Causes and consequences of bimodal grain-size distribution of tephra fall deposited during the August 2006 Tungurahua eruption (Ecuador)

Abstract

The violent August 16–17, 2006 Tungurahua eruption in Ecuador witnessed the emplacement of numerous scoria flows and the deposition of a widespread tephra layer west of the volcano. We assess the size of the eruption by determining a bulk tephra volume in the range 42–57 × 10⁶ m³, which supports a Volcanic Explosivity Index 3 event, consistent with calculated column height of 16–18 km above the vent and making it the strongest eruptive phase since the volcano’s magmatic reactivation in 1999. Isopachs west of the volcano are sub-bilobate in shape, while sieve and laser diffraction grain-size analyses of tephra samples reveal strongly bimodal distributions. Based on a new grain-size deconvolution algorithm and extended sampling area, we propose here a mechanism to account for the bimodal grain-size distribution. The deconvolution procedure allows us to identify two particle subpopulations in the deposit with distinct characteristics that indicate dissimilar transport-depositional processes. The log-normal coarse-grained subpopulation is typical of particles transported downwind by the main volcanic plume. The positively skewed, fine-grained subpopulation in the tephra fall layer shares close similarities with the elutriated co-pyroclastic flow ash cloud layers preserved on top of the scoria flow deposits. The area with the higher fine particle content in the tephra layer coincides with the downwind prolongation of the pyroclastic flow deposits. These results indicate that the bimodal distribution of grain size in the Tungurahua fall deposit results from synchronous deposition of lapilli from the main plume and fine ash elutriated from scoria flows emplaced on the western flank of the volcano. Our study also reveals that inappropriate grain-size data processing may produce misleading determination of eruptive type.

Appendix

Particle size distributions (PSD) of natural deposits commonly show polymodal and asymmetric distributions usually interpreted as a combination of various physical processes that cannot be described by a single log-normal distribution. The aim of LOGN_2D algorithm (LOGNormal Distribution Deconvolution) is to decipher natural composite PSD by a sum of independent PSDs accounting for distinct processes. This fully automated algorithm is based on a discretized Weibull-type distribution whose flexibility permits easy interpolation between a wide range of distributions and positive skewness modelling.

The Weibull distribution is defined through a probability density function of particles with diameter (x) using the two parameters (k) and (λ):

$$ {f_{\text{w}}}\left( {x;k,\lambda } \right) = \left( {\frac{k}{\lambda }} \right){\left( {\frac{x}{\lambda }} \right)^{{\left( {k - 1} \right)}}}\exp {\left( { - \frac{x}{\lambda }} \right)^k}\quad {\text{for}}\quad x > 0 $$

(A1)

The shape factor (k) permits to model from exponential (k = 1) to Gaussian (k = 3) shapes, hence allowing non log-normal distribution modelling. The shift factor (λ) depends on the mode (μ) and is defined by:

$$ \lambda = \mu {\left( {\frac{{k - 1}}{k}} \right)^{{ - \frac{1}{k}}}} $$

(A2)

The cumulative distribution function for the Weibull distribution is:

$$ F\left( {x;k,\lambda } \right) = 1 - \exp {\left( { - \frac{x}{\lambda }} \right)^k}\quad {\text{for}}\;x \geqslant 0 $$

(A3)

Then, the Weibull distribution can be used to generate a combination of several components in order to model a natural composite distribution as:

$$ f{(x)_{\text{comp}}} = {w_1}{f_1}(x) + {w_2}{f_2}(x) + \ldots + {w_n}{f_n}(x) $$

(A4)

and

$$ F{(x)_{\text{comp}}} = {w_1}{F_1}(x) + {w_2}{F_2}(x) + \ldots + {w_n}{F_n}(x) $$

(A5)

where w _i is the weight of each component that represents their relative fraction following:

$$ \sum\limits_{{i = 1}}^n {{w_i} = 1} $$

(A6)

The deconvolution of the natural distribution can be achieved by best-fit matching of synthetic and natural data. The inversion procedure uses a least-square estimation method based on the minimization function S(x) between the natural and the synthetic distribution.

$$ S(x) = {\sum {\left[ {f{{(x)}_{\text{nat}}} - f{{(x)}_{\text{synth}}}} \right]}^2} $$

(A7)

Variable parameters (k,λ, μ and w) are optimized during iterative calculations until the fitness criterion between synthetic and natural distributions is reached.

The accuracy of the deconvolution procedure is controlled for the whole sample population verifying the similarity between the Inman’s parameters (Md_Ф, σ _Ф, Sk) for the natural bulk distribution, and the Inman’s parameters for the synthetic bimodal distribution (Fig. 13). The data points are distributed on a line with the equation y = x, which suggests that the deconvolution gave realistic results.

Fig. 13

Deconvolution checking-graph: correlation between the Inman’s parameters calculated for the natural bulk distributions and the Inman’s parameters calculated for the synthetic bimodal distributions of the whole 22 PFall samples