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The densification of regional seismic networks,the proliferation of temporary portable seis-mometer deployments, and the increasingease with which traditional seismic array datamay be obtained all facilitate a new wave ofimaging Earth’s interior at the shortest-everpossible scale lengths using array methods. Infact, seismic array techniques are often neces-sary for retrieval of subtle, yet important, deepEarth seismic structures, particularly thosecontaining fine-scale features.

While only a handful of investigations overthe past few decades have used traditionalseismic array processing for imaging Earth’sdeep interior, the recent data renaissance inour community enables utilization of methodsonce predominantly devoted to the near sur-face for peering deep into the planet, fromupper mantle discontinuities to the solidinner core, from the earthquake source tonear-surface receiver structure.

Thus,it is anticipated that this branch of seismologywill become increasingly important in the

pursuit of deciphering Earth structure and theearthquake source in unprecedented detail,especially with the emergence of the U.S.National Science Foundation (NSF)-fundedUSArray of the EarthScope initiative (see http://www.earthscope. org). Presented here are a briefoutline of the history of seismic arrays, severalarray methods that enhance seismic wave fieldresolution, and some current developments inarray seismology.

In the early 1960s, seismology experienced aboost in funding and interest due to its utilityin monitoring underground nuclear explosions.Following the 1958 conference of scientificexperts at Geneva, a new seismological instru-ment was developed that has proven its bene-fits both for nuclear explosion monitoring andEarth structure studies.These “new”instrumentswere seismic arrays, a multitude of seismome-ters installed with an aperture of a few to afew hundred kilometers. Seismic arrays worksimilarly to arrays in other disciplines—forexample, sonar, radar, radio astronomy, optics,acoustics, and infra sound—and are describedby the same mathematical principles.

An array is considered to be any deploymentof seismometers that satisfies the followingcriteria: (1) three or more seismometers;

(2) an aperture of more than 1 and less thana few hundred kilometers; (3) uniform instru-mentation and recording; (4) a means ofanalysis of the data as an ensemble, ratherthan in separate channels; and (5) a commontime signal [Davies et al., 1971].This definitionapplies to classical short-period arrays as wellas the larger permanent and temporary broad-band seismometer networks that have prolif-erated recently. Stations should be separatedby at least 2 km to minimize noise coherency,and the total aperture should be less than~200 km for maximum signal coherency.Afterthe 1958 Geneva conference, the first arrayswere installed in Arizona, Oregon,Tennessee,and Utah.These employed a symmetrical dis-tribution of up to 16 short-period seismome-ters, with apertures of less than 10 km, andwere mainly used to gather knowledge aboutnoise conditions and array capabilities for further array installations.

The United Kingdom Atomic Energy Admin-istration (UKAEA) subsequently installedarrays on five continents (Eskdalemuir, U.K.;Yellowknife, Canada; Gauribidanur, India;Warramunga,Australia; and Brasilia, Brazil)configured as two roughly perpendicular ~20-km lines, totaling 18–20 seismometers each.Most of the UKAEA installations are still oper-ative today (Figure 1), and many data areavailable. In 1964, the United States constructedthe Large Aperture Seismic Array (LASA) inMontana, the largest-ever seismic array, withmore than 500 short-period stations and an

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Array Seismology AdvancesResearch Into Earth’s Interior

BY SEBASTIAN ROST AND EDWARD J. GARNERO

Fig.1.Map of sample array installations.The background shows the ETOPO5 topography model from the National Geophysical Data Center (Boul-der,Colorado). Symbols correspond to different array types.“Other arrays”are installations like LASA,NORSAR,or Graefenberg (GRF),but alsoarrays of the Canadian POLARIS consortium.Locations of regional networks, e.g.,TriNet (California), JISNET (Indonesia),and J-Array (Japan),arealso shown.

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aperture of ~200 km.While LASA was disman-tled in 1978, the similarly designed (but halfthe aperture) NORSAR array in Norway is stilloperative today.Also noteworthy is the NationalScience Foundation-supported portable seis-mometer array program of the IncorporatedResearch Institutions for Seismology (IRIS; seehttp://www.passcal.nmt.edu).

These and other important arrays are listedon an array resource Web page (http://array-seismology.asu.edu). Readers are invited tocontribute array location, type,and processinginformation to this Web page. In recent years,many dense,permanent seismometer networkswere built or fortified (Figure 1) and providemany of the advantages of classical arrays,butdo not follow traditional array designs.

Network apertures sometimes span over sev-eral hundred kilometers and contain sufficientstation density for array methods to be employed.In the following, the term “array” is used forboth the classical arrays and such distributednetworks.

Arrays have several advantages over the useof single-station recordings. If an array is largerthan one horizontal wavelength of the energyof interest, then the time lag of a transient signalarriving at individual array stations is a directmeasure of the incoming wave field’s directivity(vertical incidence angle = slowness; horizon-tal angle = back azimuth). Since noise at dif-ferent array stations should be relativelyincoherent, a station summation after remov-ing the time lag (delay-and-sum) for a specificslowness and back azimuth results in anincreased signal-to-noise ratio (SNR) for thatparticular resulting beam trace.

Summing for different slowness values, thearray can be adjusted like an antenna,enhancingseismic arrivals out of the noise according totheir arrival angles.This procedure is in princi-ple a velocity filtering of the wave field andeven allows the separation of phases coinci-dent in time (such as core phases like PKP anda mantle or surface wave).As 3-D heterogeneityalong the wave path can perturb the energyaway from the great circle path and predictedincoming angle of incidence, a grid searchover different slowness and back azimuth valuesyields the highest amplitude beam trace as wellas directivity information of the incident wavefield. In principle, this information makes earth-quake localization possible with a single array.

Commonly used array methods include (1) velocity spectral analysis (vespagram con-struction) [Kelly, 1967], whereby array dataare stacked for different slowness values andresulting amplitudes contoured in slowness-time space (also called slant-stacking); (2)Nth-root stacking [McFadden et al., 1986],where coherent signals in traces are enhancedby extracting the Nth-root from the array traceamplitude,slowness slant-stacked, then raised tothe Nth power (Figure 2a); and (3) frequency-wave number (fk) analysis [Capon, 1969],which calculates both slowness and backazimuth simultaneously from the time lags byperforming a grid search over various incidentangles and finding the maximum energy inthe stacked time window.(See Rost and Thomas[2003] for an in-depth review of these and otherapproaches.)

The elevated SNR of beam traces enablesthe detection of reflections and/or scattering

from small and weak structures in the deepEarth,which would otherwise be undetectablein single-seismogram analyses. Hence, arraysare extremely well-suited to studying Earth’sinternal boundary layer interfaces, such as theupper mantle discontinuities, possible D” lay-ering, and the core-mantle boundary (CMB)and the inner core boundary, each of whichhas important connections to chemistry anddynamics of Earth’s interior. Some of theseapplications of the array method are presentedhere.

Upper and mid-mantle studies.The rapidincrease in station coverage within regionalnetworks permits upper mantle investigationsof all types, including (for example) receiverfunction analyses that produce depths tointerfaces, triplication studies for detailedvelocity-depth profiles,and tomographic inver-sions for local 3-D structure. Incorporation ofarray methods helps to resolve even finer detail,such as localized transition zone thickness(between the 410- and 660-km deep phaseboundaries) as well as thickness over whichthe upper mantle phase transitions occur. Forexample, Yamazaki and Hirahara [1994] uti-lized recordings from a regional Japanese net-work (J-Array) of Tonga-Fiji earthquakes toconstrain the thickness of the 410-km and 660-km discontinuities to be less than 5 km.

The array approach can also be applied todense groups of earthquakes recorded at asingle location (utilizing reciprocity).However,application of source arrays requires earthquakelocation accuracy of around 1/10th of thesource array aperture, which can then betreated exactly as receiver arrays.

Fig.2.Examples of array applications that enable the detection of fine-scale structure throughout the Earth. (a) Nth root vespagram of data from theWarramunga array (WRA).The time window shown includes the P arrival and its coda.Arrivals (reflections and conversions) from the upper mantlediscontinuities (e.g., S660P,p410P) are marked.Later in the P-coda,a conversion from a depth of 921 km is seen.Also shown is a map view ofsource and receiver and a cross section through the Karason and van der Hilst P-wave tomography model [2001] (below) with the ray paths for P and S921P. The cross section shows that the existence of S921P may be due to the presence of the subducted Tonga slab. (b) Examples of P(black) and ScP (red) beam-formed wave forms from WRA.Each P and ScP pair is from a different Tonga-Fiji event.Beam-forming increases theSNR of the arrivals and makes the detection of precursors and post-cursors to ScP possible,which,when present, indicate fine layering at the CMB.(c) Detection of the inner core phase PKIIKP in data from Yellowknife.Raw data are shown. Insets show source receiver geometry (top) and crosssection (bottom).The identification of the arrival as PKIIKP was done using the travel time and slowness information from Nth root vespagramsand frequency-wavenumber analysis (not shown).

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Simultaneously combining source andreceiver arrays to focus on a common target, amethod called double beam, results in resolu-tion capabilities of even more subtle structur-al features. For example, small-scale scatterersin the mid-mantle near the Mariana slab,whichwere inferred to be related to subductedoceanic crust below the 660-km discontinuity,were detected using double beam [Krüger etal., 2001].A similar example is shown in Fig-ure 2a, where an Nth root vespagram showsevidence for a reflection from a subductedslab in the Tonga-Fiji region.

Lower mantle studies. Beam forming andmigration techniques hold great promise forelucidation of the deeper Earth as well, sincethey are well suited for imaging sources ofscattered and reflected energy.

For example, double-beam migration of J-Array data combined with coherency meas-ures resolved two non-planar lower mantle P-wave discontinuities [Kito and Krüger, 2001].Arrays are especially valuable for detectinglow-amplitude arrivals commonly below noiselevels on single seismograms (Figures 2b and2c), such as energy generated by small-scaleor weak homogeneities, reflections off discon-tinuities with small impedance contrast, or indistance ranges with unfavorable reflectioncoefficients. One recent example involves thelow-amplitude, near-vertical incidence PcP andPKiKP phases.Their differential travel timesfrom array data were used to infer long-wave-length variations of outer core thickness ofthe order of 3.5 km in specific regions [Koperet al., 2003].

In recent years, the quantity and density ofstations in permanent regional and portabletemporary installations have increased to anextent that now makes feasible multi-channelsignal processing methods adapted fromexploration seismology. Studying thin layers ofstrongly reduced seismic velocities (ultra-lowvelocity zones or ULVZ) at the base of themantle, Rondenay and Fischer [2003] used aphase-stripping principal component analysisto remove the high-amplitude main arrivalSKS from recordings to reveal the behavior ofSPdiffKS, a secondary arrival sensitive to finelayering of reduced velocities at the CMB.Using this adapted method, they were able toreveal a diffuse upper boundary to the ULVZin their studied region. Figure 2b shows anexample of how beam forming of array dataincreases the signal-to-noise ratio of subtlearrivals (ScP) probing the core-mantle-bound-ary, making the resolution of fine layering atthe CMB possible.

Core studies.Although LASA was dismantledover 25 years ago, its data collection has beenrelatively untapped. Fortunately, some of theLASA data (153 events) were recently rescuedfrom decaying magnetic tapes by the U.S.Geological Survey and are available today.One recent revisiting of LASA data detected along (200 s) coda following the inner corereflection PKiKP [Vidale and Earle,2000],whichwas interpreted to be scattered energy fromfine-scale inner core heterogeneity. Such scat-tering can be explained by distributed hetero-geneities of 1.2% with a scale length of 2 kmacross the outermost 300 km of the inner core,possibly due to compositional changes,melts,or anisotropy.Figure 2c shows the array detec-tion of the phase PKIIKP, a phase that is well-suited to studying inner core structure in greatdetail due to the long path length in the innercore.

Outlook.Only a handful of array studies aimedat Earth interior targets are noted here.Thepresent time is particularly ripe for array meth-ods and analyses primarily for two reasons: (1)Earth interior seismological research over thelast 5 to 10 years has witnessed increasinglydetailed models of structural details in bothforward and inverse studies of “single seismo-gram”data sets.The array approach is anextremely valuable tool to confirm these pro-posed fine-scale structural details, as well asto reveal new ones; and (2) past and presenttraditional array data sets are increasinglyavailable,regional networks are more commonlydense enough to use array analyses, temporaryportable seismometer experiments are similarlyavailable and useful,and EarthScope’s USArraywill soon contribute valuable data to the com-munity.

Nonetheless, some challenges remain forglobal studies of Earth’s deep interior. Manyarray data are not publicly available or arevery hard to access. In some cases, only thetriggered front part of seismograms is retained,and deep Earth studies rely on informationmuch later in the traces.Many recordings fromthe 1960s and 1970s were recorded on mag-netic tape,which are decomposing and decay-ing over time. More funding and communityeffort are necessary to rescue these yet unpar-alleled data sets.More installations in the southernhemisphere are desired, including utilization ofocean bottom seismometry, for approachingbetter global coverage. Finally, 2-D and 3-Dwave propagation methods should be foldedinto array analyses that seek to reveal structurein strongly heterogeneous environments.

With the continuing trend of more and moreavailability of array data, it can be assumedthat array seismology will provide key constraintson the interior of the planet for generations tocome. It will play an important role in bridgingthe gap between seismologically determined,medium-to-large-scale structure studies(500–1000+ km) and inferences from mineralphysics, geochemistry, and geomagnetic andgeodynamical studies, undoubtedly leading toa new understanding of the processes thatmake our planet so dynamic and fascinating.

References

Capon, J. (1969), Investigation of long-period noiseat the large aperture seismic array, J.Geophys.Res.,74, 3182–3194.

Davies, D., E. J. Kelly, and J. R. Filson (1971),Vespaprocess for analysis of seismic signals, NaturePhys. Sci., 232, 8–13.

Karason,H.and R.D.Van der Hilst (2001),Tomographicimaging of the lowermost mantle with differentialtravel times of refracted and diffracted core phas-es (PKP, Pdiff), J.Geophys.Res., 106, 6569–6587.

Kelly, E. J. (1967), Response of seismic signals towide-band signals, Lincoln Lab.Tech. Note 1967,Lincoln Lab., MIT, Lexington, Mass.

Kito,T., and F. Krüger (2001), Heterogeneities in D”beneath the southwestern Pacific inferred fromscattered and reflected P-waves, Geophys.Res.Lett., 28, 2545–2548.

Koper, K. D., M. L. Pyle, and J. M. Franks (2003), Con-straints on aspherical core structure from PKiKP-PcP differential travel times,J.Geophys.Res.,108(B3),2168, doi:10.1029/2002JB001995.

Krüger, F., M. Baumann, F. Scherbaum, and M.Weber(2001), Mid mantle scatterers near the Marianaslab detected with a double array method,Geophys.Res. Lett., 28, 667–670.

McFadden, P. L., B. J. Drummond, and S. Kravis (1986),The Nth-root stack:Theory, applications and exam-ples, Geophysics, 51, 1879–1892.

Rondenay, S., and K. M. Fischer (2003), Constraintson localized core-mantle boundary structure frommultichannel, broadband SKS coda analysis,J.Geophys.Res., 108(B11), 2537, doi:10.1029/

2003JB002518.Rost, S., and C.Thomas (2003),Array seismology:

Methods and applications, Rev.Geophys., 40(3),1008, doi:10.1029/2000RG000100,

Vidale, J. E., and P. S. Earle (2000), Fine-scale hetero-geneity in the Earth’s inner core,Nature,404,273–275.

Yamazaki,A.,and K.Hirahara (1994),The thickness ofupper mantle discontinuities,as inferred from short-period J-Array data,Geophys.Res.Lett.,21,1811–1814.

Author Information

Sebastian Rost and Edward J. Garnero,Arizona State University,Tempe