Exploring microstructure and petrophysical properties of microporous volcanic rocks through 3D multiscale and super-resolution imaging

Abstract

Digital rock physics offers powerful perspectives to investigate Earth materials in 3D and non-destructively. However, it has been poorly applied to microporous volcanic rocks due to their challenging microstructures, although they are studied for numerous volcanological, geothermal and engineering applications. Their rapid origin, in fact, leads to complex textures, where pores are dispersed in fine, heterogeneous and lithified matrices. We propose a framework to optimize their investigation and face innovative 3D/4D imaging challenges. A 3D multiscale study of a tuff was performed through X-ray microtomography and image-based simulations, finding that accurate characterizations of microstructure and petrophysical properties require high-resolution scans (≤ 4 μm/px). However, high-resolution imaging of large samples may need long times and hard X-rays, covering small rock volumes. To deal with these limitations, we implemented 2D/3D convolutional neural network and generative adversarial network-based super-resolution approaches. They can improve the quality of low-resolution scans, learning mapping functions from low-resolution to high-resolution images. This is one of the first efforts to apply deep learning-based super-resolution to unconventional non-sedimentary digital rocks and real scans. Our findings suggest that these approaches, and mainly 2D U-Net and pix2pix networks trained on paired data, can strongly facilitate high-resolution imaging of large microporous (volcanic) rocks.

Figure 1

Location, distribution, aspect and 3D imaging of Campanian Ignimbrite tuff. (a) Area covered by Campanian Ignimbrite pyroclastic density currents on land (drawn in yellow following the constrains of Silleni et al. on map from Google Earth Pro 7.3.6: https://www.google.com/earth/about/versions/). (b) Cross-section of a core (diameter: 54 mm, height: 103 mm) from the Campanian Ignimbrite tuff employed for laboratory measurement. (c) 3D multiscale X-ray imaging. Left: Tuff core (diameter ~ 20 mm, height ~ 40 mm) acquired by X-ray microtomography. Right: 3D scans obtained progressively decreasing pixel sizes and fields of view, and increasing exposure time: low resolution (LR; 16 μm/px), high resolution (HR; 4 μm/px) and very high resolution (VHR; 1.75 μm/px) scans (XZ planes). (d) Low resolution (LR) image (input) and its corresponding high resolution (HR) counterpart (ground truth) used to train and validate paired super-resolutions models.

Figure 2

Petrophysical properties of Campi Flegrei tuffs and investigated Campanian Ignimbrite tuff. (a) Literature data on Campi Flegrei caldera (CFc) tuffs using conventional laboratory approaches^–. Data on Campanian Ignimbrite (CI) tuff are shown in grey. CI tuff can be classified as a highly porous and moderately permeable material, whose hydraulic properties are strongly depending on composition, high pumice content and degree of welding of ignimbritic deposit. The other tuffs mainly originated during Neapolitan Yellow Tuff, Gauro, La Pietra, Nisida and Baia eruptions. (b) Porosity (top) and permeability (bottom) estimated through digital rock physics analyses of LR, HR and VHR images (central 640³ px) as well as of super-resolved images (all 2560³ px: 640³ px × scaling factor of 4, for total porosity; central 900³ px for intrinsic permeability, the maximum volume exploitable for our computational system, see also Fig. 6), obtained applying the best trained models (2D U-Net and pix2pix) to the LR image. The effect of threshold variations (i.e., threshold sensitivity) is also shown, estimating the total porosity as the threshold value diverges from an optimal value (i.e., Otsu value; 0 in x axis and circle symbol). Laboratory data are provided for comparison.

Figure 3

Super-resolved validation images: 2D networks trained on paired data. Validation slices for 2D CNNs (U-Net, SR-ResNet, EDSR, WDSR-a, WDSR-b) and GANs (pix2pix) employed for super-resolution imaging. LR (input) and HR (ground truth) images are also shown for comparison. Correspondent training details and image quality metrics are reported in Table 1.

Figure 4

Super-resolved validation images: 2D vs. 3D networks trained on paired data. The resulting best 2D models, pix2pix and U-Net, were trained both in 2D and 3D. LR (input) and HR (ground truth) images are also shown for comparison. Correspondent training details and image quality metrics are reported in Table 1. For LR, HR and validation data from 2D networks, which outperformed the corresponding 3D models, also segmented (binary) images are provided.

Figure 5

Super-resolved large tuff core: best models. Super-resolved images (2560³ px) obtained applying the best trained networks, 2D pix2pix and U-Net trained on paired data, to a large unseen LR image (central 640³ px; i.e., dominantly external to the training/validation dataset). LR images (input) are also shown for comparison. Slices from top, middle and bottom of the whole 3D images are presented, together with a zoom in their central portion in order to better detect the reconstructed microstructures.

Figure 6

Petrophysical features of the super-resolved large tuff core. Petrophysical measurements performed on the super-resolved images (2560³ px) obtained applying the best trained networks, 2D pix2pix and U-Net trained on paired data, to a large LR image (central 640³ px; see Fig. 5). (a) Porosity values estimated using the box-counting method to calculate the minimum Representative Elementary Volume, REV (top), as well as dividing the super-resolved images in adjacent representative (i.e., larger than the minimum REV) subvolumes to detect potential heterogeneities (bottom). (b) Example of 3D super-resolved (2D U-Net) and segmented image employed for intrinsic permeability simulations (central 900³ px, the maximum volume exploitable for our computational system).

Figure 7

Super-resolved validation images: 2D and 3D networks trained on unpaired data. CycleGAN was trained both in 2D and 3D on unpaired data (i.e., using non-corresponding LR and HR images). LR (input) images are also shown for comparison. Correspondent training details are reported in Table 1. A relatively limited training of 25 epochs (455,625 and 5750 training steps in 2D and 3D) was possible in reasonable times due to the high computational costs (see also Table 1).

Figure 8

Super-resolution networks. Convolutional neural networks (CNNs: U-Net, SR-ResNet, EDSR, WDSR-a, WDSR-b) and generative adversarial networks (GANs: pix2pix, CycleGAN) employed for super-resolution imaging. Blocks of the same color represent the same type of layer(s); if they are repeated for several times, it is reported above the blocks (e.g., 2×). For (2D or 3D) convolutional layers, the number of filters is provided at the bottom and the kernel size (together with the strides, in the bracket, when different from 1) at the top. Bottom light-gray arrows show skip connections (concatenation for U-Net, pix2pix, CycleGAN, addition for SR-ResNet, EDSR, WDSR-a, WDSR-b), whereas top dark-gray arrows indicate residual blocks for ResNet-based networks (SR-ResNet, EDSR, WDSR-a, WDSR-b) and CycleGAN.