Classification of volcanic ash particles using a convolutional neural network and probability

Analyses of volcanic ash are typically performed either by qualitatively classifying ash particles by eye or by quantitatively parameterizing its shape and texture. While complex shapes can be classified through qualitative analyses, the results are subjective due to the difficulty of categorizing complex shapes into a single class. Although quantitative analyses are objective, selection of shape parameters is required. Here, we applied a convolutional neural network (CNN) for the classification of volcanic ash. First, we defined four basal particle shapes (blocky, vesicular, elongated, rounded) generated by different eruption mechanisms (e.g., brittle fragmentation), and then trained the CNN using particles composed of only one basal shape. The CNN could recognize the basal shapes with over 90% accuracy. Using the trained network, we classified ash particles composed of multiple basal shapes based on the output of the network, which can be interpreted as a mixing ratio of the four basal shapes. Clustering of samples by the averaged probabilities and the intensity is consistent with the eruption type. The mixing ratio output by the CNN can be used to quantitatively classify complex shapes in nature without categorizing forcibly and without the need for shape parameters, which may lead to a new taxonomy.


Earth-Life Science
). This structure is thought to be formed by reworking in an unconsolidated state (Y. Suzuki, personal communication). The Hachikuboyama sample (HK15120701) has a sorted grain size distribution with a mode of −2.5ϕ ( Supplementary Fig. S1).
Hachinoyama scoria cone The Hachinoyama scoria cone (1340 m in bottom diameter, R. Noguchi, unpublished data) is located in the southern HIMVG field. The rock type of this scoria cone is high-Al basalt 4 . Hachinoyama consists of alternate layers of red-oxidized scoria and black volcanic sand with bombs (maximum 15 cm diameter, Supplementary Fig.   S2). The Hachinoyama sample (HN15120701) has a sorted grain size distribution with a mode of −2.0ϕ, and no −4ϕ peak caused by larger size bombs beyond our sieving range ( Supplementary Fig. S1).
Inatori scoria cone The Inatori scoria cone (910 m in bottom diameter, R. Noguchi, unpublished data) is located in the southern coastal area of the HIMVG field. The rock type of this scoria cone is tholeiitic basalt 4 . This scoria cone has slightly reversed grading of red-oxidized scoria layers ( Supplementary Fig. S2), some of which have fluidal shape bombs (50 cm for the major axes). The Inatori sample (IT15120501) has a sorted grain size with a mode of -2.5ϕ ( Supplementary Fig. S1). The -4ϕ peak is caused by larger size bombs beyond our sieving range. (Supplementary Fig. S1).

Sukumoyama scoria cone
The Sukumoyama scoria cone (790 m in bottom diameter, R. Noguchi, unpublished data) is located in the northern HIMVG field. The rock type of this scoria cone is tholeiitic basalt 4 . This scoria cone consists of lower black scoria layers and an upper yellowish-brown altered scoria layer ( Supplementary Fig. S2). The samples were collected from the black scoria layer. The Sukumoyama sample (SK15101201) has a sorted grain size distribution with a mode of −2.5ϕ ( Supplementary Fig. S1).

Miyakejima, Japan
Whole Miyakejima samples in this study were products of the 1983 A.D. fissure eruption event, which started on October 3 and ended on October 4 5 . In this event, the initial eruption started from the southwestern flank of the Oyama volcano with a NE-SW trend, and then fissure vents propagated toward the northeast and southwest 5 . The rock type formed in this event is augite basalt 6 .

NP15113001-06, and NP16102407
A preatomagmatic eruption in the S vent 5 produced a tuff ring in the Nippana area of southern Miyakejima Island. The edifice originally had a bottom diameter of 400 m and was 25 m in height, and half of it was destroyed by subsequent typhoons and erosions after formation 7 . We collected seven NP samples from the lower to upper layers at the crosscut outcrop, NP15113001 for the lowest layer and NP16102407 for the uppermost layer ( Fig. 1, Supplementary Fig. S3). These sample has a poorly sorted grain size distribution ( Supplementary Fig. S1). Excluding large counts due to the sieving range, the modes of the grain size distributions are −0.5ϕ for NP1511001 and NP15113002, −1ϕ for NP16102407, −1.5ϕ for NP15113004, −2ϕ for NP15113003 and NP15113005, and −2.5ϕ for NP15113006.

Myvatn, Iceland
The Myvatn samples investigated in this study were collected from edifices of rootless cones, which are pervasively distributed around the Myvatn region in northern Iceland (Fig. 1).
In 2170±38 cal yr BP 8 , basaltic lava (Younger Laxárhraun 9 ) erupted from fissure swarms, and then flowed over wetlands, lakes (including old Lake Myvatn), rivers, and flood plains before reaching the northern bay. Explosive interactions between the lava and wet substrate sediments created more than a hundred rootless cones over the lava surface 10 Supplementary Fig. S4). There is no layering and grading at outcrops of Myvatn rootless cones that we observed.

MY13091004 and MY13091006
For a DRC on Geitey Island in Lake Myvatn, samples were collected from the outer conical edifice (referred to as the outer cone 13 ; MY13091004) and the inner conical edifice (referred to as the inner cone 13 ; MY13091006), as shown in  Fig. S1).

MY13091305 and MY13091306
The MY13091305-MY13091306 pair were taken from the same cone (67 m in bottom diameter 13 ). MY13091305 and MY13091306 were collected from the bottom and middle of the crosscut outcrop, respectively ( Supplementary Fig. S4).
MY13091305 has a sorted grain size distribution with a mode of −2ϕ (Supplementary Fig.   S1). 13 ) in Hagi, which is located 45 km from the fissure vents (Fig. 1). Since there was no crosscut outcrop, we collected the sample from the top of the cone (Supplementary Fig. S4).

MY13091402 MY13091402 was sampled from a rootless cone (51 m in bottom diameter
MY13091402 has a sorted grain size distribution with a mode of −3ϕ (Supplementary Fig.   S1).
MY13092002 MY13092002 was collected from the bottom of a large rootless cone (112 m in bottom diameter 13 ). This sample is poorly sorted relative to the other Myvatn samples ( Supplementary Fig. S1).

Microscope observations for the FN, NP, and MY samples
We observed ash particles (2ϕ to 3ϕ) of the Funabara, Nippana, and Myvatn samples using a digital microscope (VHX-2000, KEYENCE) for verification of the CNN-cluster analysis classification result. First, we observed dispersed ash particles. Furthermore, we prepared cross-sectional samples of the ash particles, and then observed them using a magnification of 500× under both incident and reflected light. We measured bubbles in ash particles using the ImageJ software (http://imagej.nih.gov/ij/). The bubbles include those estimated by the arc appearing in the outline of the particle.
The Funabara samples are dominantly red oxidized opaque grains ( Fig. 1 and Supplementary Fig. S5), and the surfaces of the particles appear glassy under incident lighting.
Some of the particles are coated with red oxidized magna and are therefore opaque in transmission mode (e.g., in FN15101208, Supplementary Fig. S5). Transparent particles in the Funabara samples are brownish-yellow grains and freecrystals (plagioclase, olivine, and pyroxene). Brownish-yellow grains, which have a glassy surface, are more dominant in FN15101206.
The bubble size of the Funabara ash particles is between 16 and 107 µm.
Most of the particles in the Nippana samples are glass fragments, which often contain microlites (plagioclase and magnetite) on the microscopic scale ( Fig. 1 and Supplementary   Fig. S6). The other particles are free from crystals (plagioclase). NP16102407 contains black opaque grains, which are highly microcrystalline. Qualitatively, the characteristics of the grain shapes differ among samples, having concave shapes (NP15113001, NP15113002, and NP15113003) and rectilinear edges (NP15113004, NP15113005, and NP15113006). The bubble size of the Nippana samples is between 9 and 181 µm.
Most of the particles in the Myvatn samples are glassy ( Fig. 1 and Supplementary Fig.   S7). Plagioclases are found as both free crystals and microlites. Some particles have patchy textures due to heterogeneous crystallization (e.g., in MY13091306, Supplementary Fig. S7). In

Transparency of samples
Using a Morphologi G3S TM , we obtained the following transparency parameters for each image 14 , the mean (I m ) and standard deviation (I SD ) of the intensity: where I i is the intensity (0-255) of the ith pixel, and N is the total number of pixels for one grain. I m and I SD were calculated for every grain. For the cluster analysis of the samples, in order to obtain the overall transparency values for each sample, we calculated the mean, median, and standard deviation of I m and I SD .
4 Particle shape parameters in Table 3 In Table 3 shows values of general particle shape parameters to demonstrate our quantitative particle selection. We chose four parameters: aspect ratio (A r ), convexity (C v ), HS (high sensitivity) circularity (H c ), and solidity (S d ). These parameters are derived as follows: where W is the length along the minor axis of the grain, L is the length along the major axis of the grain, P c is the perimeter of the convex hull, P g is the perimeter of the grain, A c is the area of the convex hull, and A g is the area of the grain 14 . We obtained these parameter values using the ImageJ software (http://imagej.nih.gov/ij/). The threshold for the binarization is 0-128. After the four parameters for every basal image were calculated, we averaged them over each basal shape. Figure S1: Grain size distribution for each sample in this study. Figure S2: Outcrops, which were samples collected from Izu Peninsula, Japan. Figure S3: Outcrops, which were samples collected from Miyakejima Island, Japan.