[PPT] - Ba y esian Decon v olution of Seismic Arra y Data for PowerPoint Presentation

SLIDE 1 Ba y esian Decon v

lution
f

Seismic Arra y Data for RippleFired Explosions Eric A Suess Advisor Professor Rob ert Sh um w a y

SLIDE 2 Outline

The

Problem

Mo

del

Ba

y esian Statistics

Ba

y esian Decon v

lution
f

Seismic Arra y Data

Results
Sim

ulated Data

Real

Data

Conclusions

and F uture W

rk

SLIDE 3 T reaties

Limited

Nuclear T est Ban T reat y L TBT

NonProliferation
f

Nuclear W eap

ns

T reat y NPT

Threshold

T est Ban T reat y TTBT

P

eaceful Nuclear Explosions T reat y PNET

Comprehensiv

e T est Ban T reat y CTBT

SLIDE 4 Bac kground Muc h

f

the fo cus in the past has b een

n

distinguishing p

ssible

n uclear explosions from earthquak es

Curren

tly

since

the testing treaties ha v e put limitations

n

the p ermissible sizes

f

the n uclear explosions

ther

smaller seismic ev en ts suc h as industrial mining explosions ha v e b ecome

f

in terest in the discrimination problem The w

rk

presen ted here is related to distinguishing lo wlev el n uclear explosions from ripplered mining explosions that are

n

the same seismic lev el

SLIDE 5 The Problem

Monitoring

seismic ev en ts at Regional Distances for lo wlev el n uclear tests

Other

seismic sources need to b e ruled

ut
RippleFired

Mining Explosions

SLIDE 6 RippleFired Explosions This is a mining tec hnique in whic h explosions

f

single devices

r

groups

f

devices are detonated in succession

SLIDE 7 Monitoring Arra ys

f

receiv ers are put in place at Regional Distances and seismic data is con tin ually collected

Seismic

disturbances that are ab

v

e the baseline noise

f

the area are in v estigated

SLIDE 8 Mo del y k t

s

k t

m

X j

a

j s k t

j
k

t A mplitudes are distributed according to a random BernoulliGaussian mo del ref Cheng Chen and Li

pa

j j

I

a j

T

N

I

a j

Signal

and p ath ee cts follo w an AR

mo

del ref DargahiNoubary

Tjstheim
s

k t

s

k t

p

s k t

p
e

k t e k t iid N

and

dene the precision

k

t iid N

c
c
S

N R

c
is

xed

SLIDE 9 T runcated Normal pa j

c
p
exp
a

j

I

a j

where

c

Z
p
exp
x

SLIDE 10 Ba y esian Statistics Mo del pY j Prior distribution p Join t distribution pY

pY

j p

P
sterior

distribution pjY

pY

j p

R

pY j p d

pY

j p

SLIDE 11 Gibbs Sampler ref Gelfand and Smith

pjY
p
jY
Giv

en

and
for

h

R

eps

Sample
h
from

p

jY
h
Sample
h
from

p

jY
h
Set

h

h
and

go to

B

ur nI n

B

ur nI n

R

eps

R

eps

SLIDE 12

R

eps are realizations

f

a stationary Mark

v

Chain with transition probabilit y from

h

to

h
T
h
h
p
jY
h
p
jY
h
By

Ergo dic theory

w

e can calculate estimates

f

sa y

b

y

R

eps X h

i
as
E
jY
R

eps

SLIDE 13 Priors

B

E T A

N

p

GAM

M A

SLIDE 14 The Mo del y k t

s

k t

m

X j

a

j s k t

j
k

t The parameter set

f
a
Sg

Hyp erparam ters

Fixed

parameters c m

SLIDE 15 Lik eliho

d

Y

y
y

q

y

k

y

k

y

k n

pY

j

q

Y k

py

k j

q

Y k

n
c
n

exp

c

X t

k

t

SLIDE 16 Ov erall Prior p

p
a
S
p

paj p p pSj

Join

t Densit y pY

pY

j p

Join

t P

sterior

p jY

pY

j p

SLIDE 17 Conditional Marginal P

sterior

Distributions p jY

r

est

beta
F
r

xed j

m

pa j jY

r

est

j

I a j

j

T N

a

j

a

j I a j

p

jY

r

est

N

p

p

jY

r

est

g

amma

F
r

xed i

n

and k

q

ps k ijY

r

est

N
s

k i

s

k i

SLIDE 18

jY
r

est

beta
m
n

a

n

a

SLIDE 19 a j jY

r

est

BernoulliGaussian
a

j

a

j

c
X

k X t

k

tj s k t

j
a

j

c
X

k X t s

k

t

j
j
c

a j

a

j

c
a

j

exp
a

j

a

j

SLIDE 20 jY

r

est

N

p

X

k X t s k t

s

k t

X

k X t

s

k t

s
k

t

where
s

k t

s

k t

s

k t

p

SLIDE 21

jY
r

est

g

amma

q

n

l
p
c

X k X t

k

t

X

k X t e

k

t

SLIDE 22 s k tjY

r

est

Normal
s

k i

s

k i

c
X

t a ti

ti
X

t

ti

e

k

ti

s

k i

c
X

t a

ti
X

t

ti

SLIDE 23 Steps T

P

erform The Gibbs Sampler Giv en the initial v alues n

a
S
for

h

to

Reps

Sample
h

from a b eta

Sample

a h j

j
m

from a BernoulliGaussian

Sample
h

from a pv ariate normal

Sample
h

from a gamma

Sample

s k i h

i
n

k

q
from

a normal

Set

h

h
and

go to Step

SLIDE 24 Conclusions and F urther W

rk
ne
t

w

SLIDE 25 References Cheng Q Chen R and LiTH

Sim

ultaneous W a v elet Estimation and Decon v

lution
f

Reection Seismic Signals IEEE T r ansactions On Ge

scienc

e and R emote Sensing

DargahiNoubary
Sto

c hastic Mo deling and Iden tication

f

Seismic Records Based

n

Established Deterministic F

rm

ulations Journal

f

Time Series A nalysis

Tjstheim

D

Autoregressiv

e Represen tation

f

Seismic Pw a v e Signals with an Application to the Problem

f

ShortP erio d Discriminan ts Ge

phys

J R astr So c

SLIDE 26 Gelfand AE and Smith AFM

SamplingBased

Approac hes to Calculating Marginal Densities Journal

f

the A meric an Statistic al Asso ciation

P

earson DC Strump BW and Anderson DP

Ph

ysical Constrain ts

n

Mining Explosions httpwwwge

lo

gysmue du dp awwwp ap erssrlSRLhtml