D'Alessandro A., Capizzi P., Luzio D., Martorana R., Messina N.

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25 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

56 εμφανίσεις

D'Alessandro A.
, Capizzi P., Luzio D., Martorana R., Messina N.


1

If

the

shape

of

the

H/V

curves

is

controlled

by

the

S
-
wave

transfer

function

within

the

shallowest

sedimentary

layers,

then

both

H/V

peak

frequencis

and

amplitudes

may

be

straightforward

related

to

subsoil

resonance

frequencies

and

site

amplification

factors
.


On

the

other

hand,

if

the

shape

of

the

H/V

curves

is

controlled

by

the

polarization

of

fundamental

Rayleigh

waves

(ellipticity)
,

then

only

an

indirect

correlation

between

the

H/V

peak

amplitude

and

the

site

amplification

may

exist
.

Relibility

SESAME

Criteria


Time Domain

Frequency Domain

Most

authors

tend

to

exclude

from

the

computation

of

the

average

the

non
-
stationary

portion

of

the

recorded

noise,

thus

considering

only

the

low
-
amplitude

part

of

signal
;



Some

authors

(i
.
e
.

Mucciarelli

(
1998
))

showed

that

the

use

of

non
-
stationary,

high
-
amplitude

noise

windows

improves

the

capability

of

the

HVSR

curve

to

mimic

the

response

obtained

with

weak

motion

recordings

of

earthquakes
.


Can

you

use

a

non
-
arbitrary

approach?


Cluster analysis!


Cluster

analysis

or

clustering

is

the

task

of

grouping

a

set

of

objects

in

such

a

way

that

objects

in

the

same

group

(called

cluster
)

are

more

similar

(internal

cohesion

-

homogeneity)

to

each

other

than

to

those

in

other

groups

(external

isolation

-

separation)
.

So,

a

clustering

algorithm

is

used

to

group

together

those

objects

which

are

most

similar

(nearest)

to

each

other
.

Many

clustering

algorithms

exist,

and

can

be

categorized

into

two

main

types
:



Hierarchical methods;


Non
-
hierarchical methods or model based.

Advantages

of

the

Hierarchical

Methods
:



You

work

from

the

Similarity/Dissimilarity

between

the

objects

to

be

grouped

together
.

A

type

of

Similarity/Dissimilarity

can

be

chosen

which

is

suited

to

the

subject

studied

and

the

nature

of

the

data
;


One

of

the

results

is

the

dendrogram

which

shows

the

progressive

grouping

of

the

data
.

It

is

then

possible

to

gain

an

idea

of

a

suitable

number

of

classes

into

which

the

data

can

be

grouped
;


It

is

an

explorative

method

and

is

not

necessary

to

define

a

priori

the

number

of

clusters
;


Agglomerative
:

in

agglomerative

hierarchical

clustering,

each

object

begins

the

process

as

the

only

member

of

its

own

cluster
.

If

there

are

N

objects,

the

process

then

starts

with

N

clusters
.

The

two

most

similar

objects

then

combine

to

form

a

cluster,

producing

N
-
1

clusters

in

total
.

This

process

is

repeated

until

all

objects

are

finally

members

of

a

single

cluster
.


Divisive
:

This

is

a

"top

down"

approach
:

all

observations

start

in

one

cluster,

and

splits

are

performed

recursively

as

one

moves

down

the

hierarchy
.

Similarity

coefficients
:

Cooccurrence,

Cosine,

Covariance

(n
-
1
),

Covariance

(n),

Dice

coefficient

(also

known

as

Sorensen

coefficient),

General

similarity,

Gower

coefficient,

Inertia,

Jaccard

coefficient,

Kendall

correlation

coefficient,

Kulczinski

coefficient,

Ochiai

coefficient,

Pearson’s

correlation

coefficient,

Pearson

Phi,

Percent

agreement,

Rogers

&

Tanimoto

coefficient,

Sokal

&

Michener

coefficient

(or

simple

matching

coefficient),

Sokal

&

Sneath

coefficient,

Spearman

correlation

coefficient,


...


Dissimilarity

coefficients
:

Bhattacharya's

distance,

Bray

and

Curtis'

distance,

Canberra's

distance,

Chebychev's

distance,

Chi²

distance,

Chi²

metric,

Chord

distance,

Squared

chord

distance,

Dice

coefficient,

Euclidian

distance,

Geodesic

distance,

Jaccard

coefficient,

Kendall

dissimilarity,

Kulczinski

coefficient,

Mahalanobis

distance,

Manhattan

distance,

Ochiai

coefficient,

Pearson's

dissimilarity,

Pearson's

Phi,

General

dissimilarity,

Rogers

&

Tanimoto

coefficient,

Sokal

&

Michener's

coefficient,

Sokal

&

Sneath

coefficient,

Spearman

dissimilarity,

..

Normalized


Standard

Correlation

Simple

linkage
:

The

dissimilarity

between

A

and

B

is

the

dissimilarity

between

the

object

of

A

and

the

object

of

B

that

are

the

most

similar
.


Complete

linkage
:

The

dissimilarity

between

A

and

B

is

the

largest

dissimilarity

between

an

object

of

A

and

an

object

of

B
.


Average

linkage
:

The

dissimilarity

between

A

and

B

is

the

average

of

the

dissimilarities

between

the

objects

of

A

and

the

objects

of

B
.

A

dendrogram

is

a

tree

diagram

frequently

used

to

illustrate

the

arrangement

of

the

clusters

produced

by

hierachical

clustering
.

About
1,000 seismic noise measurements
each
46
minutes
long

There no is correspondence between variation in the HVSR content
and the high
-
energy transients in the recordings;



Cluster analysis can be used to automatically process HVSR data
allowing us to discriminate the part of the signals related to
geological structures from those linked to the sources;



Extension to the spatial clustering of the HVSR curves to identify
homogeneous areas in seismic perspective;