Upper mantle P velocity structure beneath the Midwestern United States derived from triplicated waveforms



[1] Upper mantle seismic velocity structures in both vertical and horizontal directions are key to understanding the structure and mechanics of tectonic plates. Recent deployment of the USArray Transportable Array (TA) in the Midwestern United States provides an extraordinary regional earthquake data set to investigate such velocity structure beneath the stable North American craton. In this paper, we choose an Mw5.1 Canadian earthquake in the Quebec area, which is recorded by about 400 TA stations, to examine the P wave structures between the depths of 150 km to 800 km. Three smaller Midwestern earthquakes at closer distance to the TA are used to investigate vertical and horizontal variations in Pvelocity between depths of 40 km to 150 km. We use a grid-search approach to find the best 1-D model, starting with the previously developed S25 regional model. The results support the existence of an 8° discontinuity inP arrivals caused by a negative velocity gradient in the lithosphere between depths of 40 km to 120 km followed by a small (∼1%) jump and then a positive gradient down to 165 km. The Pvelocity then decreases by 2% from 165 km to 200 km, and we define this zone as the regional lithosphere-asthenosphere boundary (LAB). Beneath northern profiles, waves reflected from the 410 discontinuity (410) are delayed by up to 1 s relative to those turning just below the 410, which we explain by an anomaly just above the discontinuity withPvelocity reduced by ∼3%. The 660 discontinuity (660) appears to be composed of two smaller velocity steps with a separation of 16 km. The inferred low-velocity anomaly above 410 may indicate high water concentrations in the transition zone, and the complexity of the 660 may be related to Farallon slab segments that have yet to sink into the deep mantle.

1. Introduction

[2] Upper mantle seismic velocity structure and its variations in both vertical and horizontal directions provide key information about plate dynamics and the role of the “tectosphere” that underlies stable Precambrian cratons [Jordan, 1978]. Jordan argues that thick continental lithosphere is neutrally buoyant on account of a balance between increased buoyancy from iron depletion and decreased buoyancy from cold temperatures in a thick thermal boundary layer. The subsequent accumulation of research on the structure and evolution of continental lithosphere finds much merit in this tectosphere hypothesis, but also growing evidence that the stability of thick continental lithosphere is not universal [Carlson et al., 2005; Lee et al., 2011]. Removal of continental lithosphere has been suggested beneath the Wyoming and north China Archean cratons [Carlson and Irving, 1994; Gao et al., 2002] and beneath Proterozoic provinces of the southwestern Great Plains [Song and Helmberger, 2007] and Colorado Plateau [Bird, 1979; Levander et al., 2011]. Resolving detailed P and S velocity structure beneath additional cratonic regions will better illuminate the prevalence of lithospheric instabilities beneath continental interiors and the physical and chemical characteristics of intact Precambrian lithosphere. Recently acquired USArray Transportable Array (TA) data provides a new opportunity to survey upper mantle structure beneath a large portion of the North America's stable Precambrian interior.

[3] Further insight into mantle processes active beneath the continental lithosphere as well as the nature of the transition zone between the upper and lower mantle can be gained by determination of seismic velocity structure between depths of ∼300–700 km. Discontinuities near 410 km and 660 km depth formally delimit the mantle transition zone and are thought to primarily reflect phase transitions of olivine with increasing pressure and temperature [Ringwood, 1975]. Seismic observations suggest a second discontinuity near 660 km depth exists in some regions [Simmons and Gurrola, 2000; Ai et al., 2003; Deuss et al., 2006] consistent with the majorite garnet to perovskite transition expected for a pyrolitic mantle [Vacher et al., 1998]. In addition to constraints on bulk composition, upper mantle velocity structure may also provide constraints on mantle water concentration. The presence of low-velocity layers atop the 410 km discontinuity is potentially a sign of high water concentrations in the transition zone [e.g.,Bercovici and Karato, 2003]. There are increasing reports that such low-velocity layers exist sporadically beneath North America [Song and Helmberger, 2006; Gao et al., 2006; Courtier and Revenaugh, 2006; Jasbinsek and Dueker, 2007; Schaeffer and Bostock, 2010; Schmandt et al., 2011] and globally [Tauzin et al., 2010], but there are no previous investigations of its presence beneath the central U.S. The depths of olivine phase transitions, the relative importance of garnet phase transitions, and mantle water concentrations may all be altered by subduction of ocean lithosphere, which has been occurring beneath the western margin of North America for >150 Ma [Engebretsen et al., 1985]. This history of subduction is suggested to influence upper mantle discontinuity structure beneath the western U.S. [Cao and Levander, 2010; Eagar et al., 2010; Schmandt et al., 2011] and part of the central U.S. [Li et al., 1998]. Influence of subduction on upper mantle structure far beneath the continental interior may be expected on account of low-angle subduction during the Laramide orogeny [Coney and Reynolds, 1977; Liu et al., 2008].

[4] Various teleseismic imaging methods have been applied to TA data to map upper mantle seismic structure. Body wave travel-time tomography [Burdick et al., 2009; Sigloch et al., 2008; Roth et al., 2008; Obrebski et al., 2010; Schmandt and Humphreys, 2010] and surface wave dispersion tomography [Moschetti et al., 2010; Pollitz and Snoke, 2010], and receiver function analysis [Cao and Levander, 2010] are among the most frequently applied methods. Model variability from body wave travel-time inversions appears quite high [e.g.,Sun and Helmberger, 2011]. While these inversions can explain well travel-time residuals for teleseismic phases, their use of global 1-D reference models typically renders them inconsistent with measurements of phases that are sensitive to regional 1-D structure (e.g., upper mantle triplications). Indeed, synthetic waveforms produced by such models are found to provide poor fits to regionalP waveforms for phases that travel horizontally in the upper mantle [Chu et al., 2012]. Replacing the commonly used AK135 reference model [Kennett et al., 1995] with mT7 (Figure 1) is shown to greatly improve regional waveform fits [Chu et al., 2012].

Figure 1.

Proposed upper mantle models with (left) S velocities and (right) P velocities. (a) Comparison of S velocity models for the Pacific Basin, PAC06 [Tan and Helmberger, 2007] and PA5 [Gaherty et al., 1996], and the North America shield [Grand and Helmberger, 1984]. (b) Comparison of P velocity models for the North American craton (CR), the Canadian Shields (S25) [LeFevre and Helmberger, 1989], global average model PREM [Dziewonski and Anderson, 1981] and AK135 [Kennett et al., 1995], and the Basin and Range (mT7) [Chu and Helmberger, 2011].

[5] Modeling of the differential waveforms such as SS-S, or pure-path regional modeling, can help alleviate source uncertainty issues and improve vertical resolution of regional 1-D velocity structure [Grand and Helmberger, 1984] and consequently allow improved comparison of different tectonic regions. Examples of Pacific Basin shear-velocity models are displayed inFigure 1a, with a 1D model PAC06 determined by modeling multibounce Swaves using a grid-search method to fully investigate interdependencies among model parameters [Tan and Helmberger, 2007]. Another velocity model, PA5, is determined by complete seismogram inversion [Gaherty et al., 1996]. The VSH > VSV transverse anisotropy appears compatible among these models as well as those reported by Ekström and Dziewonski [1998] and is expected for oceanic upper mantle structure produced by plate spreading [Zhang and Karato, 1995]. Radial anisotropy with VSH > VSV is also reported beneath stable continental regions [Godey et al., 2004; Matzel and Grand, 2004; Nettles and Dziewonski, 2008; Yuan and Romanowicz, 2010], although beneath stable parts of continents the maximum radial anisotropy is found within the high-velocity lid whereas in oceanic regions it tends to occur in the low-velocity zone [Nettles and Dziewonski, 2008]. Another difference between oceanic and continental regions is that the S velocity gradient between 200 and 400 km depth in Pacific models is much steeper than that beneath the North American craton (i.e., SNA) [Grand and Helmberger, 1984]. Gaherty et al. [1999] argue that such features could reflective convective processes beneath oceanic plates, which differs from stable continental interiors where a thicker conductive boundary is thought to exist. Other hypotheses, including changing grain size with depth [Faul and Jackson, 2005], transition from pure dislocation to diffusion creep with depth [Karato and Wu, 1993], and variations in pyroxenite contribution to velocity structure with depth [Stixrude and Lithgow-Bertelloni, 2005] have also been proposed to explain this steeper velocity gradient. A corresponding Pvelocity structure would help address the causes of the vertical velocity gradient as well as understanding of the structural contrasts between the lithosphere-asthenosphere boundary in oceanic and continental regions. A recent review byFischer et al. [2010]provides an up-to-date perspective on the lithosphere-asthenosphere boundary beneath oceanic plates, stable cratons, and tectonically active continental regions.

[6] To demonstrate the profound variations between global and regional 1-D models we display several commonly usedP velocity models in Figure 1b along with the recently introduced mT7 model for western United States [Chu and Helmberger, 2011]. A relatively old regional model for stable North America, S25, is derived from a combination of travel-time data from large Early Rise explosions fired in the Great Lakes [Mereu and Hunter, 1969] and PP-P bounce data from the same events used to derive SNA [Grand and Helmberger, 1984]. The latter study uses hand digitized analog data from old Air Force linear arrays, long-range seismic measurements (LRSM). An important advantage of such studies is that the explosions have known locations and origin times, although the disadvantage is the lack of station coverage. Even with sparse station coverage by today's standards, it is clear that the Gnome explosion in eastern New Mexico produces distinctly different record sections for waves propagating east and west from the source [Romney et al., 1962]. The two models mT7 (West) and S25 (East) roughly explain the reported travel time differences and many characteristics of the waveforms recorded by the TA for recent earthquakes near the Rocky Mountain Front tectonic boundary. The preferred 1-D model resulting from this study, CR, has many similarities with S25. The most prominent differences between CR and S25 are a more complicated lithosphere and a double discontinuity near 660 km that comprises the boundary with the lower mantle.

[7] The objective of this study is to introduce a 1-D referenceP velocity model for the upper mantle beneath the stable region of North America by modeling waveforms of regional earthquakes recorded by the TA. First, we address the source properties of the small earthquakes used in this study. We then briefly review the triplications predicted by three reference models (PREM, AK135, and S25), and compare them to a stacked record section of waveforms from the Quebec event (Mw= 5.1) recorded by the TA. This comparison is followed by detailed presentation of results from forward modeling of triplication data with 1-D velocity models using a grid-search method. A separate section is devoted to lithospheric structure constrained by the modeling of shallow upper mantle phases produced by three other earthquakes that occurred at closer distances to most TA stations (<15°). In the final section we discuss implications of the new regional 1-DP velocity model for continental structure, physical and chemical properties of the mantle transition, and the history of subduction beneath North America.

2. Earthquake Data

[8] Large explosions are particularly useful for studying the 1D P velocity structure because of their relatively simple waveforms as exploited by many researchers [e.g., Given and Helmberger, 1980]. Although small explosions are still popular in crustal studies, large explosions are less common nowadays. Therefore we have to rely on the relatively low seismicity of the stable craton and exploit the dense wide-aperture receiver coverage provided by the TA (Figure 2). In this study, we select four earthquakes located in and around the North American craton. Among them, the Quebec earthquake is the most important because its 15°–25° raypaths provide nearly complete radial sampling of upper mantle velocity structure (Figure 2).

Figure 2.

Map of the United States displaying the locations of earthquakes and broadband seismic stations used in this study. Beach balls represent focal mechanism obtained using the CAP method with source information given in Table 1. The Quebec earthquake provides the triplication data with three profiles of data at ranges 15° to about 25° indicated by dotted lines. Detailed observations will be presented along sub-corridors, AA′–DD′, and stacks bracketed by I and II discussed later in the text.

[9] Before we can study the Pwave propagations of these earthquakes, we need to determine their source parameters. Various focal-mechanism solutions have been provided by different organizations (Table 1) along with our regional mechanism that employs the Cut-and-Paste (CAP) method (Figures S1–S3 in theauxiliary material). This technique fits Pnl and surface wave segments between observed and synthetics that are allowed to shift independently in timing for alignment [Zhu and Helmberger, 1996]. Thus, the procedure automatically determines the travel-time delays along each path. This particular event is difficult to locate withP wave travel times because of the nodal first Pn arrivals at local stations. Regional Rayleigh waves at period of 10 s have proven useful in locating earthquakes as discussed by Tan et al. [2010]. Thus, we search for a location that has similar delays in all azimuths and found the SLU location to be preferable. In Figure 3a, we display the Rayleigh wave delays using the SLU location.

Table 1. Earthquake Used in This Study
IDOrigin TimeLatitudeLongitudeH (km)MwStrike/Dip/Rake (deg)Source
  • a

    United States Geological Survey National Earthquake Information Center, last accessed on June 24, 2010.

  • b

    Natural Resources Canada.

  • c

    From http://www.eas.slu.edu/Earthquake Center/MECH.NA, last accessed March 3, 2011. See Herrmann et al. [2011] for more details.

  • d

    The velocity model used here is modified from Herrmann [1979].

  • e

    At the frequency range of 0.02 to 1.0 Hz, we cut the waveform using a time window of 13 s. See Chu et al. (submitted manuscript, 2011) for more details.

Quebec2010/06/23, 17:41:42.645.95284.4519.05.0162/46/88NEICa
 2010/06/23, 17:41:41.045.90284.5016.45.0NANRCANb
 2010/06/23, 17:41:42.045.86284.5422.05.0145/60/80SLUc
 2010/06/23, 17:41:46.045.97284.4222.75.0152/49/82GCMT
Oklahoma2010/10/13, 14:06:29.535.21262.6914.04.3120/80/5SLU
Indiana2010/12/30, 12:55:21.040.43274.1114.03.8305/65/10SLU
Arkansas2011/02/28, 05:00:50.235.26267.664.04.7295/80/−5SLU
Figure 3.

Source parameters derived for the Quebec earthquake. (a) The stations used in the regional Cut-and-Paste (CAP) inversion are given as triangles in the map view. The inset shows locations and mechanisms from different organizations (Table 1). Our focal mechanism derived by modeling the regional and teleseismic waveforms are compared to those in the inset. Regional Rayleigh-wave travel-time residuals (paths with travel-time delays) from the regional inversion favor the SLU location. The two beach balls are focal mechanisms inverted using regional (CAP) and teleseismic (CAPt) waveforms. (b) Comparison of observed velocity in the vertical direction (black) and synthetics (red) recorded by stations on the west coast. These observations are recorded at azimuths enclosed by the dashed vectors in Figure 3a, essentially from south to north. DirectP and the depth phases, pP and sP, are labeled on the bottom. Both data and synthetics are filtered at frequency band of 0.8–2.0 Hz and align on the direct P. Unfortunately, the direct P and pP become nodal at triplication distance but sP remains strong.

[10] We also invert the focal mechanism of the Quebec earthquake using a teleseismic version (CAPt) (R. Chu et al., Inversion of source parameters for moderate earthquakes using short-period teleseismicP waves, submitted to Geophysical Journal International, 2011), obtaining a slightly different solution (Figure 3a and Table 1). In Figure 3b, we include the fits of synthetic waveforms of teleseismic data observed in western United States for the Quebec earthquake whose azimuths sample the TA stations. Both P and pP are relatively weak on the waveforms. The strongest phase is the depth phase sP which is well separated from P. Such source complexity, unfortunately, must be accepted since it is the only event available in the region. Note that the sPphase is commonly observed in this region for small earthquakes and has been successfully used in double-difference relocations [Ma and Eaton, 2011].

3. Stacking of Triplicated Waveforms

[11] At regional distances between 10° and 30°, waveforms of the Quebec earthquake are complicated by upper mantle triplications, which result from discontinuities near 410 km and 660 km. Before presentation of the regional Pwave record sections, we review the triplications generated from three reference models for a simple impulsive explosion-type source (Figure 4). To generate synthetics, we employ a variety of methods including generalized ray theory (GRT), standard frequency wave number integration, WKM (a generalization of WKB), and finite difference codes. See Chu et al. [2012] for applications similar to this study. In Figure 4, the GRT technique is applied to three reference models (PREM, AK135, S25), which produce distinctly different upper mantle raypaths. Perhaps the most obvious difference between the reference models is that the 220 km discontinuity unique to PREM produces an extra triplication, with particularly strong arrivals for distances beyond 25° and reduced times greater than 50 s. Model S25 has a late arriving AB branch at large distances and displays an offset near 19° caused by its low-velocity zone starting at 170 km depth. This branch is observed for cratons in several regions as discussed byLeFevre and Helmberger [1989].

Figure 4.

Raypaths and synthetics for velocity model (a) PREM, (b) AK135, and (c) S25. Triplicated arrival times are displayed in red lines. Seismic rays travel above the 410 discontinuity, in the transition zone, and below the 660 discontinuity are referred to as AB, CD, and EF branch, respectively. The heavy dotted lines indicate the positions of the major transition discontinuities. Due to the LAB of S25 between 165 and 210 km, the AB branch has an offset at the distance of 19° and 21°, and can be seen at distance larger than 27°. An extra triplication for PREM is observed because of the discontinuity at 220 km, which is not observed and not labeled.

[12] A convolution with the radiation pattern of the Quebec earthquake produces a complex profile with a rather weak direct P and pP followed by a strong sP arrival (Figure 5). The nodal characteristics of direct P make it difficult to decipher the P branches but the CD branch of sP is readily identified. We add a reference line to help compare the synthetics with the observed CD branch. In Figure 5b, we include three cross-sections sampling several azimuths. The station coverage is not uniform as a result of the source-array geometry (Figure 2). Nevertheless, the CD and AB branches of sP are apparent, especially at the larger ranges. These features become clearer when the data are stacked.

Figure 5.

(a) Comparison of observed data and synthetics generated from velocity model PREM, AK135, and S25 for profile AA’ indicated in Figure 2. Red dashed line is for reference only. It is obvious that model S25 fits the data better among the three models. (b) Comparison of vertical displacement (black) and finite difference synthetics (red) for profiles BB’, CC’, and DD’ for velocity model S25. Both data and synthetics are filtered using a frequency band of 0.02–1.0 Hz.

[13] To improve stack coherence, we take some liberty in making some small timing adjustments to correct for local structure. This is done by cross-correlating S25 synthetics with individual records, and allowing small shifts in timing so phase slownesses that are representative of the 1-D velocity structure near ray turning depths can be better identified. Examples of records requiring time shifts for local structure are presented inFigure 6. At the nearest distances (∼15°), sPAB is slightly early or late (M35A–V37A in Figure 6), but because the sPCD branch is stronger, it is used to control the alignment. At greater distances (∼18–20°, Y39A–S28A in Figure 6), the AB and CD arrivals interfere as the extended AB branch is bottoming below the LAB. The S25 predictions require some local timing adjustments, which are, again, controlled by the stronger sPCD arrival. At distances beyond 22°, the time separation between sPCD and sPABis greater and the cross-correlation coefficients (CCs) between synthetic and observed waveforms increase. This character of improved waveform fit with increasing distance is apparent inFigure 6b, where waveforms from most stations have CCs greater than 85%. The delays for all TA stations and their cross-correlation values are shown inFigure 6b. There are a few stations with very low CCs but excluding them does not lead to a different optimal model so all stations are included in this analysis. Noteworthy is a zone of relatively slow arrivals near the South Dakota and Nebraska border that will be addressed in section 6 (Figure 6b).

Figure 6.

(a) Examples of waveform fits for velocity model S25. The number after each station name is the epicentral distance in degrees. Two numbers below each trace are the time shifts with respect to the initial picking and cross-correlation coefficient (CCs). (b) Travel-time residuals and CCs across the whole TA for velocity model S25. The dashed oval represents the slow arrivals near the South Dakota (SD) and Nebraska (NB) border.

[14] The stacked data along with synthetic waveforms for the best fitting model (CR) are presented in Figure 7, excluding the nearly nodal phases P and pP. A complete comparison is given in Figure S4. Remarkably, even this small event produces a detailed image of the sP phase triplications. Weaker and mostly nodal P and pP phases are also present, but less obvious. The sPABbranch is clear at distances less than 18°, but at slightly greater distances the shadow zone (low-velocity zone) starting near the depth of 165 km reduces its strength. Increased amplitude of thesPABbranch occurs beyond 22° where its raypaths turn below the low-velocity zone. ThesPCD branch dominates the triplication associated with the 660 discontinuity. This observation can be explained by the presence of two closely spaced jumps in velocity rather than the single jump present in global reference models (see section 4). Note that sPEF appears at about 19° and only becomes the apparent first arrival beyond 25°. Unfortunately, at about this range, we are reaching the tectonic western province and the western extent of the TA stations at the time of this event. In the next section, we will discuss in detail how the CR model was constructed and present evidence for lateral variations near the 410 discontinuity.

Figure 7.

Comparison of stacked data (black) with synthetics (red) for the final model CR. In order to minimize the effect from the Texas coast and the Black Hills, the data for the southern stations between an azimuth of 230° and 265° (denoted by line I and II in Figure 2, respectively) is stacked using a bin size of 0.1°. Since P and pP are in the nodal direction, only sP is displayed in synthetics. Triplications of P, pP, and sP are labeled.

4. Waveform Modeling of Triplications

[15] Although the upper mantle structure is a complex 3-D structure, we will assume that the triplications involving the transition zone discontinuities are dominantly 1-D in nature. Our basic approach is forward modeling through trial-and-error where we test models near S25 until we find one that fits the observed data. To reduce the number of parameters in the model construction, we have broken the model into mostly linear segments (Figure 8) where grid searches can be used to fine-tune the waveform fits, similar to the approach ofTan and Helmberger [2007]. We start from the top to minimize the trade-off between depth effects caused by shallow versus deep velocity variations.

Figure 8.

Grid search for the depth and thickness of the LAB. (a) Velocity models and (b) their root-mean square (RMS [Zhu and Helmberger, 1996]) are shown. The velocity models are color-coded for identification between A and B. (c) Waveform fits for our preferred model CR and three typical velocity models (m10, m15, and m17) are displayed. The m10 model has the largest separation between AB and CD branches; m15 has smaller AB amplitude, while the AB branch of m17 can be seen at about 18°, which are displayed in the shaded area.

[16] In Figures 8a and 8b, a collection of models are displayed for waveforms sampling the LAB region, which we define as the transition from the high-velocity lid to the upper mantle low-velocity zone. The points b and c (Figure 8a) define the depth and value of the maximum lid velocity and the depth and value of the minimum of the low-velocity zone, respectively. To determine the optimal values of b and c we conduct a grid search in two directions, parallel and perpendicular to the S25 starting model. Moving the point b and c in the parallel direction will not change the slope of ab and cd, whereas moving b and c in the perpendicular direction changes the ab and cd slopes. Because the relative amplitude ratio of AB and CD branches is very sensitive to the slope of ab and cd (Figure S5), we fixed the slopes of ab and cd and grid-search the best positions of point b and c. This strategy determines the depth and sharpness of the LAB. In short, we generate synthetic waveforms for ∼10 combinations of b and c to identify possible improvements to S25 starting model. However, none of the fits are particularly good because interference from other phases involvingP and pP make it difficult to define the extension of the AB branch into the shadow zone beyond 17° (Figure 8b). Thus, the CR model does not stand out even though the synthetic overlays for the CD branch compare well with the data. Waveform fits for our preferred model CR and three models with greater RMS are displayed in Figure 8c, with the shaded area highlighting poorly fit waveform segments.

[17] A similar search was conducted to investigate the structure of the 410 and 660 discontinuities, with example waveform fits shown in Figure 9. The most striking result is that a 660 discontinuity composed of two smaller jumps in velocity separated by 16 km fits the observed waveforms much better than the single larger jump in velocity from the S25 model. The primary reason for the double arrival is that the timing of the observed PEF branch at the range 19° to 21° is not in agreement with the 22° to 23.5° branch for a single 660 jump. Thus, the initiation of the EF branch samples the upper boundary, but at larger ranges the deeper boundary dominates and explains the small offset in timing. Velocity models with broad gradients or single velocity jumps near 660 consistently provide poor fits to the data (Figure S6). It is possible that lateral variations in velocity structure could also produce the observed timing of the EF branch. However, this feature is consistent at all azimuths so we consider a robust regional feature (Figure S7).

Figure 9.

Display of some models tested for (a) the velocity-gradients above the 410 discontinuity and (b) sharpness of the 660 discontinuity. SeeFigures S5–S7 for more comparisons.

[18] Upper mantle arrivals with turning depths near the 410 discontinuity exhibit significant differences between northern and southern TA stations (Figure 10). We divide the data along an azimuth indicated in Figure 2. We present a comparison of northern (I) and southern (II) waveforms for the distance from 18° to 20.5°. The comparison highlights differences in shape of the CD pulse near 19.5° where the northern stations are broadened and poorly fit by the CR synthetics compared to the southern profile. Broadened CD branches can be caused by late arrival of BC branch, which is reflected from the 410 discontinuity and usually has small amplitude and similar arrival time as CD. We examine all waveforms at this distance range and map the anomalous stations and their turning points in Figure 10b along with timing difference between BC and CD. It becomes difficult to separate these two arrivals by injecting anomalous velocities above 300 km since the raypaths sample the same region at shallower depths. Thus, structural changes just above or below the 410 prove the most effective. A possible explanation is inserting a box of slow velocities, reduced by ∼3% with a thickness of 20 km and a width of about 100 km (Figures 10c and 10d). Similar features have been found to explain triplication data in the western U.S. as discussed by Song and Helmberger [2006]. We acknowledge that a well-placed anomaly at slightly shallower depth could also cause such features. In short, we can explain the main features of the observed upper mantle triplications with the 1-D CR model quite well, but there is evidence for interesting small-scale deviations from the 1-D structure.

Figure 10.

(a) Comparison of stacked data (black) and synthetics (red) for (left) the southern and (right) the northern stations between 18° and 20.5°. Note the broadened waveform for the northern stations, which is caused by larger CD-BC separations. The stations with larger CD-BC separations are displayed in (b) as color triangles. The colored circles represent the mid-points of anomalous paths. (c) Raypath for BC and CD branches at the distance of 18° to 20°. A low-velocity zone (LVZ) on the 410 discontinuity, denoted by the red box, will slow down the BC branch. Therefore the CD-BC separation will be larger. The LVZ,P velocity reduced by 3%, has a thickness of 20 km and a width of about 100 km. (d) Observed TCD-TBC (black dots) from individual records along with the predictions (red line) match reasonably well, although the scatter probably means variation in thickness or degree of possible melt. The black line denotes the TCD-TBC for 1D model CR.

5. Uppermost Mantle Constraints

[19] The velocity structure below 200 km appears to be well approximated by a 1-D model, but stronger lateral variations are expected in the upper 200 km. We seek to obtain high-resolution estimates of the radial P velocity structure of the continental lithosphere, allowing for small timing shifts to account for lateral variations. Analysis of the first arrival transition fromPn to P provides sensitivity to the radial P velocity gradient in the lithosphere and thickness of the lithosphere that cannot be achieved by other methods such as receiver functions or surface wave dispersion [e.g., Eaton et al., 2009]. Here, we display a few record sections that confirm earlier studies reporting an 8° discontinuity in first arrivals [Thybo and Perchuć, 1997].

[20] We first take advantage of the TA stations and the Oklahoma earthquake (Figure 2). The data and synthetics are scaled in absolute amplitude multiplied by the distance (Figure 11). Amplitude decay with increasing distance is much less than observed in western data sets [Romney et al., 1962]. Additionally, the waveforms are not coherent from station-to-station, which is common at this distance range and has been previously modeled with alternating fast-slow fine-scale layering [Perchuć and Thybo, 1996]. We do not attempt to model this feature and instead concentrate on the shadow zone where Pn decays and the deeper sampling P emerges near 8–9°, consistent with Thybo and Perchuć [1997]. Timing lines predicted by S25, CR, and AK135 illuminate the substantial differences between predicted arrival times. Note that AK135 travel times are over 5.0 s late at the larger ranges. Since the event is well located and the profile is completely covered with stations (Figure 11a), the absolute velocities are unusually well constrained. Modeling Pn waveforms at longer periods is possible as demonstrated by Chu et al. [2012], but because the magnitude of this event is small, periods greater than about 2 s are found to have poor signal-to-noise.

Figure 11.

Record section for the Oklahoma earthquake is plotted with a reduce velocity of 8.3 km/s. (a) The travel-time predictions for the three models are displayed with color lines, S25 (blue), AK135 (green), and CR (red). Note that AK135 does not have a LAB and has a continuous travel time curve. Dotted lines denotePn while the solid lines indicate the P arrivals. (b) The synthetic waveforms generated from the CR model are displayed. The data and synthetics are scaled in the true amplitude multiplied by the epicentral distance in km. The model CR predicts the low amplitude and velocity change at 8° quite well.

[21] In Figure 12, we present the station distribution for two other events, one in Arkansas and one in Indiana, to the east of the Oklahoma earthquake. These events are strike-slip earthquakes with the mechanisms given inTable 1. Individual observations are cross-correlated with synthetics from CR and shifted for best alignment, the same processing we use for the Quebec earthquake. These shifts are mapped inFigure 12. The largest shifts are >1 s and in general the timing shifts indicate significant lateral variations in structure. Moreover, the smoothness of timing shifts over length-scales of a few hundred km suggests they are predominantly associated with variations in the lithospheric mantle rather than variations in upper crustal structure. The record sections inFigure 13 are chosen for an azimuth corridor with strong P wave radiation and stacked with normalized amplitudes. When stacked along an azimuth corridor, the waveform patterns are remarkably coherent and the degree of consistency between observed and CR synthetic waveforms at high frequencies (up to 2 Hz) is impressive. These record sections are plotted relative to the nearest stations along these profiles. The Indiana event (12 km) is deeper than the Arkansas event (4 km) (Table 1), thus the Pn phase arrives earlier for the former event by over a second. Note that the 1.5 s backward jump in arrival time of the Indiana event at the ∼9° change from Pn to Pcannot be caused by strong lateral variations as this would be apparent in the travel-time shifts shown inFigure 12. The record sections with and without corrections are shown in Figure S8 and the change in travel time slope is easily observed near ∼8–9°. The backward jump in arrival time at the change from Pn to Pis more pronounced for the Indiana event on account of its deeper hypocenter (which separates the direct and surface-reflected arrivals) and higher frequency filtering (0.8–2 Hz for the Indiana event, 0.3–2 Hz for the Arkansas event). This abrupt transition results from a 1% velocity jump at 120 km in CR, which separates a slight negative velocity gradient in the shallower portion of the lid from a positive gradient in the deeper part of the lid.

Figure 12.

Travel-time residuals for (a) the Arkansas earthquake and (b) the Indiana earthquake. The distances are indicated with dotted arcs, starting at 5°. IA: Iowa.

Figure 13.

Comparison of vertical Pdisplacement (black) and synthetics (red) for (a) the Arkansas earthquake and (b) the Indiana earthquake. The data are stacked using a bin size of 0.1° and aligned using the travel-time residuals shown inFigure 12. The Arkansas earthquake is filtered at 0.3–2.0 Hz, while the Indiana earthquake is filtered at 0.8–2.0 Hz. Blue lines denote arrival time of Pn waves.

6. Discussion

[22] Constraints on the 3-D velocity structure of eastern North America are bound to increase because the TA has just now crossed the Mississippi River at the time of this reporting. Nevertheless, by modeling these events just beyond the array, we have established a useful upper mantle reference model for future seismic studies and for consideration of the properties and history of the tectosphere beneath a portion of the interior of North America. Knowledge of the basal structure of North America and mantle transition zone structure beneath the continental interior has become increasingly important in light of evidence that flat subduction beneath the continental lithosphere during the Cretaceous [Coney and Reynolds, 1977] probably extended as far inboard as the western edge of the Great Lakes [Liu et al., 2008; Spasojevic et al., 2009]. The basic idea is that the pattern of subsidence created by emplacement of the cold slab beneath the continent is fundamentally linked to the distribution of sedimentation in Cretaceous interior sea [Smith et al., 1994]. A suggested trigger for the slab flattening event is ∼90 Ma subduction of a thick buoyant oceanic plateau beneath the southwestern U.S. margin [Livaccari et al., 1981; Saleeby, 2003; Liu et al., 2010]. The interior sea disappeared about 60 Ma and dynamic modeling predicts the slab fell away from the base of North America at about this time and began to sink into the lower mantle with an east-dipping trajectory [Liu et al., 2010; Spasojevic et al., 2009]. The question is, can we find any evidence for this hypothesis in high-resolution seismology other than the present deep tomographic images [e.g.,Grand, 2002; Sigloch, 2011]?

[23] Our modeling produces a relatively simple 1-D structure without much evidence for deep lateral heterogeneity. However, there appear to be anomalous features of phase transition boundaries that may be indicative of slab history. InFigure 14, we display a cross-section through the tomographic model along with some of our results [Grand, 2002]. This tomographic image was generated from a mixture of modern digital data and older analog seismograms used in constructing SNA and TNA (see Figure 1). The reference model is the average of the two regional models and the top 300 km is heavily saturated so that the lower structure can be observed. The tomography model shows only small±0.4% variations in the transition zone. On the left, the craton structure transitions into TNA that appears to be overly simplified in Grand's [2002] model. The multipathing results presented by Sun and Helmberger [2011]indicates a strongly heterogeneous structure extending eastward beyond the Black Hills with a sharp horseshoe-shaped boundary extending beneath Nebraska (Figure 14b). This slow feature is also apparent in travel time delays from the CR modeling experiment and extended further in Figure 12a beneath Iowa. This corridor is discussed by Liu et al. [2010] as the path of a sinking hypothetical thickened slab and still appears anomalous where perhaps warmer upwelling material has replaced the cold slab.

Figure 14.

(a) S velocity perturbation from Grand [2002]along the path from the Quebec earthquake to the Black Hills showing the possible downgoing Farallon slab and the relatively high velocity near the 660 discontinuity near position 4. (b) The location of the profile is shown. In Figure 14b, bid-points of the CD branch (red) and EF branch (blue) for TA are enclosed by the polygons. The travel-time residuals (triangles) and anomalous CD branch (colored circles) are displayed. Black dots are epicentral distance with intervals of 1°. Dashed oval denotes the Black Hills anomaly. BH: Black Hills; NB: Nebraska; WI: Wisconsin.

[24] The anomalous zone above the 410 discontinuity is near the expected region of slab penetration and occurs at the western edge of a mild slow region in the tomography, i.e., location 9, beneath Wisconsin (Figure 14b). A low-velocity anomaly could represent partial melt created by upward return flow across the 410 if the transition zone is sufficiently hydrated [e.g.,Bercovici and Karato, 2003]. However, our inference of a low-velocity anomaly above the 410 is a non-unique explanation for the late arrival of the BC branch so interpretations regarding the origin of such an anomaly are speculative. The expected disturbance of this discontinuity is difficult to interpret because of the uncertainties in the presence of water versus temperature as recently discussed byCao and Levander [2010]. They find a 25 km upward shift of the 410 beneath Nevada and a 35 km downward shift of the 660 beneath Utah that are spatially correlated with high-velocity slabs [Sigloch et al., 2008]. They also observe a double 660 discontinuity associated with the subducting Gorda slab, as found in this study, at the eastern edge of this structure (see their Figure 13). These features are compatible with many tomographic models and waveform analysis [Chu et al., 2012]. In short, there appears to be some seismic evidence for such a slab passageway along this corridor. This report concentrated on mostly horizontal paths while tomographic models address mostly vertical paths. Combining these two approaches should greatly improve resolution and will be attempted with the completion of the TA experiment.

[25] P waveforms from the small events consistently indicate a changeover from Pn to P near 8°. These events sample the same region where Green and Hales [1968]first noted this discontinuity from refraction profiles produced by the Early Rise experiment (explosions in Lake Superior). The apparent discontinuity, which has recently been called the mid-lithospheric discontinuity (MLD), is observed in many different types of data as discussed byAbt et al. [2010]. The original explanation of MLD is that it is a phase change from spinel to garnet, but Stixrude and Lithgow-Bertelloni [2005] dispute this conclusion. Thybo [2006] argues for a small percentage of melt caused by the presence of carbon or water. More recently, Yuan and Romanowicz [2010] interpret the MLD as a sudden change in anisotropy. Van der Lee et al. [2008] suggest that the Farallon slab has provided the volatiles to generate such zones of weakness. A number of new events have occurred in the last few months and display more evidence for lateral variation [Chu and Helmberger, 2011]. Perhaps, with a larger data set of regional events a clearer picture of lateral variations in lithospheric structure will emerge.

[26] We have modeled waveforms from four earthquake sources in the interior of North America to determine a suitable reference model and identify isolated areas that are inconsistent with purely 1-D structure. The strongest event was used to conduct a grid-search analysis of the major upper mantle discontinuities. Our results are similar to earlier models, such as SNA, except we find the 660 boundary better explained by two smaller velocity jumps 16 km apart rather than a single larger velocity jump. Additionally we find that a compact low-velocity anomaly may exist just above the 410 beneath Wisconsin. The relationship, if any, between these structures and subduction history will become clearer as the TA proceeds eastward. Small earthquakes were used to investigate the lithospheric structure, and our results support earlier reports on the existence of the 8° discontinuity caused by a low-velocity zone from 40 to 120 km followed by a significant jump of 1% and positive gradient down to 165 km.


[27] We would like to thank Thorsten Becker, the associated editor, and two anonymous reviewers. Their suggestions and comments made significant improvements to the manuscript. Seismic data in this study was obtained from IRIS data management center. This work was supported by National Science Foundation through grant EAR-0639507 and the Caltech Tectonic Observatory. Contribution number 10071 of the Seismological Laboratory, California Institute of Technology.