MODELS OF VOLCANIC ASH FIELDS RECONSTRUCTION Raputa V.F., - PowerPoint PPT Presentation

MODELS OF VOLCANIC ASH FIELDS RECONSTRUCTION Raputa V.F., Yaroslavtseva T.V. Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk

Vulcan Puyeue (Chile), June 2011

1. Experimental studies

Fig. 1. Paramushir Island. Volcanoes.

Eruption of 2003, 2007

Tephra eruptions after 1853 and 1986

1. Problem statement  n 1 a n        n aw (1) N w w e , n 1 , a  Г n w ( 1) m       (2) ( , ) x y w q x y ( , ,0, , ) w t N w dwdt ( ) 0 0      2 2 q q q q q     ( ) (3) u z w K K      x y 2 2 t x z x y

      q Q ( ) ( ) ( x y z H ) t 0 (4)       q 0 ; q 0 , x , y , t  z H   H z H z     2 2 K U , K U , x z y z w w H 1 (5)      U z ( ) u ( ) d H z z

HU    0 Q H U N ( ) 0 x   ( ,0) x (6)   3 2 x H   2     h h  2     1     (7) P x ( , ) Q h ( ) exp dh 2     3 x x x H 1    n 1 aU        0 (8) , n 1 , aU    1 2 3 0 Г n 2 ( 1)

2. Kinematic model estimation of ash fallout thickness H x  (9) w U 2 y  1     2 (10) 2 x f x y , e 0  2 x 0  n 1 a n        (11) n aw N w w e , n 1, a    Г n w 1 m

      2 y       3 4 (12)   P x y , , x exp , 2 1 2   x x    n n 1 T a U H 1           , n 1, aU H ,      1 2 3 4 2 Г n 2 2 1 0 0     2 M           2 J r P x y , , min (13)   j j j j     j 1

Fig. 2. The scheme of tephra sampling in the vicinity of the volcano Chikurachki, eruption in 1853. Recovered from model (12) field fallout. ● - position of sampling points.

Fig. 3. The scheme of tephra sampling in the vicinity of the volcano Chikurachki, eruption in 1986. Recovered from model (12) field fallout. ● - position of sampling points.

Fig. 4. Measured and numerical reconstruction of tephra fallout thickness at sampling points : a) eruption of 1853 , b) eruption of 1986

3. Model estimation of particle size of tephra 2 y  1     k x      2 2 2 2 ( ) x (14) 0.5 f x y , e ,   2 ( ) x w HU    2 w cd d (15) c c x      2 y       3  P x y , , x exp 2 (16)  1 2   x k HU 1         , 0.5 ,  1 2 3 2 c 2 k

Fig. 5. Measured and numerically reconstructed particle size of tephra by volcanic axes ashfalls for 1853 . ● - support points, ● - control points of observation

Fig. 6. Measured and numerically reconstructed particle size of tephra eruption for 1986

Conclusion - to reconstruct the fields of ash deposition thickness and particle size developed polydisperse models with small number parameters; - was carried out testing of these models on field data in the vicinity of the volcano Chikurachki; - to restore the field deposition can be used in a very limited number of measurement points, it creates certain advantages for the analysis of available data.

Thanks for attention