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[PPS07-P17] Spatial and size distributions of spherical iron rinded concretions
Keywords:spherical iron concretion, size distribution, spatial distribution
Background
The spherical iron concretions in Escalante National Monument, Utah, U.S.A., range in size from 1 mm to several centimeters, and are composed of iron oxide rinds that fill the gaps between sandstone particles. Yoshida et al. (2018: Sci. Adv. 4, eaau0872) found that the first step in the formation of spherical iron concretions is the formation of carbonate calcium concretions. (2018: Sci. Adv. 4, eaau0872). The spatial and size distributions of spherical iron concretions that we observe now reflect the spatial and size distributions of calcium carbonate concretions. The nucleation of calcium carbonate concretions is a random stochastic process. However, Potter and Chan (2011: Geofluids, 11, 184) reported that the spatial distribution was not random and was close to evenly spaced. On the other hand, the size distribution has peaks at 1 mm, 1 cm, and 3 cm in diameter, and the width of each peak is positively correlated with the diameter (Potter et al., 2010 EPSL 201, 444). However, the sample size of these previous studies is not necessarily large (the number of concretions used to calculate the spatial distribution is about 20), so in this study, we used a larger data set to obtain the spatial and size distributions. We also constructed a model to reproduce the characteristics of the size distribution and performed numerical simulations.
Image analysis
Three types of images taken in Escalante National Monument were used to measure the spatial and size distributions. 1: Images of an area of about 1000 m2 . Due to low resolution, iron concretions larger than 1 cm in diameter were analyzed. 2: Four images of an area of about 0.1 m2 , to analyze mm-sized concretions that cannot be analyzed in dataset 1. 3: Images used in Potter and Chan (2011) (provided by Dr. Potter). For the spatial distribution, the frequency distribution of the nearest neighbor distance is calculated and compared with the analytical solution in the random case. As a result of the analysis, there was a clear deviation from the random spatial distribution in some of the images (5 images) provided by Dr. Potter, but there was no deviation from the random distribution in the other dataset (95 images). This indicates that the spatial distribution is basically random, although it may deviate from the random distribution by some mechanism in the small size stage. This result suggests that the nucleation of calcium carbonate proceeds uniformly in the sandstone and that each nucleus grows independently. Although the peak of the size distribution at 1 cm in diameter reported in previous studies was not observed due to the limited resolution of the images, the peaks at 1 mm and 3 cm were identified in this study. A positive relationship between size and spacing was also observed. This result indicates that the content of calcium carbonate in a unit volume of sandstone is constant regardless of the size of the concretion.
Numerical simulation
The steady-state solution of the one-dimensional spherically symmetric diffusion equation shows that the precipitation rate of calcium carbonate increases with radius, while the dissolution rate decreases with radius. Under the constraint that the amount of dissolution and precipitation are always equal, we conducted numerical simulations to see how the size distribution evolves. As a result, we found that the size distribution evolves in a similar manner to that of Ostwald ripening, with the width of the distribution increasing in proportion to the average size (Fig. 1). On the other hand, there was a large uncertainty in the formation time, and the time required to grow to 1 cm was limited to several thousand to several hundred thousand years. It was found that there was a relationship between pH during dissolution, supersaturation during precipitation, dissolution time and precipitation time.
The spherical iron concretions in Escalante National Monument, Utah, U.S.A., range in size from 1 mm to several centimeters, and are composed of iron oxide rinds that fill the gaps between sandstone particles. Yoshida et al. (2018: Sci. Adv. 4, eaau0872) found that the first step in the formation of spherical iron concretions is the formation of carbonate calcium concretions. (2018: Sci. Adv. 4, eaau0872). The spatial and size distributions of spherical iron concretions that we observe now reflect the spatial and size distributions of calcium carbonate concretions. The nucleation of calcium carbonate concretions is a random stochastic process. However, Potter and Chan (2011: Geofluids, 11, 184) reported that the spatial distribution was not random and was close to evenly spaced. On the other hand, the size distribution has peaks at 1 mm, 1 cm, and 3 cm in diameter, and the width of each peak is positively correlated with the diameter (Potter et al., 2010 EPSL 201, 444). However, the sample size of these previous studies is not necessarily large (the number of concretions used to calculate the spatial distribution is about 20), so in this study, we used a larger data set to obtain the spatial and size distributions. We also constructed a model to reproduce the characteristics of the size distribution and performed numerical simulations.
Image analysis
Three types of images taken in Escalante National Monument were used to measure the spatial and size distributions. 1: Images of an area of about 1000 m2 . Due to low resolution, iron concretions larger than 1 cm in diameter were analyzed. 2: Four images of an area of about 0.1 m2 , to analyze mm-sized concretions that cannot be analyzed in dataset 1. 3: Images used in Potter and Chan (2011) (provided by Dr. Potter). For the spatial distribution, the frequency distribution of the nearest neighbor distance is calculated and compared with the analytical solution in the random case. As a result of the analysis, there was a clear deviation from the random spatial distribution in some of the images (5 images) provided by Dr. Potter, but there was no deviation from the random distribution in the other dataset (95 images). This indicates that the spatial distribution is basically random, although it may deviate from the random distribution by some mechanism in the small size stage. This result suggests that the nucleation of calcium carbonate proceeds uniformly in the sandstone and that each nucleus grows independently. Although the peak of the size distribution at 1 cm in diameter reported in previous studies was not observed due to the limited resolution of the images, the peaks at 1 mm and 3 cm were identified in this study. A positive relationship between size and spacing was also observed. This result indicates that the content of calcium carbonate in a unit volume of sandstone is constant regardless of the size of the concretion.
Numerical simulation
The steady-state solution of the one-dimensional spherically symmetric diffusion equation shows that the precipitation rate of calcium carbonate increases with radius, while the dissolution rate decreases with radius. Under the constraint that the amount of dissolution and precipitation are always equal, we conducted numerical simulations to see how the size distribution evolves. As a result, we found that the size distribution evolves in a similar manner to that of Ostwald ripening, with the width of the distribution increasing in proportion to the average size (Fig. 1). On the other hand, there was a large uncertainty in the formation time, and the time required to grow to 1 cm was limited to several thousand to several hundred thousand years. It was found that there was a relationship between pH during dissolution, supersaturation during precipitation, dissolution time and precipitation time.