Array-seismology - Lecture 1 Matthias Ohrnberger Universität Potsdam Institut für Geowissenschaften Sommersemester 2009 29. April 2009
Outline for 29. April 2009 1 Array seismology: overview What is an array Benefits of arrays Practical issues 2 A little history of array seismology Early times - before 1960s The roaring 60s The digital revolution 3 Necessity for signal/noise models Signal 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 elements are selected by one or more indices or keys, theoretically equivalent to a vector or an n-tuple in engineering an antenna array (radar), a telescope array (astronomy), microphone array or directional sound speaker array (speech, acoustic) in seismology a spatially distributed set of seismological sensors (geophones, seismometers, accelerometers usually deployed along the earth s surface) recording with a common time base.
Seismic arrays vs. seismic network? Seismic Array - preliminary definition A spatially distributed set of seismological sensors recording with a common time base. The above definition is not sufficiently precise. Any seismological network fulfills the above criterion, still we usually don t speak of an array. So, what makes the difference? Seismic Array - refined definition Simply spoken, the sensors of an array need additionally to be located sufficiently close to each other in space, whereas in a seismological network they don t. sufficiently close certainly is a very vague formulation, which we should try to quantify. Let s try to figure out by example.
Seismic arrays vs. seismic network? German regional seismological network (GRSN). set of sensors with common time base (GPStime), may act both as array or network.
Seismic arrays vs. seismic network? GRSN in typical network operation (Koblenz, 2007)
Seismic arrays vs. seismic network? GRSN in array operation (Sichuan 12.05.2008)
Seismic arrays vs. seismic network? Network vs. array operation at GRSN Do you note the difference? How can the observation be related to spatial proximity?
Why do we need arrays? The benefit of seismic arrays can be immediately recognized by considering the information content 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 wave propagation (by location) seismic array (1 or 3 components) arrival times, amplitudes, (polarization), direction of wave propagation apparent velocity of wave propagation, SNR improvement
Array benefits Arrays allow to improve signal to noise ratio (SNR) Arrays allow to determine signal characteristics (wave propagation 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 propagation phenomena 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-temporal evolution of seismic wave radiation.
CTBTO - IMS
26.12.2004, Sumatra M w = 9.3 rupture
What, why, how History Signal model References 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) - time requirement: 10 seconds. Determines array size and layout - time requirement: 60 to 3600 seconds Adapt ideal array layout to real environment (find appropriate locations for sensor installation and desired noise properties) - time requirement: 1 h to months. Installation of sensors in the field - time requirement: minutes to 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 the analog output of geophones deployed in groups. The output voltage corresponds to the sum of the individual signal and thus is much stronger for an in-phase arriving signal at the sensors. Summing or stacking is a fundamental principle in multisensor analysis and is the base of array seismology. The expected result is an 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 one geophone on each recording channel with the hope of increasing signal-to-noise ratio, where signal is taken to mean recorded reflection and noise means any undesired recorded amplitude....
The roaring 60s In the seismological context the development and use of array techniques is closely related to the start of nuclear test ban negotiations in Geneva 1958 Proposed concept: a high number of small arrays to monitor nuclear underground test activities around the world (planned 170 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 political reasons (array installations blocked). Therefore: second best solution for detection and verification purposes 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 multiple observations of the wavefield recorded at sensors distributed in space (usually Earth s surface) and combines those observations to an output quantity using certain predictions about the spatio-temporal characteristics of the wavefield. predictions about the spatio-temporal characteristics of the (signal and/or noise) wavefield require a particular wave propagation model. the simplest wave propagation model to be used is plane wave propagation 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): 2 D(x, t) x 2 = 1 2 D(x, t) c 2 t 2 2 D( x, t) = 1 2 D( x, t) c 2 t 2 D(x, t) resp. D( x, t) is the displacement and c a (locally) constant medium 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 x) = (ωt ± kx) c (ωt ± k x) if we take a snapshot at some particular time instance t = t 0 and require a constant value of the phase, it is easy to see that all position vectors fullfilling these conditions will lie on a plane (the inner product k x must be constant for all x). The set of positions of constant phase are called wavefront. Here, the geometry of wavefronts are planes! The parameters ω, t, k, x define the propagation characteristics of a plane wave. T = 1/f = 2π/ω k = 2π/λ = 2πf /c = ω/c = ωu c = λf = λω/2π = ω/k
Plane wave geometry - backazimuth & incidence angles u = (u x, u y, u z ) u = 1/c u = 1 (sin(i) sin(θ), sin(i) cos(θ), cos(i)) c
Plane wave propagation direction - be careful! slowness/wavenumber vector points into direction of wave propagation. but... seismologists are usually more interested in the direction where the wave came from sometimes inconsistent use of orientation can be found. u hor = 1/c app = sin(i)/c = p u = u hor (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 Processing Series, Alan v. Oppenheim, Series Editor, 1993. H.L. Van Trees, Optimum Array Processing, Part IV of Detection, Estimation, and Modulation Theory, John wiley and 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 of Geophysics, 2002.