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

, 1 , ( 1)

n n aw m

a n N w w e n a Г n w

 

    

( , ) ( , ,0, , ) ( ) x y w q x y w t N w dwdt 

 

  

2 2 2 2

( )

x y

q q q q q u z w K K t x z x y              

• 1. Problem statement

(1) (2) (3)

( ) ( ) ( )

t

q Q x y z H   

 



; 0 , , ,

z H

q q x y t



     

2 2

, , 1 ( ) ( )

x z y z H z

H z H z K U K U w w U z u d H z           

(5) (4)

3

( ) ( ,0) 2 HU Q H U N x x x       

2 2 1 2 3 1

( , ) ( ) exp H h h P x Q h dh x x x H                  



 

1 1 2 3

, 1 , 2 ( 1)

n

aU n aU Г n    



     

(6) (7) (8)

• 2. Kinematic model estimation
• f ash fallout thickness

H x w U 

(9)

 

2 2

2

1 , 2

y x

f x y e x









(10)

   

1

, 1, 1

n n aw m

a n N w w e n a Г n w

 

    

(11)

   

2 2 1

, , min

M j j j j j

J r P x y



  

   

      



(13)

 

2

2 3 4 1 2

, , exp , y P x y x x x



            

   

1 1 2 3 4 2

1 , 1, , 2 2 1

n n

T a U H n aU H Г n      



      

(12)

• 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 2

2 ( )

1 , , 2 ( )

y x

f x y e x



 





2 2

k x   

0.5  

2

w cd 

w HU d c c x  

 

2

2 3 1 2

, , exp y P x y x x

 

          

1 2 3

1 , 0.5 , 2 2 k HU c k         

(14) (15) (16)

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

• Fig. 6. Measured and numerically reconstructed particle size
• f 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