28th Seismic Research Review: Ground-Based Nuclear Explosion Monitoring Technologies

Transcription

1 DEVELOPMENT OF SURFACE WAVE DISPERSION AND ATTENUATION MAPS AND IMPROVED METHODS FOR MEASURING SURFACE WAVES Jeffry L. Stevens, Jeffrey W. Given, G. Eli Baker and Heming Xu Siene Appliations International Corporation Sponsored by Air Fore Researh Laboratory Contrat No. FA C-003 ABSTRACT The objetive of this projet is to optimize measurement of surfae waves, partiularly at regional and loal distanes and at periods of 8 15 s. An important part of the projet is the development of global regionalized dispersion and attenuation maps, with a partiular fous on determining attenuation maps for Eurasia in the 8 15 s period band. Both the dispersion and attenuation maps are orreted for sattering and diffration from heterogeneous earth struture, and amplitude orretion maps are also being developed. Surfae wave propagation in the frequeny band of interest is strongly affeted by heterogeneous earth struture as well as attenuation, partiularly along paths rossing deep sedimentary basins. Two suh basins of interest in Eurasia are the Tarim Basin in Western China, and the West Siberian Basin. Explosions within these basins generate unusually high amplitude and persistent high frequeny fundamental mode surfae waves. The Quartz3 and Kimberlite peaeful nulear explosions (PNEs) were onduted in the West Siberian Basin, and their data give a partiularly good sampling of the surfae wave propagation aross the basin, so we are analyzing these events in detail. We implemented the algorithm of Zhou et al. (004) for alulating finite frequeny sensitivity kernels for dispersion and amplitude variations, and have been testing the algorithms using the one-degree dispersion maps of Stevens et al. (005). We performed a large test inversion similar to our earlier great irle path inversions, but using the finite frequeny sensitivity kernels. While the inversion looks reasonable, it is not yet lear whether the results fit the data signifiantly better than the simpler great-irle representation. Amplitude orretions predited by the Born approximation for the one degree model seem unreasonably large on long paths. This likely reflets the limit of the approximation when large veloity ontrasts are enountered. In order to validate and improve the results, we test whether the Born approximation is giving orret results for strutural variations of the magnitude present in the Stevens et al. (005) models at the frequenies of interest. We ompare theoretial Rayleigh wave spetra derived using the Born approximation with those alulated by a 3D finite differene method. The test model was the Tarim Basin struture embedded in a uniform struture typial of the Eurasian shield regions. The soure was loated immediately east of the basin and the predited wavefields were ompared out to several hundred km west of the basin. The Born approximation is generally onsistent with the finite-differene results, but there are loalized, strong interferene effets in the finite-differene results not apparent in the Born alulation. As expeted, the approximation is less aurate at 10 s periods than at 0 s beause of the larger phase veloity variation at shorter periods. We define a path orreted time domain magnitude, whih ombines the time domain narrow-band surfae wave magnitude proedure of Russell (006) with the path orreted spetral magnitude of Stevens and MLaughlin (001). The dispersion and attenuation orretions being developed in this projet will be used to define regionalized orretion fators for this magnitude. 73

2 OBJECTIVES The objetive of this projet is to optimize measurement of surfae waves, partiularly at regional and loal distanes and at periods of 8 15 s. An important part of the projet is the development of global regionalized dispersion and attenuation maps, with a partiular fous on determining attenuation maps for Eurasia in the 8 15 s period band. Both the dispersion and attenuation maps are being orreted for sattering and diffration from heterogeneous earth struture. RESEARCH ACCOMPLISHED Overview Surfae wave amplitudes are affeted by both attenuation and earth struture. The effet on surfae wave amplitudes of propagation normal to variations in earth struture is predited fairly well by energy onservation. Propagation along paths at grazing inidene to large struture variations, however, are muh more diffiult to predit. Our main interest in this projet is on understanding amplitude variations in 8 15 s surfae waves. In this frequeny band, surfae waves may be affeted as strongly or more strongly by earth struture than by intrinsi attenuation, partiularly along shorter paths. Our goal is therefore to be able to model and orret for both of these effets. Our plan for doing so is illustrated in Figure 1. Collet or Measure Phase and Group Veloity Dispersion Data Collet or Measure Spetral Amplitude and Attenuation Data Invert for Earth Struture Inluding Born Approximation for Sattering and Diffration Calulate Amplitude Variations Due to Heterogeneous Earth Struture and Corret Amplitudes Predit Surfae Wave Dispersion Along Any Path Invert for Q Struture Inluding Born Approximation for Sattering and Diffration Use Dispersion for Event Assoiation and Phase-Mathed Filtering Predit Surfae Wave Amplitude Along Any Path Measure Path Correted Amplitude/ Magnitude for Any Observed Surfae Wave in Optimal Frequeny Band at Loal, Regional or Teleseismi Distanes Figure 1. Overview of the surfae wave dispersion and attenuation projet. In an earlier projet (Stevens et al., 005) we developed global, regionalized dispersion models that allow the phase and group veloity to be alulated between any two points on the earth. We did this by aumulating a large data set onsisting of more than one million dispersion measurements derived by a number of researhers, and then inverting this data set to determine earth struture, whih in turn was used to generate dispersion maps at all frequenies. In that projet, we modeled surfae waves in a heterogeneous earth using the following approximations: (1) surfae waves propagate along great irle paths, () surfae wave phase and group veloities and anelasti attenuation an be modeled using a path integral between soure and reeiver, and (3) energy is onserved with no mode onversion aross material boundaries. This approximation is quite good for large parts of the world, partiularly at lower frequenies, but the unmodeled variations beome important in regions of strutural omplexity. In the first year of this projet, we have foused on understanding the variations in surfae wave dispersion and amplitude aused by heterogeneous earth struture. We have realulated our tomographi inversions using finite frequeny Born sensitivity kernels in plae of the great irle path integrals. We have alulated amplitude variations along Eurasian paths using the resulting earth models, again using the Born approximation to alulate amplitude variations. We are looking in detail at surfae waves propagating in highly heterogeneous regions, and trying to understand and model their behavior. Two partiularly heterogeneous areas in Eurasia are the Siberian Basin and the Tarim Basin, and so we have been analyzing surfae waves in these areas in detail. Our plan is to 74

3 develop Born amplitude orretions first, to assess their performane by omparison with data, and then to inorporate the amplitude orretions into inversions for surfae wave attenuation. The ombination of the attenuation orretion and amplitude orretions is neessary to allow aurate predition of surfae wave amplitudes. Surfae Wave Amplitude Preditability An important goal of this projet is to be able to predit surfae wave amplitudes in both simple and omplex strutures, to determine under what onditions the more ompliated alulations for laterally heterogeneous struture are required, and under what onditions the approximations generally used for alulating surfae waves in omplex strutures beome inadequate. In the following, we disuss alulations of surfae waves in simple and omplex strutures. Surfae Wave Propagation in Simple Strutures We define simple strutures to mean those strutures in whih the surfae wave propagation is normal to all hanges in struture, and lateral hanges in struture are negligible. In that ase we an predit surfae wave amplitude and phase using an approximation originally due to MGarr (1969) that uses propagation of surfae waves along great irle paths with onservation of energy aross material interfaes and no mode onversion. With these approximations, surfae wave propagation in a heterogeneous, anelasti struture takes the following form, separating soure, path and reeiver (notation follows Harkrider et al, 1994): u z (ω,r,ϕ) = 1 ( ) a e sin r a e A R1 πω 1 ( ) A R exp i π 4 ωr / p γ p r F (ω,ϕ, h), (1) s where ω is angular frequeny, r is soure to reeiver distane, h is soure depth, a e is the radius of the earth, ϕ is azimuth, A R is the Rayleigh wave amplitude funtion, is phase veloity, γ is the attenuation oeffiient, and the subsripts 1,, and p refer to parameters derived from the soure region struture, parameters derived from the reeiver region struture, and parameters whih are defined by path averages, respetively. All soure properties are ontained in the funtion F s. For an isotropi explosion soure, the Rayleigh wave spetrum an be written: u z (ω,r) = M 0 ' S x 1 (ω, h x )S (ω )exp[ γ p (ω )r + i(ϕ 0 ωr / p (ω ))], () a e sin(r / a e ) x where ϕ 0 is the initial phase equal to -3π/4, S depends on the soure region elasti struture and the explosion 1 ' soure depth, and S depends on the reeiver region elasti struture. M 0 = 3β M α 0 where M 0 is the explosion ' x isotropi moment. M 0 is defined this way so that the funtion S 1 does not depend expliitly on the material properties at the soure depth. More details are given in Stevens and MLaughlin (001) and Stevens and Murphy (001). Surfae Wave Propagation in Complex Strutures In more omplex strutures, Equations (1) and () may be inadequate to desribe surfae waves. Consequently, we have been testing algorithms that may be more appropriate for these strutures. We implemented the algorithms of Zhou et al. (004) for alulating finite frequeny sensitivity kernels for dispersion and amplitude variations. Using the forward sattering, forward propagating approximation, the phase and amplitude orretions are: δφ = K φ ( δ ) dω, where K φ = k 3/ sin k( Δ '+ Δ'' Δ)+ π 4 and (3) 8π sin Δ 'sinδ'' sin Δ δ ln A = K A ( δ ) dω, where K A = k 3/ os k( Δ '+Δ'' Δ)+ π 4, (4) 8π sin Δ 'sinδ'' sin Δ where distane is in radians, k is wavenumber, and Δ', Δ" and Δ refer to the soure to satterer, satterer to reeiver, and soure to reeiver distanes, respetively. The integrals run over the entire earth s surfae, although in pratie 75

4 (and in this paper) are limited to the first Fresnel zone, whih is defined by k(δ' + Δ" - Δ) < 3π/4. Dahlen and Zhou (006) extend these equations to derive group delay and intrinsi attenuation kernels. Appliation of Corretions to Surfae Wave Amplitudes We have been testing the algorithms desribed above using the 1 degree dispersion maps of Stevens et al. (005). While the results are reasonable for predition of dispersion variations, the predited amplitude orretions seem unreasonably large, partiularly on long paths. Consequently, we have been investigating how model roughness affets amplitudes. Figure shows the 10 s phase veloity model for Eurasia; Figure 3 shows the predited amplitude variation for paths through this region from the Lop Nor test site using the model shown in Figure diretly, and using a smoothed version of the amplitude variation in whih the phase slowness was modeled with a bilinear funtion instead of disrete bloks. For both of the amplitude figures, the anomalies have been trunated where they exeed log 10 (amplitude) = 0.6. The amplitude variations beome quite large on longer paths, and it is not lear whether the Born approximation is giving reasonable answers on these paths. Figure. Eurasian phase veloity model at 10 s from Stevens et al. (005). Figure 3. Left predited amplitude variations at 10 s through the phase veloity model of Figure on paths out of Lop Nor. Right same, but the veloity model has been smoothed by modeling it as a bilinear rather than pieewise disontinuous funtion. 76

5 In order to validate/orret the results, we need to determine whether the Born approximation is giving orret results for strutural variations of the magnitude present in the Stevens et al. (005) models, and at the frequenies of interest. To do this, we performed a test ase of a struture for the Tarim Basin embedded in a uniform struture typial of shield regions of Eurasia, suh as those that surround the Tarim Basin (Figure 4). We then performed a Born approximation alulation and a 3D finite differene alulation for a soure loated just east of the Tarim Basin and examined the wavefield for several hundred km west of the Tarim Basin. The results showed that although the Born approximation is generally onsistent with the finite differene results, there are notieable interferene effets leading to high and low amplitudes in the finite differene alulation that are not present in the Born approximation. The differenes are signifiantly larger at 10 s than at 0 s. Figure 4. Comparison of Born approximation (left) with finite differene alulation (right) of amplitude perturbations at 0 s (top) and 10 s (bottom). The retangular inlusion is modeled after the Tarim Basin struture, and the external struture after a Eurasian shield earth struture. The soure is on the horizontal axis at the right edge of the plot. There is general agreement in the features of the two alulations. The amplitude is inreased in a band above and to the left of the inlusion in both ases, and dereased above that. However, there are some interferene effets in the finite differene alulation that are not reprodued in the Born alulation. 77

6 One reason for this inrease in omplexity is illustrated in Figure 5. Propagation of the ylindrial wave leaving the soure through the Tarim Basin model leads to a strong diffrated wave generated by the wavefront passing along the top of the basin. This seondary wave interferes with the diret wave and ompliates analysis, partiularly in the interpretation of spetra. Sine the first order Born approximation only models the diret wave, it annot reprodue this strongly diffrated seondary wave, although it may do an adequate job of prediting the primary arrival. Also shown in Figure 5 are two observed waveforms that traveled through the Tarim Basin. There are two distint surfae wave arrivals similar to the figure on the left. Although we have not done suffiient analysis to say that the split in these seismograms was due to the effet illustrated in the left figure, it does suggest that strong diffration may be responsible. Figure 5. Vertial omponent veloity after propagation aross the low veloity basin (left). There is a strong diffrated wave that interferes with the diret wave. The right figure shows two observed waveforms that passed through the Tarim Basin and have two distint surfae wave arrivals. Appliation of Corretions to Inversion for Earth Struture As disussed earlier, our plan is to inorporate Born orretions for sattering and diffration into our tomographi inversion sheme. Although we are primarily interested in amplitude estimates, it is neessary to first realulate the dispersion inversions for earth struture in order to aount orretly for the strutural effets on amplitude. We have inorporated the finite frequeny sensitivity kernels (Equation 3) into our inversion ode, and rerun the global tomographi inversions (Stevens et al., 005) with these orretions. As of this writing, we are still evaluating the results. The hanges from the previous inversion are modest in most areas, so more analysis is needed to determine whether results represent an improvement over the inversion using great irle paths. We antiipate that the inversions will give more realisti earth struture with slightly improved data fits in areas of strong lateral heterogeneity. Data Analysis We have been identifying data sets in Eurasia that an be used to determine attenuation, as well as dispersion, from 5 to 0 s surfae waves. These data sets inlude nulear test data, PNEs of the former Soviet Union, moderate size earthquakes reorded at the International Monitoring System (IMS) stations with Harvard Centroid Movement Tensor (CMT) solutions, and deep seismi sounding (DSS) data. The DSS data are potentially very interesting, even though the instrument response of the short period geophones used in those studies is not optimal for longer period (~10 0 s) surfae waves. Two of the DSS explosions, Kimberlite 1 (8.5 kt) and Quartz 3 ( kt), were detonated within the Siberian Basin, and showed very strong surfae waves along the entire seismi line, even at long periods. Reordings of both events outside of the basin at 3,300 km, at the very quiet IRIS/GSN station KONO, have surfae waves of the amplitude expeted from 8.5 and Kt explosions at that distane. This suggests that long period site amplifiations may be espeially high within the basin. Figure 6 shows data from Kimberlite 1 reorded at 349 km, in 5 passbands (left) and synthetis for a basin struture (right). An interesting harateristi of the data that an be 78

7 seen in this figure is that while the syntheti seismogram exhibits smoothly inreasing dispersion between low and high frequenies, the data show more of a disontinuous jump. That is, the Rg data near 1 Hz is onsistent with the syntheti, and the main arrival of the long period surfae wave at the lowest frequenies is also onsistent with the syntheti, however there is not a smooth transition between them. Instead, the Rg and long period surfae waves or appears almost as two distint phases, with the long period part of the data growing with dereasing frequeny and the Rg dereasing with dereasing frequeny. Figure 6. Vertial omponent Kimberlite-1 reord at 349 km (left) in 5 passbands (entered approximately on 1, 3.5, 6, 9, and 13 s from top down), and orresponding synthetis for the first five modes for a Siberian Basin struture. 79

8 Regionalization and Improvement of Surfae Wave Magnitudes Regionalization of earth struture, dispersion, and attenuation allows surfae wave magnitude estimates to be made more onsistent by taking into aount regional differenes. In addition, onsistent surfae wave measurement at short distanes requires a different proedure than has traditionally been used. Surfae wave measurements have typially been made by measuring a time domain amplitude at a period near 0 s and then alulating a surfae wave magnitude M s. This proedure is problemati at regional distanes beause the surfae wave is not well dispersed and a distint 0 s arrival may not be present. It is possible to measure time domain amplitudes at higher frequenies with orretions (e.g. Marshall and Basham, 197), however measurements may be inaurate due to differenes in dispersion aused by differenes in earth struture. Stevens and MLaughlin (001) suggested as an alternative replaing time domain measurements with a path orreted spetral magnitude. Russell (006) proposed a time domain magnitude based on a Butterworth filtered signal, whih similarly removes many of the problems assoiated with time domain magnitudes at lose distanes. In the following, we suggest a regionalized version of the Russell magnitude whih then orresponds to a path orreted time domain magnitude. Path Correted Spetral Magnitudes The path orreted spetral magnitude, logm 0, is alulated by dividing the observed surfae wave spetrum by the Green s funtion for an explosion of unit moment and taking the logarithm of this ratio, averaged over any desired frequeny band. The path orreted spetral magnitude is defined as the logarithm of: M 0 ' = U (ω,r,θ) S x 1 (ω,h x )S (ω )exp[ γ p (ω )r] a e sin(r / a e ), (5) where U is the observed surfae wave spetrum, and as above S 1 x depends on the soure region elasti struture and the explosion soure depth, S depends on the reeiver region elasti struture, and γ p is the attenuation oeffiient that depends on the attenuation integrated over the path between the soure and reeiver. All of the funtions in equation 5 are easily derived from plane-layered earth models (Stevens and MLaughlin, 001) and allow the measurement to be regionalized to aount for differenes in earth struture at the soure and reeiver and due to attenuation along the path. Regionalized path orreted spetral magnitudes inorporate geographi variations in soure exitation and attenuation. It an be measured over different frequeny bands to optimize the signal-to-noise ratio. M s and logm 0 share some limitations: spetra from earthquakes vary due to soure mehanism and depth, and errors an our if the measurement is made in a spetral dip or at high frequenies for a deep event. Azimuthal variations in amplitude aused by foal mehanism also affet the amplitudes of both log M 0 and M s. logm 0 an also be orreted for strutural heterogeneity using the amplitude orretions desribed earlier. Path Correted Time Domain Magnitudes Russell (006) proposed a new type of surfae wave magnitude M s(b) whih differs from a traditional 0 s magnitude in that it uses a Butterworth filter to measure a time domain amplitude in a narrow band around any desired frequeny, and then applies a orretion for the soure funtion similar to the explosion soure funtion used in the path orreted spetral magnitude desribed above. The main purpose of M s(b) is to allow surfae waves to be measured at regional distanes at higher frequenies. Bonner et al. (006) showed that it gave onsistent results in a test study. The magnitude is defined by M s(b) = log( A b )+ 1 0 log( sin Δ) T 1.8 Δ 0.66log 0 T log () f 0.43, (6) where A b is the filtered amplitude, T is the measured period, and f is the Butterworth filter width. It is instrutive to ompare the terms in the Russell magnitude with the Rezapour and Peare (1998) M s and the path orreted spetral magnitude logm 0 desribed above. This is shown in Table 1. 80

9 Table 1. Comparison of time domain and spetral magnitude measurement and orretion terms Magnitude Amplitude Geometri Soure Reeiver Attenuation Dispersion Filter Norm Type Measure Spreading 1 1 M s log(a/t) log ( sin Δ ) Δ log Δ.37 3 M s(b) log(a b ) 0.66 log 0 T 1 log sin ( Δ ) 1 log sin logm 0 log(u z ) -log(s 1 ) -log(s ) ( Δ ) T 1.8 γ Δ log e p Δ ( f ) log log a e Note that eah magnitude makes a slightly different set of orretions. logm 0 orrets for both soure and reeiver struture based on earth models at those loations and an explosion Green s funtion at the soure. Similarly, M s(b) applies a soure orretion based on typial explosion soure exitation. The Airy phase dispersion orretion aounts for superposition of waves with similar group veloities, and is needed only in the time domain. M s(b) uses a Butterworth filter that is suffiiently narrow to avoid this problem. The filter orretion orrets for the width of the Butterworth filter. The normalization for the two M s measurements is hosen to make it onsistent with historial M s magnitudes at a hosen distane range. logm 0 has natural units of log moment and is not otherwise normalized; however, Stevens and MLaughlin (001) showed that subtrating makes logm 0 onsistent with the Rezapour and Peare M s. Attenuation for M s is an empirial orretion based on a very large number of 0 s measurements. M s(b) similarly uses an empirial attenuation orretion, but also inludes an empirial orretion for the hange in attenuation with frequeny; logm 0 uses attenuation alulated from earth (veloity, density, and Q) models along a soure to reeiver path. A path orreted time domain magnitude an be derived by ombining the path orreted spetral magnitude with M s(b), using the soure and path orretions from earth models to replae the empirial average orretions. We define the path orreted time domain magnitude M s(bp) as M s(bp ) = log( A b )+ 1 log ( sin Δ )+ γ Δ log e log () S log( S p 1 ) log()+ f C bp, (7) where C bp is a onstant hosen to make M s(bp) onsistent with historial magnitudes. Although equation 7 may appear more ompliated than equation 6, the funtions S 1, S, and γ p are easily tabulated and stored in files, and a omputer an quikly alulate them for any path based on a simple lookup table. There is substantial regional variation in these quantities that should be removed to ensure onsistent measurements (examples of S 1, S, and γ for ontinental and oeani strutures are shown in Stevens and MLaughlin, 1996). Another advantage of this approah is that it an ensure that f, whih must be less than a minimum value alulated from the group veloity ( f < 0.6 ( T Δ), delta in degrees) is always set appropriately. None of the magnitude measurements desribed above inlude orretion for amplitude variations aused by laterally heterogeneous earth struture. To do so requires an additional term that depends on the earth struture in the Fresnel zone surrounding the soure to reeiver path. The extra term an in priniple be alulated using Equation 4, although as disussed previously, the auray of this orretion partiularly for long paths and omplex strutures requires further investigation. 81