Noisy Gravity Data Reconstruction Using the Convolutional Autoencoder

  Objectives  CAE (convolutional autoencoder) combines the autoencoder neural network structure and the convolutional network structure. This paper processes the gravity data based on the deep learning, and reconstructs the gravity contour image from the noisy gravity data with the CAE. The autoencoder structure contains the equal dimensional input and output data, which goes for the gravity data processing. The convolutional network structure is widely used in image recognition recent years, which can learn and recognize the specific objects in an image.

  Methods  To create the training set, we generate 1 000 hexahedrons with the random triaxial length parameters and the random density to simulate the natural gravity source bodies. The 2D gravity data set for these bodies is fast computed with the gravity forward formula and the noisy gravity data set is generated by adding Gaussian noise to the computed data. Meanwhile the accuracy of the length parameters and density is limited in order to improve the representativeness of the training data set. Hence the 2D gravity data and the noisy data will be output and input data of the CAE. We design 5 layers CAE. The input and output layers both are 26×26. 32 and 64 feature maps are generated with 3×3 convolution kernels in the inner layers. The training is executed using RMSProp(root mean square propagation) optimizer.

  Results  To test the generalization of the trained CAE, the testing set with 500 samples is generated in the same way with the training set. The relative error histogram on the testing set shows that the reconstructing error is less than 5% and most of the error is around 0. To test the recognition of the gravity features in the 2D gravity, we test the CAE with simulated gravity data which contain 2 and more gravity anomalies. The results show that the CAE can recognize all gravity anomalies in an noisy gravity image and reconstruct them and the output image shows fairly fine reconstruction from the gravity with 10% noise. The measured gravity data of Kauring testing ground are used to test the generalization performance of the CAE. The reconstructed image is compared with the traditional FFT(fast Fourier transform) filtering and db wavelet filtering results. To increase the reconstruction difficulty, the Kauring data is added with 10% Gaussian noise. The results show that the trained CAE performs significantly less error than the FFT filter and the wavelet filter.

  Conclusions  In terms of reconstructing performance, the CAE can avoid over-processing that may eliminate the real gravity anomaly, which is often seen in filtering especially for FFT filtering. The CAE reconstructs all of the 3 gravity anomalies of Kauring while the FFT filtering reconstructs 2. And the over-smoothing artifact is less than filtering methods.The CAE can process 2D gravity data and show lower error and generate less artifacts than filtering methods in our tests with testing set, simulated gravity data and measuring data. Beyond that, this article reveals that the deep learning can learn gravity image. With the convolution structure in a neural network, the network can learn single gravity anomaly samples and extensively recognize all gravity anomalies in a gravity image, which signifies that the gravity can integrate with the artificial intelligence technology.