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What, why, how History Signal model References

Array-seismology - Lecture 1

Matthias Ohrnberger

Universitat PotsdamInstitut fur Geowissenschaften

Sommersemester 200929. April 2009


Outline for 29. April 2009

1 Array seismology: overviewWhat is an arrayBenefits of arraysPractical issues

2 A little history of array seismologyEarly times - before 1960sThe roaring 60sThe digital revolution

3 Necessity for signal/noise modelsSignal models

4 Literature index


What is array seismology

Array definition

An array is a systematic arrangement of objects, e.g.

in computer science → a compound data type whose elementsare selected by one or more indices or keys, theoreticallyequivalent to a vector or an n-tuple

in engineering → an antenna array (radar), a telescope array(astronomy), microphone array or directional sound speakerarray (speech, acoustic)

in seismology → a spatially distributed set of seismologicalsensors (geophones, seismometers, accelerometers usuallydeployed along the earth’s surface) recording with a commontime base.


Seismic arrays vs. seismic network?

Seismic Array - preliminary definition

A spatially distributed set of seismological sensors recording with acommon time base.

The above definition is not sufficiently precise. Any seismologicalnetwork fulfills the above criterion, still we usually don’t speak ofan array. So, what makes the difference?

Seismic Array - refined definition

Simply spoken, the sensors of an array need additionally to belocated sufficiently close to each other in space, whereas in aseismological network they don’t.

sufficiently close certainly is a very vague formulation, which weshould try to quantify. Let’s try to figure out by example.



German regional seismo-logical network (GRSN).

set of sensors with com-mon time base (GPS-time), may act both as ar-ray or network.



GRSN in typical network operation (Koblenz, 2007)



GRSN in array operation (Sichuan 12.05.2008)



Network vs. array operation at GRSN

Do you note the difference? How can the observation be related tospatial proximity?


Why do we need arrays?

The benefit of seismic arrays

can be immediately recognized by considering the informationcontent of seismic observations given the actual recording setting:

single station single component →arrival times, amplitudes

single station three component →arrival times, amplitudes + polarization (local particle motion)

seismic network (1 or 3 component) →arrival times, amplitudes, (polarization) + direction of wavepropagation (by location)

seismic array (1 or 3 components) →arrival times, amplitudes, (polarization), direction of wavepropagation apparent velocity of wave propagation, SNRimprovement


Array benefits

Arrays allow to improve signal to noise ratio (SNR)

Arrays allow to determine signal characteristics (wavepropagation direction and apparent wave speed)

Arrays allow to filter good from bad signals

Natural application domains given the benefits

investigation of weak phase arrivals and wave propagationphenomena related to path and site (aim: better earth models,hazard estimation)

weak signal detection (explosion monitoring, IMS, CTBTO)

direct imaging of source processes by tracking spatio-temporalevolution of seismic wave radiation.


CTBTO - IMS


26.12.2004, Sumatra Mw = 9.3 rupture


How to build an array, how to process?

Colfiorito, Italy (from NERIES field campaign, March/April 2008)


How do we build an array?

Define target application (temporal vs. fixed installation,detection vs. estimation) - time requirement: 10 seconds.

Select appropriate equipment (sensor, digitizer) - timerequirement: 10 seconds.

Determines array size and layout - time requirement: 60 to3600 seconds

Adapt ideal array layout to real environment (find appropriatelocations for sensor installation and desired noise properties) -time requirement: 1 h to months.

Installation of sensors in the field - time requirement: minutesto months


How do we do array processing?

Subject of this course!

Not a single answer - depends on target application,equipment, geometry, etc. - different methods in use

f-k based (frequency wavenumber methods)

Bartlett beamformer (conventional f-k - shift-and-sum)Generalized beamformer (weighted shift-and-sum)Adaptive beamformer (Capon,Minimum-Variance-Distortionless-Look)

correlation based approaches

Spatial autocorrelation method (SPAC, Aki, 1957)Modified SPAC (Bettig et al., 2001)Centerless circle / Double circle (Cho et al. 2005, Tada et al.,2006)and many derivatives of the above ...


Historical context - Early times

Multisensor recording in geophysical exploration

Since the 1920’s exploration geophysicists started to combine theanalog output of geophones deployed in groups. The outputvoltage corresponds to the sum of the individual signal and thus ismuch stronger for an in-phase arriving signal at the sensors.Summing or stacking is a fundamental principle in multisensoranalysis and is the base of array seismology. The expected result isan increase of the Signal to Noise Ratio (SNR) of weak arrivals.

Abstract from Klipsch (1936)

Considerable attention has been given to the use of more than onegeophone on each recording channel with the hope of increasingsignal-to-noise ratio, where ”signal” is taken to mean ”recordedreflection” and ”noise” means any undesired recorded amplitude.. . .


The roaring 60s

In the seismological context the development and use of arraytechniques is closely related to the start of nuclear test bannegotiations in Geneva 1958

Proposed concept: a high number of small arrays to monitornuclear underground test activities around the world (planned170 small aperture arrays with 10 sensors each)

First experimental arrays from 1960 to 1963 in U.S. and U.K.(VELA program)

but: small array concept could not be realized due to politicalreasons (array installations blocked).

Therefore: second best solution for detection and verificationpurposes of explosions ⇒ Very large arrays at few spots:LASA (Montana, 1965, 200km aperture, 525 stations!),NORSAR (Norway, 1971, 100 km aperture, 198 stations).


Today: Digital global broadband seismology


Need for wave propagation model

Simple array concept

Array seismology is conceptually simple: it uses multipleobservations of the wavefield recorded at sensors distributed inspace (usually Earth’s surface) and combines thoseobservations to an output quantity using certain predictionsabout the spatio-temporal characteristics of the wavefield.

predictions about the spatio-temporal characteristics of the(signal and/or noise) wavefield require a particular wavepropagation model.

the simplest wave propagation model to be used is plane wavepropagation

Harmonic plane wave representation:

D(x , t) = A exp(jω(t± x/c)) D(~x , t) = A exp(j(ωt±~k~x))


Plane wave propagation model

Plane wave revisited

D(x , t) = A exp(jω(t ± x/c)) D(~x , t) = A exp(j(ωt ± ~k~x))

is a special solution to homogeneous wave equation (1D/3D):

∂2D(x , t)

∂x2=

1

c2

∂2D(x , t)

∂t2∇2D(~x , t) =

1

c2

∂2D(~x , t)

∂t2

D(x , t) resp. D(~x , t) is the displacement and c a (locally) constantmedium propagation velocity.


Phase, wavefronts and plane wave parameters

The argument of the harmonic exponential is termed phase:

ω(t ± x/c) ω(t ± ~u~x)

(ωt ± ω

cx) = (ωt ± kx) (ωt ± ~k~x)

if we take a snapshot at some particular time instance t = t0 andrequire a constant value of the phase, it is easy to see that allposition vectors fullfilling these conditions will lie on a plane (theinner product ~k~x must be constant for all ~x). The set of positionsof constant phase are called wavefront. Here, the geometry ofwavefronts are planes! The parameters ω, t, k, x define thepropagation characteristics of a plane wave.

T = 1/f = 2π/ωk = 2π/λ = 2πf /c = ω/c = ωuc = λf = λω/2π = ω/k


Plane wave geometry - backazimuth & incidence angles

~u = (ux , uy , uz) |~u| = 1/c

~u =1

c(sin(i) sin(θ), sin(i) cos(θ), cos(i))


Plane wave propagation direction - be careful!

slowness/wavenumber vector points into direction of wavepropagation.

but . . . seismologists are usually more interested in thedirection where the wave came from → sometimesinconsistent use of orientation can be found.

~uhor = 1/capp = sin(i)/c = p~u = ~uhor (sin(θ), cos(θ), 1/ tan(i))


Spatial wavefield snapshot in x and z


Temporal wavefield evolution along surface in x


Dense wavefield recording along surface in x


References

D.H.Johnson & D.E.Dudgeon, Array Signal Processing -concepts and techniques, Prentice Hall Signal ProcessingSeries, Alan v. Oppenheim, Series Editor, 1993.

H.L. Van Trees, Optimum Array Processing, Part IV of’Detection, Estimation, and Modulation Theory, John wileyand Sons, Inc., New York, 2002.

Schweitzer, J., Fyen, J., Mykkeltveit, S. and Kvaerna, T.(2002). Chapter 9: Seismic Arrays, In: Bormann, P. (Ed.),IASPEI New Manual of Seismological Observatory Practice,GeoForschungsZentrum Potsdam, Vol. 1, 51pp.

Mykkeltveit, S., Astebol, K., Doornbos, D.J., and Husebye,E.S. (1983). Seismic Array configuration Optimization, BSSA,73(1), pp. 173-186.

Rost, S. and Ch. Thomas, Array Seismology, Reviews ofGeophysics, 2002.

array-seismology - lecture 1 - geophysics homepagejowa/master09/arraycourse... · array-seismology...

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