Location Maldives

8/13/2019 Location Maldives

1/40

Earthquake Location

The basic principles S-P location (manual)

location by inversion

single station location

depth assessment velocity models

Relocation methodsjoint hypocentral location

master event location

Other related topics Waveform modeling

Automated phase picking


2/40

Basic Principles

4 unknowns - origin time, x, y, z

Data from seismogramsphase arrival times


3/40

S-P time

Time between P and S

arrivals increases with

distance from the

focus.

A single trace can

therefore give the origintime and distance (but

not azimuth)

D Ts Tp 8

Ts Tp D Vs Vp

1 1

approximates to


4/40

Manual Method

C

SEISMIC STATION

A

* EPICENTRE

D

B

EPICENTRE

HYPOCENTRE

H

*

X

D

SEISMOGRAPH

STATION

D T

s T

p 8

Ts Tp DVs Vp

1 1


5/40

Seismogram


6/40


7/40


8/40


9/40


10/40


11/40


12/40

S-P method

1 stationknow the distance - a circle of possiblelocation

2 stationstwo circles that will intersect at twolocations

3 stations3 circles, one intersection = unique

location

4+ stationsoverdetermined problem

can get an estimationof errors


13/40

Wadati diagram

gives the origintime (where S-P

time = 0)

Determines Vp/Vs

(assuming itsconstant and the P

and S phases are

the same type

e.g. Pn and Sn, or

Pg and Sg)

indicates pick

errors

S-P time against absolute P arrival time


14/40

Locating with P only

Thelocationhas 4 unknowns

(t,x,y,z) so with

4+ P arrivals

this can besolved.

The P arrival time has a non-linear

relationship to the location, even in thesimplest case when we assume constant

velocitytherefore can only be solved

numerically


15/40

Numerical methods

Calculated travel time:

Simplest possible relation between travel

time and location:

Find location by minimizing the summed

residual (e):

tci=T(xi,yi,zi,x0,y0,z0) + t0

n

ri=titci e = (ri)2

i=1

ti= (x0-xi)2+(y0-yi)2v


16/40

Least squaresthe outlier problem

http://www.mathworks.com/

The squaring

makes the

solution very

sensitive tooutliers.

Algorithms

normally leave

out points with

large residuals


17/40

Numerical methodsgrid search

courtesy of Robert Mereu


18/40

solving using linearization

Assume a starting location and assume that

the change needed (x y z t) is small

enough that a Taylor series expansion withonly the linear term keep is a good

approximation:

tci=T(xi,yi,zi,x0,y0,z0) + t0 ri=tit

ci

ri=(T/xi)x+ (T/yi)y+ (T/zi)z+ t


19/40

solving using linearization

In matrix notation: r = G mri=(

T/xi)

x+ (

T/

yi)

y+ (

T/

zi)

z+

t

r - the vector of residualsG - the partial derivatives

(each entry in the 4th

column = 1)

m - the correction factor foreach variable


20/40

iterative solution

Counteract the

approximation of

linearizing the problem

by taking the solution asa new starting model.

starting location

calc solutiontrue location

1 2 3 4iteration

residu

al


21/40

The residuals are

not always a well

behaved function,

can have local

minima

DEPTH

(KM

)

200

150

100

50

0

III

RMS ( SEC )

0.60.40.20

II

I

1.00.8

A grid searchmay show if

there is a

better solution


22/40

The S-P time give thedistance to the epicenter

The ratio of movement on thehorizontal components gives

the azimuth

W

Single station method N

S

W E

E

DOWN

UP

UP

N

W

Particle motionP wave

Station

Station

to event

to event


23/40

Depth estimation

The distance between the

station and the event islikely to be many kilometers.

Therefore a small variation

in focal depth (e.g. 5 km) will

have little effect on thedistance between the event

and the station.

Therefore the S-P time and P

arrival time are insensitiveto focal depth

ANSS station spacing ~280 km

10 km

20 km

tens to hundreds of kilometers


24/40

Synthetic tests of variation in depth

resolution - used in designing the network.

As the distance for the quake to the nearest

station increases the network becomesinsensitive to the depth of the event (which

was 10km for this test data).

courtesy of Robert Mereu


25/40

DepthpP and sP

The phases that reflect

from the Earth surface

near the course (pP

and sP) can be used to

get a more accuratedepth estimate

Stein and Wysession An Introduction to Seismology, Earthquakes, and Earth Structure


26/40

Velocity models

For distant events may use a 1-D referencemodel (e.g. PREM) and station corrections


27/40

Local velocity model

For local earthquakes need a model thatrepresents the (1D) structure of the local

crust.

SeisGram2K


28/40

Determining the local velocity model

Refraction datathe best for Moho

depth and

velocity structure

of the crust.

Winnardhi and Mereu, 1997.

Art Jolly http://www.giseis.alaska.edu/Seis/Input/martin/physics212/seismictomo.html


29/40

Tomography

Local tomographyfrom local

earthquakes can give

crust and upper

mantle velocities Regional/Global

tomography from

global events gives

mantle velocitystructure.

Seismic Tomography at the Tonga Arc Zone

(Zhao et al., 1994)

y p g p p y


30/40

Station Corrections

Station corrections allow

for local structure and

differences from the 1D

model

91 92 93 94 95 96

25

26

27

28

-2.43

-1.93

-1.43

-0.93

-0.43

0.07

0.57

1.07

1.57

2.07

Shillong

Plateau

MikirHills

Indo

-Burm

a

rang

es

AssamValley

Contours of the P-wave Station Correction, NE India

(Bhattacharya et al., 2005)


31/40

Location in subduction zones

Poor station distribution

Good location

Poor location


32/40

Operational

PlannedCourtesy L. Kong

Stations in the Indian Ocean

N t k l ti


33/40

Relocation methods

Recalculate the locations

using the relationship

between the events. Master Event Method

Joint hypocentral

determination

Double difference method

Waldhauser and Schaff Improving Earthquake Locations in Northern California UsingWaveform Based Differential Time Measurements

Network locations

relocations


34/40

Master event relocation

Select master event(s)quakes with good

locations, probably either the largest

magnitude or event(s) that occurred after a

temporary deployment of seismographs.

Assign residuals from this event as the

station corrections.

Relocated other events using these stationcorrections.


35/40

Cross-correlation to improve picks

Phases fromevents with similar

locations and focal

mechanisms will

have similar

waveforms.

realign traces to

maximize thecross-correlation

of the waveform.

Analyst Picks

Cross-correlated Picks

Rowe et al 2002. Pure and Applied Geophysics 159


36/40

Some additional related topics...

Waveform modeling

Automated phase pickers

location of great earthquakes


37/40

Waveform modeling

Generate synthetic

waveforms andcompare to the

recorded data to

constrain the event

Stein and Wysession An Introduction to Seismology, Earthquakes, and Earth Structure


38/40

Waveform modeling

u(t) = x(t) * e(t) * q(t) * i(t)

seismogram

source timefunction instrument

responsereflections &

conversions

at interfaces

attenuation

U()= X() E() Q() I()

Construction

of thesynthetic

seismogram


39/40

Automatic phase picks

Short term average - long term average(STA/LTA)developed in the 1970s, still used

by Earthworm and Sac2000

Sleeman and von Eck 1999, Physics of Earth and Planetary Interiors 113


40/40

Location of Great Earthquakes

With great earthquakes theslip area is very large

(hundreds of kilometers)

For hazard assessment theepicenter and centroid are

not very informative. Need

to rupture area, but this is

not available in time fortsunami warnings/disaster

management.

Epicenter

Centroid

Documents

Location Maldives