversion. We have successfully applied the proposed algorithm to synthetic experiments and the field inversion of Southern African Magnetotelluric Experiment (SAMTEX) data collected in southern Africa.",{"type":17,"tag":25,"props":50,"children":51},{},[52],{"type":17,"tag":29,"props":53,"children":54},{},[55],{"type":23,"value":56},"1. MT Forward Modeling",{"type":17,"tag":25,"props":58,"children":59},{},[60],{"type":23,"value":61},"For 2D MT forward modeling, the frequency-domain Maxwell equation is required:",{"type":17,"tag":25,"props":63,"children":64},{},[65],{"type":17,"tag":66,"props":67,"children":69},"img",{"alt":7,"src":68},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/359bf06761314b97a3e1dd5c5388caac.png",[],{"type":17,"tag":25,"props":71,"children":72},{},[73],{"type":23,"value":74},"Formula 1",{"type":17,"tag":25,"props":76,"children":77},{},[78],{"type":23,"value":79},"Based on the uniform two-dimensional structure along the x direction, electric field equations in the transverse magnetic (TM) mode and transverse electric (TE) mode are obtained:",{"type":17,"tag":25,"props":81,"children":82},{},[83],{"type":17,"tag":66,"props":84,"children":86},{"alt":7,"src":85},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/86fdc9c3028640729b65d531b922cb84.png",[],{"type":17,"tag":25,"props":88,"children":89},{},[90],{"type":23,"value":91},"Formula 2",{"type":17,"tag":25,"props":93,"children":94},{},[95],{"type":17,"tag":66,"props":96,"children":98},{"alt":7,"src":97},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/5f7f3315a6c149459f6791032a242ab2.png",[],{"type":17,"tag":25,"props":100,"children":101},{},[102],{"type":23,"value":103},"The finite difference method (FDM) is used to discretize the subsurface structure into rectangular grids with even horizontal width and increasing depth. The difference equations of TM and TE modes are listed, and the matrix equations are constructed and solved. The measured apparent resistivity and impedance phase are calculated by the electric and magnetic fields on the surface.",{"type":17,"tag":25,"props":105,"children":106},{},[107],{"type":17,"tag":66,"props":108,"children":110},{"alt":7,"src":109},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/30f412885e224d2591c3069a1971c6cb.png",[],{"type":17,"tag":25,"props":112,"children":113},{},[114],{"type":23,"value":115},"Formula 4",{"type":17,"tag":25,"props":117,"children":118},{},[119],{"type":17,"tag":66,"props":120,"children":122},{"alt":7,"src":121},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/07073773c936429ea557d0cb3c85a400.png",[],{"type":17,"tag":25,"props":124,"children":125},{},[126],{"type":23,"value":127},"Formula 5",{"type":17,"tag":25,"props":129,"children":130},{},[131],{"type":17,"tag":29,"props":132,"children":133},{},[134],{"type":23,"value":135},"2. Feature-based MT Data Inversion with a VAE",{"type":17,"tag":25,"props":137,"children":138},{},[139],{"type":23,"value":140},"A VAE has a typical encoder-decoder structure. The output of the VAE decoder is trained to make it closer to that of the encoder, while the distribution of latent variables is closer to a predefined simple distribution (for example, standard normal distribution).",{"type":17,"tag":25,"props":142,"children":143},{},[144],{"type":17,"tag":66,"props":145,"children":147},{"alt":7,"src":146},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/56792758ce074220ba46eadc33752b06.png",[],{"type":17,"tag":25,"props":149,"children":150},{},[151],{"type":23,"value":152},"Formula 6",{"type":17,"tag":25,"props":154,"children":155},{},[156],{"type":23,"value":157},"After the training is completed, mapping between images constructed by the decoder and latent variables can be obtained.",{"type":17,"tag":25,"props":159,"children":160},{},[161],{"type":17,"tag":66,"props":162,"children":164},{"alt":7,"src":163},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/08cf06bf85bb4d2a8c5603d4f1611059.png",[],{"type":17,"tag":25,"props":166,"children":167},{},[168],{"type":23,"value":169},"Formula 7",{"type":17,"tag":25,"props":171,"children":172},{},[173],{"type":23,"value":174},"Under the framework of deterministic inversion, the objective function can be summarized as follows:",{"type":17,"tag":25,"props":176,"children":177},{},[178],{"type":17,"tag":66,"props":179,"children":181},{"alt":7,"src":180},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/c24ea249a01d4f6faa52ccdf6c609e0d.png",[],{"type":17,"tag":25,"props":183,"children":184},{},[185],{"type":23,"value":186},"Formula 8",{"type":17,"tag":25,"props":188,"children":189},{},[190,192,197,199,204],{"type":23,"value":191},"The first term indicates data residuals, ",{"type":17,"tag":29,"props":193,"children":194},{},[195],{"type":23,"value":196},"dobs",{"type":23,"value":198}," indicates the measured data, and ",{"type":17,"tag":29,"props":200,"children":201},{},[202],{"type":23,"value":203},"F",{"type":23,"value":205}," indicates the MT forward modeling operator. Items 2, 3, and 4 are different regularization items. Based on the VAE decoder, the parameterized representation of a resistivity distribution image in feature space is constructed. The objective function of feature-based inversion is obtained as follows:",{"type":17,"tag":25,"props":207,"children":208},{},[209],{"type":17,"tag":66,"props":210,"children":212},{"alt":7,"src":211},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/686da8ce990d4c2ab0cc34f3b7b15dd9.png",[],{"type":17,"tag":25,"props":214,"children":215},{},[216],{"type":23,"value":217},"Formula 9",{"type":17,"tag":25,"props":219,"children":220},{},[221],{"type":23,"value":222},"The Gauss-Newton optimization method is used, that is, in the _k_th iteration, the following matrix equation needs to be solved:",{"type":17,"tag":25,"props":224,"children":225},{},[226],{"type":17,"tag":66,"props":227,"children":229},{"alt":7,"src":228},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/ff0c3774745649f48372a6a88ba79ccf.png",[],{"type":17,"tag":25,"props":231,"children":232},{},[233],{"type":23,"value":234},"Formula 10",{"type":17,"tag":25,"props":236,"children":237},{},[238,240,245,247,252],{"type":23,"value":239},"Where ",{"type":17,"tag":29,"props":241,"children":242},{},[243],{"type":23,"value":244},"G(vk)",{"type":23,"value":246}," and ",{"type":17,"tag":29,"props":248,"children":249},{},[250],{"type":23,"value":251},"g(vk)",{"type":23,"value":253}," are respectively the first- and second-order derivatives of the objective function:",{"type":17,"tag":25,"props":255,"children":256},{},[257],{"type":17,"tag":66,"props":258,"children":260},{"alt":7,"src":259},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/e14104b9ab7946f8ad4d069db60a99d8.png",[],{"type":17,"tag":25,"props":262,"children":263},{},[264],{"type":23,"value":265},"Formula 11",{"type":17,"tag":25,"props":267,"children":268},{},[269],{"type":17,"tag":66,"props":270,"children":272},{"alt":7,"src":271},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/237351d854544ca0b2d68d2e94fcf7de.png",[],{"type":17,"tag":25,"props":274,"children":275},{},[276],{"type":23,"value":277},"Formula 12",{"type":17,"tag":25,"props":279,"children":280},{},[281],{"type":23,"value":282},"Latent variables are updated iteratively. After the data residuals converge, the data passes through the decoder.",{"type":17,"tag":25,"props":284,"children":285},{},[286],{"type":17,"tag":66,"props":287,"children":289},{"alt":7,"src":288},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/67e23110351b45189eb8b7ab4b1a7a31.png",[],{"type":17,"tag":25,"props":291,"children":292},{},[293],{"type":23,"value":294},"Formula 13",{"type":17,"tag":25,"props":296,"children":297},{},[298],{"type":23,"value":299},"The inversion reconstruction result of the image domain is obtained.",{"type":17,"tag":25,"props":301,"children":302},{},[303],{"type":23,"value":304},"We build a VAE and implement the training and inference processes under the MindSpore framework. Automatic differentiation on MindSpore flexibly calculates the gradients of the generator during iterations, and embeds the gradients into the Gauss-Newton optimization algorithm. The VAE introduces additional regularization to limit the distribution of the inverted model to specific patterns, embedding complex priori knowledge of multiphysics into inversion. The following figure shows the effect to be achieved by inversion:",{"type":17,"tag":25,"props":306,"children":307},{},[308],{"type":17,"tag":66,"props":309,"children":311},{"alt":7,"src":310},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/a43ef6f872d6480a8dd007a382714105.png",[],{"type":17,"tag":25,"props":313,"children":314},{},[315],{"type":23,"value":316},"Figure 1 Effect to be achieved by inversion",{"type":17,"tag":25,"props":318,"children":319},{},[320],{"type":17,"tag":29,"props":321,"children":322},{},[323],{"type":23,"value":324},"3. Experiments and Conclusions",{"type":17,"tag":25,"props":326,"children":327},{},[328],{"type":17,"tag":29,"props":329,"children":330},{},[331],{"type":23,"value":332},"3.1 Example 1: Inversion Experiments for Simulation",{"type":17,"tag":25,"props":334,"children":335},{},[336],{"type":23,"value":337},"In the simulation example, the research area is 10-km wide and 1-km deep. Through simulation, data of 16 receivers that are uniformly distributed on the surface is generated, including 14 frequencies. It is assumed that there is priori knowledge shown in the following figure for the inversion area, that is, approximate resistivity-depth distribution obtained by non-electromagnetic means (for example, from an earthquake).",{"type":17,"tag":25,"props":339,"children":340},{},[341],{"type":17,"tag":66,"props":342,"children":344},{"alt":7,"src":343},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/d00eba29c6484385bd633cf1c0925daf.png",[],{"type":17,"tag":25,"props":346,"children":347},{},[348],{"type":23,"value":349},"Figure 2 Priori knowledge in the inversion area",{"type":17,"tag":25,"props":351,"children":352},{},[353],{"type":23,"value":354},"First, construct the encoder, decoder, sampling, and KL divergence computing modules of the VAE based on the convolutional neural network and other modules of MindSpore. The following displays part of the code of the VAE structure. You can customize parameters such as the size of the convolution kernel, regularization, and activation function.",{"type":17,"tag":25,"props":356,"children":357},{},[358],{"type":23,"value":359},"class MeanModel(nn.Cell):",{"type":17,"tag":361,"props":362,"children":364},"pre",{"code":363},"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",[365],{"type":17,"tag":366,"props":367,"children":368},"code",{"__ignoreMap":7},[369],{"type":23,"value":363},{"type":17,"tag":25,"props":371,"children":372},{},[373],{"type":23,"value":374},"Then, integrate simulation code to priori knowledge to design a training dataset, and complete VAE training on the simulation training dataset. The following displays part of the VAE training code. You can customize parameters such as the training loss function, optimization mode, and learning rate.",{"type":17,"tag":361,"props":376,"children":378},{"code":377},"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",[379],{"type":17,"tag":366,"props":380,"children":381},{"__ignoreMap":7},[382],{"type":23,"value":377},{"type":17,"tag":25,"props":384,"children":385},{},[386],{"type":23,"value":387},"After VAE training is completed, perform feature-based MT inversion based on the generator obtained through training. The following displays the code for automatic differentiation during inversion.",{"type":17,"tag":361,"props":389,"children":391},{"code":390},"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]\nJD[uu*(ZN_pr2-ZN_pr1):(uu+1)*(ZN_pr2-ZN_pr1), uu*latent_dim:(uu+1)*latent_dim] = jacb1\n",[392],{"type":17,"tag":366,"props":393,"children":394},{"__ignoreMap":7},[395],{"type":23,"value":390},{"type":17,"tag":25,"props":397,"children":398},{},[399,401,406],{"type":23,"value":400},"The ",{"type":17,"tag":29,"props":402,"children":403},{},[404],{"type":23,"value":405},"ms.ops.grad",{"type":23,"value":407}," instruction is used to perform automatic differentiation on the Jacobian matrix of the generator (that is, the VAE decoder), which is multiplied by the Jacobian matrix of the MT forward problem to calculate the gradient direction during iterative solution.",{"type":17,"tag":25,"props":409,"children":410},{},[411],{"type":23,"value":412},"The following figure shows the results of the actual resistivity distribution (first row), conventional MT inversion (second row), and feature-based MT inversion (third row) in the simulation test.",{"type":17,"tag":25,"props":414,"children":415},{},[416],{"type":17,"tag":66,"props":417,"children":419},{"alt":7,"src":418},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/d296560426404fe285dba5706104bb71.png",[],{"type":17,"tag":25,"props":421,"children":422},{},[423],{"type":23,"value":424},"Figure 3 Simulation test results",{"type":17,"tag":25,"props":426,"children":427},{},[428],{"type":23,"value":429},"It can be seen that the feature-based MT inversion with a VAE successfully integrates priori knowledge of the distribution of abnormal blocks into the inversion. For the two data groups, data residuals of reconstruction results of conventional inversion and feature-based inversion are close. The model residuals of conventional inversion are 0.023 and 0.024, while those of feature-based inversion are 0.0056 and 0.0054, only 1/4 of model residuals of conventional inversion.",{"type":17,"tag":25,"props":431,"children":432},{},[433],{"type":17,"tag":29,"props":434,"children":435},{},[436],{"type":23,"value":437},"3.2 Example 2: Inversion Experiments on the SAMTEX MT Dataset",{"type":17,"tag":25,"props":439,"children":440},{},[441],{"type":23,"value":442},"Under the MindSpore framework, the feature-based MT inversion algorithm with a VAE is tested for the open source dataset SAMTEX. The inversion test area is located near the west coast of southern Africa with a length about 750 km and depth of 80 km. The area is characterized by a highly conductive structure that exists in a shallow area, which is located between 100 km and 400 km in the horizontal direction and at a depth less than 20 km. Due to the attenuation of low-frequency electromagnetic waves in conductors, the MT method has low sensitivity to the lower area of highly conductive structures. Therefore, it is difficult for conventional MT inversion without priori knowledge constraints to accurately reconstruct the lower boundary position of highly conductive formations.",{"type":17,"tag":25,"props":444,"children":445},{},[446],{"type":23,"value":447},"The feature-based MT inversion algorithm built based on the MindSpore framework is introduced with priori knowledge, that is, the thickness of the highly conductive structure is about 15 km. Based on the priori knowledge, a training dataset is generated through simulation. After the VAE training is complete and the feature-based MT inversion is performed, the reconstruction result is as follows:",{"type":17,"tag":25,"props":449,"children":450},{},[451],{"type":17,"tag":66,"props":452,"children":454},{"alt":7,"src":453},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2024/02/04/33611ebf669c46b7b86ea0fcea907f0c.png",[],{"type":17,"tag":25,"props":456,"children":457},{},[458],{"type":23,"value":459},"Figure 4 MT inversion reconstruction result",{"type":17,"tag":25,"props":461,"children":462},{},[463],{"type":23,"value":464},"The upper figure shows the reconstruction result of conventional MT inversion, and the lower figure shows the reconstruction result of feature-based MT inversion under the MindSpore framework. Feature-based MT inversion is clear and accurate for the lower boundary reconstruction of highly conductive formations, as the priori knowledge of formation thickness is well integrated into inversion. The experiments further demonstrate that the proposed feature-based MT inversion with a VAE can effectively improve the accuracy and resolution of MT inversion.",{"type":17,"tag":25,"props":466,"children":467},{},[468],{"type":17,"tag":29,"props":469,"children":470},{},[471],{"type":23,"value":472},"4. Summary and Outlook",{"type":17,"tag":25,"props":474,"children":475},{},[476],{"type":23,"value":477},"Based on MindSpore Elec, we proposed a feature-based MT inversion solver with a VAE. With the help of MindSpore neural network operators and automatic differentiation framework, multiphysics priori knowledge on blocks is integrated into the inversion algorithm to improve the accuracy and resolution of MT inversion. The algorithm implemented on MindSpore is used to successfully process the SAMTEX data. We are expecting that more enterprises and research institutes can participate in the development and maintenance of the MindSpore Elec suite.",{"type":17,"tag":479,"props":480,"children":482},"h2",{"id":481},"references",[483],{"type":17,"tag":29,"props":484,"children":485},{},[486],{"type":23,"value":487},"References",{"type":17,"tag":25,"props":489,"children":490},{},[491],{"type":23,"value":492},"[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":494,"children":495},{},[496],{"type":23,"value":497},"[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":499,"children":500},{},[501],{"type":23,"value":502},"[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":504,"children":505},{},[506],{"type":23,"value":507},"[4] T. Khoza, et al., Lithospheric structure of an Archean craton and adjacent mobile belt revealed from 2-D and 3-D inversion of magnetotelluric data: Example from southern Congo craton in northern Namibia, Journal of Geophysical Research: Solid Earth [J], 2013",{"title":7,"searchDepth":509,"depth":509,"links":510},4,[511],{"id":481,"depth":512,"text":487},2,"markdown","content:technology-blogs:en:2975.md","content","technology-blogs/en/2975.md","technology-blogs/en/2975","md",1776506108458]