P and S waveform modeling of continental ... - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, B07319, doi:10.1029/2007JB004942, 2007

P and S waveform modeling of continental sub-lithospheric detachment at the eastern edge of the Rio Grande Rift Teh-Ru Alex Song1,2 and Don V. Helmberger1 Received 18 January 2007; revised 11 April 2007; accepted 4 May 2007; published 31 July 2007.

[1] East of the Rio Grande Rift, tomographic images of teleseismic data have revealed a SE

dipping, slab-like structure underneath the western edge of the Great Plains in the southwestern United States. However, finite difference synthetics require an amplified tomographic model to reproduce the waveform distortions as observed in broadband waveform data recorded along the LA RISTRA Transect. In addition to travel time anomalies, Song and Helmberger (2007) demonstrated how to use S waveforms and their amplitude patterns to further constrain the magnitude of the anomalous structure. Their preferred S velocity model suggests that the slab-like structure is about 4% fast, 120 km thick and dipping 70–75° to the SE to about a depth of 600 km. We adapt the preferred S wave model from Song and Helmberger (2007) and scale the P wave model using a suite of scaling factors (SF dlnVs/dlnVp). We find that synthetics from the P model generated by SF 1.25 can distort P waveforms and fit the amplitude pattern best. Such a low SF indicates that the slab-like anomaly is not only cold but also compositionally distinct. We make use of SF and the S wave anomaly simultaneously to obtain corresponding Vp/Vs anomaly and infer the origin of the slab-like anomaly. Our result suggests that the observed sub-lithospheric detachment is 310 ± 20°C colder and more depleted than the adjoining mantle asthenosphere by 3 units of Mg# (Mg / (Mg + Fe) 100). It is negatively buoyant and is geodynamically consistent with the observed foundering of the continental lithosphere at the eastern edge of the Rio Grande Rift. In short, we demonstrate the importance of seismic waveform anomalies in geochemical and geodynamic inferences. Citation: Song, T.-R. A., and D. V. Helmberger (2007), P and S waveform modeling of continental sub-lithospheric detachment at the eastern edge of the Rio Grande Rift, J. Geophys. Res., 112, B07319, doi:10.1029/2007JB004942.

1. Introduction [2] The longevity of continental roots and their variations from region to region are often debated [Jordan, 1978, 1979; Forte et al., 1995; King and Anderson, 1998; Lenardic and Moresi, 1999; Forte and Perry, 2000; King and Ritsema, 2000; Poudjom Djomani et al., 2001; O’Reilly et al., 2001; Morency et al., 2002; Lenardic et al., 2003; Cooper et al., 2004; Griffin et al., 2004; Zandt et al., 2004; Lee et al., 2005; King, 2005; Carlson et al., 2005; Cooper et al., 2006; Conrad and Lithgow-Bertelloni, 2006]. The depleted, less dense and more viscous continental roots have to overcome the erosion of convective mantle flows [Lenardic et al., 2003]. However, if the continental lithosphere is thick and sufficiently dense, it is possible that instability may occur [Shapiro et al., 1999a; Cottrell et al., 2004]. Once delamination or litho1 Division of Geological and Planetary Sciences, Seismo Lab, Caltech, Pasadena, California, USA. 2 Now at Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, District of Columbia, USA.

Copyright 2007 by the American Geophysical Union. 0148-0227/07/2007JB004942$09.00

spheric removal occurs [Zandt et al., 2004], the stress field in the crust and shallow mantle is modified to be extensional, and it often accompanies extension, rifting, and magmatism at the surface [Pourhiet et al., 2006]. [3] At tectonic boundaries, these issues are being pursued by detail seismic experiments. In particular, tomographic models from dense Program for the Array Seismic Studies of the Continental Lithosphere (PASSCAL) deployment across continental rift zones or mobile belts often reveal linearly dipping fast anomalies near the edge of continental cratons [Gao et al., 2003, 2004; Yuan and Dueker, 2005]. To understand how the rift zone and adjacent continental lithosphere interact with each other appears to be a fundamental issue. For example, Gao et al. [2004] inverted travel time anomalies recorded by the LA RISTRA Transect across the Rio Grande Rift in the southwestern US and found a SE dipping fast velocity anomaly down to 600 km. They interpreted this down-welling as a result of small-scale convection beneath the Rio Grande Rift. It is possible that temperature contrast between the Rio Grande Rift zone and the western Great Plains is large enough to drive small-scale convection [King and Anderson, 1998; King and Ritsema, 2000]. Alternatively, mechanical weakening of lithosphere

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SONG AND HELMBERGER: WAVEFORM MODELING SUB-LITHOSPHERIC DETACHMENT

might also be a plausible mechanism to peel the deep continental lithosphere [Pourhiet et al., 2006]. [4] In short, a key issue is the detailed velocity structure of such a dipping anomaly. Although body-wave travel time tomographic model images these structures, they often suffer from smearing depending on the length of a seismic array and inversion scheme used to derive the model. Song and Helmberger [2007] have shown how broadband waveforms and amplitude systematic can be used to refine the velocity structure underneath a dense array. They amplified the S wave travel time tomographic images by Gao et al. [2004] (Figure 1) and found that synthetics computed from such an amplified model explained the waveform data and amplitudes better since a sharp velocity contrast can cause diffraction, partition the energy, and produce the observed waveform distortion and pulse broadenings. Song and Helmberger [2007] performed a series of synthetic tests and demonstrated how the amplitude decay recorded at stations directly above the slab can be utilized along with travel time delays to model the slab thickness and its dipping angle, penetration depth, and velocity perturbation. Their preferred model features a slab-like fast anomaly near the western edge of the Great Plains dipping SE down to nearly 600 km, with S velocity contrast reaching 4% within a 50-km zone. In addition, they also constructed simplified models to mimic the tomographic image and explain the data as well as the amplified tomographic model (Figure 2). Their best simplified model also features a 4% fast slab dipping 70– 75° to the southeast, with a thickness of 120 km. However, it is difficult to access its physical origin with S wave anomaly alone. [5] To study the physical origin of velocity anomalies, the scaling factor dlnVs/dlnVp (SF) obtained from seismic studies is useful to infer the origin of mantle heterogeneities [Karato, 1993; Robertson and Woodhouse, 1996b; Masters et al., 2000; Goes et al., 2000; Karato and Karki, 2001; Saltzer et al., 2001]. However, it is not straightforward to obtain this SF directly since P and S wave velocity structures are usually determined separated for a given region, while raypaths included constraining velocity model are not uniform. Moreover, to make a meaningful interpretation, it is also necessary to consider frequency-dependent anelastic effects of temperature on seismic velocity structure [Karato, 1993] since P wave and S wave models used to correlate are obtained separately using high frequency P wave (1 second) and surface waves (20 seconds or longer), respectively. In this analysis, we focus on the SF directly by modeling P and S waves record sections of the same sourcereceiver pair using the same model geometry. This will ensure that the measure of SF is self-consistent for later inferences on the origin of the slab-like anomaly. Note that regardless of the origin of the seismic anomaly for such a slab feature, it is very likely that this material was derived from the deep continental lithosphere beneath the western Great Plains and the Rio Grande Rift. Along with the S wave anomaly, the SF factor can be directly converted to a change in Vp/Vs ratio, which provides a good constraint on variations in Mg# (Mg / (Mg + Fe) 100) and temperature between the slab-like anomaly and its adjoining mantle asthenosphere [Lee, 2003]. [6] In this study, we model the P waveforms following the same procedure used in the S wave study. First, we

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attempt to fit the P waveforms by amplifying the P velocity image produced by Gao et al. [2004] (Figure 1), but synthetics generated by propagating through these models failed to reproduce waveform distortions observed in the data. To model these records, we scale the S wave model obtained from S waveform modeling to P wave models using different SFs ranging from 1 to 2. We find that the P waveforms are best fit in shapes, time delays, and amplitude ratios using an SF near 1.25 (Figure 3). This estimated SF is derived using the same source-receiver pairs and model geometry. The geometry of the problem allows a direct comparison of the continental lithosphere and the mantle asthenosphere. Our P and S determinations allow us to estimate contrast in Mg#, temperature and density in the deep upper mantle across the slab-like anomaly and adjoining mantle asthenosphere. Finally, we speculate on the possible mantle processes that are related to the continental sublithospheric detachment near the Rio Grande Rift.

2. Observations [7] The P waveforms recorded along the LA RISTRA transect display a strong azimuthal dependence as do the S waveforms. Observations from events arriving from the NW show relatively uniform amplitude along the array, while events from the SE (South America) display strong amplitude decay (Figure 3). For example, the P wavelets from this particular event (990915) have two distinct pulses indicating the earthquake source complexity, when recorded at stations NM07 and NM08. However, it is clear that the long period tail starts to develop and follows the second peak of P wavelets at other stations further to the northwest. Moreover, other phases such as PcP, pP, and sP also reveal similar wave phenomena (Figure 4), which are very consistent with observations in S waveforms [Song and Helmberger, 2007]. These observations are robust and can be reproduced at several other record sections without much data processing (Figure 5). Note that the amplitude reduction and pulse broadening spanning the stations NM07 to NM15 are indicative of a waveform diffraction pattern. This amplitude pattern is stable and consistently displays a large amplitude decrease up to 50% at stations toward the NW from all events arriving from the south (Figure 5, Table 1). [8] After we deconvolve the raw data with the simple P wavelet recorded at station NM07 and remove the source effect, it is even more evident that all record sections reveal similar amplitude drops and waveform distortions at stations near the edge of the slab (Figure 6). Note that these stations (Figure 1) are directly above the fast anomaly where the attenuation is less a factor [Song and Helmberger, 2007]. Thus it appears that multi-pathing and diffraction along the fast/slow boundary are the dominant features controlling the amplitude pattern [Song and Helmberger, 2007]. We compare the deconvolved P wave record section against the deconvolved S wave record section of a South American event (990915), and they both reveal very similar pattern in waveform distortion, amplitude decay, and pulse broadenings at stations toward the NW (Figure 7). This waveform similarity suggests a propagational origin, and it is distinct from a thermally dominant feature where the P wave anomaly is expected to be much smaller than the S wave

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Figure 1. P wave tomographic image (top panel) and enhanced S wave tomographic image (bottom panel) [Gao et al., 2004; Song and Helmberger, 2007]. The original S wave tomographic model is enhanced two times in the fast regions and four times in the slow regions. This procedure increases the velocity contrast between the fast slab-like structure and ambient mantle. A few stations along the LA RISTRA Transect are included for reference. 3 of 17

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Figure 2. Simplified slab geometry under LA RISTRA transect. The geometry of the slab is constructed to mimic the S wave tomographic image by Gao et al. [2004] and explain the observed travel time delays and amplitude ratios for events from South America [Song and Helmberger, 2007, see also Table 1]. Both SD2 (dlnVs = 3.75%, red line) and SD4 (dlnVs = 4.5%, yellow line) explain the data reasonably well, while SD1 (dlnVs = 6%, blue line) and SD3 (dlnVs = 4.5%, green line) are not consistent with the timings and amplitude patterns, respectively.

anomaly. The next step is to perform a waveform modeling study and derive a suitable P wave model that is consistent with observations.

3. Modeling P Broadband Waveform [9] We apply the two-dimensional finite difference (FD) algorithm [Helmberger and Vidale, 1988] to compute synthetics along the one-dimensional array of LA RISTRA transect. We use a grid spacing of 2.5 km and a time step of 0.07 seconds to ensure the stability of the FD calculation with an accuracy at periods of 3 seconds and longer. We first propagate waves through the P wave tomography model by Gao et al. [2004] embedded in a one-dimensional Gulf of California (GCA) P model [Walck, 1984]. Then we examine the waveform distortions and their amplitude variations across the range (Figure 8). However, these synthetics do not reproduce the waveform broadening and amplitude decay shown in the deconvolved record sections (Figure 6 and Figure 7) although some favorable waveform distortions are produced even after amplifying the P wave model by a factor of 3. We do not observe similar waveform distortion shown in the data since the P velocity model lacks the slab-like feature beneath these stations, the multipathing associated with dipping slab-like structure does not take place even with such an amplified model.

[10] Since the waveform distortions and amplitude behaviors are similar between S waveforms and P waveforms, it is possible that a P wave model properly scaled from the S wave model can reproduce observed features in P wave record sections. Song and Helmberger [2007] have performed detailed analysis on all S wave record sections and found that the amplified tomography model (Figure 1) can produce fairly good fits to all S waveform data collected. We use the preferred amplified S tomography model derived by Song and Helmberger [2007] and scale it to P models using a suite of SFs and examine their synthetics. With an SF less than 1.3, the synthetics start to produce waveform distortions similar to observations (Figure 9). When examining travel time delays and amplitude ratios of these stations, we find that an SF of 1.25 explains both travel time anomalies and amplitude ratios reasonably well (Figure 10, Table 2). Note that travel time anomalies are better explained in terms of the overall pattern. With an SF of 2, the predicted pattern is too smooth to explain the data. With an SF of 1.25, the amplitude pattern is reproduced. However, the travel time anomalies recorded at stations near the eastern side of the slab-like structure are still somewhat too fast. Using a lower SF of 1.0 would overpredict the amplitude drop within the whole range, and it is not consistent with the observations (Table 2). [11] We also implement the simplified S wave models obtained from S waveform modeling [Song and Helmberger,

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Figure 3. Comparison of P and SH displacement record sections for event 990915 from South America (SE) against synthetic record sections. Synthetics are computed with model A (Figure 1, S model) using SF of 1.25. Both data and synthetics are bandpass filtered with corners at 0.02 and 0.3 Hz for P wave and 0.01 and 0.125 Hz for S wave, respectively. Dashed lines mark the timings of the onset and waveform peaks relative to station NM07.

2007] (models SD-2, SD-4, Figure 2) and scale them to P wave models. Again, using an SF of less than 1.3, we can explain P wave record sections (Figure 11, Figure 12, Figure 13, Figure 14, Table 3, Table 4). As presented earlier in Figure 3, the amplified S wave tomography model can explain the S wave and P wave record section of the same source-receiver pairs using an SF of 1.25. Predicted amplitude patterns also work reasonably well against data from other events, assuming the SF of 1.25 (Figure 15). This result demonstrates that our modeling is robust with constraints from amplitude variations across the western edge of the Great Plains and the eastern Rio Grande Rift. Note that the geometry of the problem is defined and investigated in twodimensional and the slab-like structure might not extend infinitely off the great-circle path. Considering the wavelength of the signal (l 30 km) and the depth of the slab-like structure beneath the array (H 500 km), pffiffiffiffiffiffiffias long as it is continuous over the Fresnel zone limit ( lH 120 km) off the great-circle path, a two-dimensional approximation should be valid.

4. Compositional Versus Thermal Origin? [12] We have shown that broadband waveforms recorded at stations between the Rio Grande Rift and the western Great Plains require a significant amplification in velocity

contrast relative to the estimation obtained by travel time tomography [Gao et al., 2004]. The existence of such a slab-like feature on the western edge of the Great Plains is certainly of interest for regional geodynamics. In the following sections, we will use the seismic observables (SF, DVs/Vs) to constrain contrast in the physical properties of the slab-like feature and adjoining mantle asthenosphere such as temperature, Mg#, and density. If the net buoyancy of this detachment is positive, it is less likely to promote observed lithospheric foundering. [13] As discussed by Gao et al. [2004], the average ratio ts/tp is about 2.9 beneath the LA RISTRA Transect, where ts is the S wave travel time delay, and tp is the P wave travel time delay. It yields an average SF of about 1.68 if we assume Vp/Vs of 1.73 [Masters et al., 2000]. This estimate is not very different from a compilation of a global dataset of P and S station corrections [Robertson and Woodhouse, 1996a]. Goes et al. [2000] and Cammarano et al. [2003] have shown that the SF due to temperature effect is probably around 1.5– 2.0 depending on mantle temperature. It supports the idea that the upper mantle structure imaged beneath LA RISTRA Transect is primarily due to variations in temperature. Furthermore, Karato [2003] shows that the SF due to variations in water content is also in the range of 1.5– 2.0. However, the preferred SF of 1.25 for the fast slab-

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Figure 4. P, PcP, pP, sP recorded at NM07, NM08, NM15, and NM16. The data are bandpass filtered with corners at 0.01 and 0.3 Hz. Top panel: raw traces. Bottom panel: deconvolved traces. Note all phases give consistent waveform distortion at stations NM15 and NM16 near the edge of fast/slow boundary, implying that the cause of the waveform distortion is near the receiver.

like anomaly beneath the western edge of the Great Plains is much lower than the average. [14] As suggested by Karato and Karki [2001] and Karato [2003], such a low SF indicates that compositional effects are probably also important. Is it possible that such a slab-like anomaly is not only cold but compositionally distinct as well? A depleted continental lithosphere is presumably less dense due to its higher Mg# (Mg / (Mg + Fe) 100), and it would prevent the lithosphere from sinking unless it is sufficiently colder than the mantle asthenosphere. From a geometrical perspective, this dipping velocity anomaly was likely part of the continental lithosphere, and it is probably depleted in comparison to the adjacent, more fertile mantle asthenosphere beneath the Rio Grande Rift. The geometry of this anomaly presents a robust measure of their thermal and compositional differences. In short, it is important to put some bounds on variations in Mg# and the temperature anomaly DT across the region so that we can estimate the density perturbation and discuss issues related to lithosphere stability.

[15] However, it is difficult to distinguish the temperature effect from compositional effect based solely upon the S wave anomaly [Goes and Van der Lee, 2002; Cammarano et al., 2003; Godey et al., 2004; Goes et al., 2005]. A decrease in Mg# can increase the seismic velocity, while a decrease in temperature can do the same. Previous efforts focus on determining the compositional effect with independent constraints on mantle temperature from xenoliths data [Deen et al., 2006] or including additional constraints on density by modeling mantle flows and fitting geoid and gravity data using a scaling between density and seismic velocity, @lnr/@lnVs [Forte and Perry, 2000; Deschamps et al., 2001, 2002; Perry et al., 2003; Godey et al., 2004; Van Gerven et al., 2004]. However, uncertainties of mantle viscosity structures and crustal isostasy corrections can introduce a bias in estimates of Mg#, which makes it difficult to infer @lnr/@lnVs at short wavelength. [16] One way to simultaneously estimate change in Mg# and temperature anomaly is to measure changes in the Vp/Vs ratio, D(Vp/Vs) since it is very sensitive to change in Mg#,

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Figure 5. P record section of events 990915, 000512, and 000423 from South America. The data are bandpass filtered with corners at 0.01 and 1 Hz. All these sections reveal similar amplitude decrease up to 50% for stations toward the NW.

D(Mg#) ( 4.07 103) [Lee, 2003]. Although the temperature effect on D(Vp/Vs) is relatively small (2.3 106) [Lee, 2003; Niu et al., 2004], it becomes important when DT is large so that D(Vp/Vs) D(Vp/Vs)T + D(Vp/ Vs)Mg#. In our study, we are able to provide important quantities such as SF and DVs/Vs of this slab-like anomaly and obtain the change in Vp/Vs ratio D(Vp/Vs) using the expression D(Vp/Vs) [(1 + DVp/Vp) / (1 + DVs/Vs)] 1, where DVp/Vp = (DVs/Vs) / SF. With SF of 1.25 and DVs/Vs of 4%, we obtain D(Vp/Vs) 0.77%. If we assume that this slab-like anomaly reflects primarily differences in Mg# and temperature T only, these two observables (D(Vp/Vs), DVs/Vs) then allow inferences on D(Mg#), temperature

variation DT, and density variation Dr/r to be made for upper mantle peridotite compositions. Other components such as Al and eclogite are relatively minor because of their smaller fractions, and we will mainly discuss compositional effect in the context of Mg#. [17] The net DVs/Vs due to the change in the temperature and Mg# can be expressed as DVs/Vs = DVs(T)/Vs + DV s(Mg#) /V s . DV s(Mg#) /V s is computed according to Table 5 in the study of Lee [2003], and DV s(T) /V s is computed as b DT/Vs, where b is approximately 0.00033 km s1 °C1 [Fei, 1995]. Because the dominant period of P and S waves used in our analysis is about 3 – 7 seconds, the attenuation Qs appropriate for such a fast slab-

Table 1. Earthquake Source Parameters Event Date

Longitude

Latitude

Depth

Strike

Dip

Rake

Mw

99/09/15 00/05/12 00/04/23

67.37 66.85 63.04

20.73 23.72 28.41

217.5 226.6 607.9

351 5 171

82 80 88

70 96 86

6.4 7.1 6.9

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Figure 6. Deconvolved P record section of events 000512 and 000423 located beneath South America (see also Table 1). All record sections show consistent waveform and amplitude behaviors independent of their source parameters.

like anomaly is probably around 300– 1400 and similar to Qs obtained for the shield [Der et al., 1986; Gudmundsson et al., 1994]. We adapt Qs 300 to correct the anelastic effect of temperature on seismic velocity following the works of Karato [1993] and Goes et al. [2000]. After correcting the anelastic effect, b is about 0.00045 km s1 °C1. [18] The following calculation is demonstrated for the upper mantle at a depth of 300 km according to Table 5 in the study of Lee [2003]. We normalized the perturbations in our estimates using the velocity in Tectonic North America (TNA) [Grand and Helmberger, 1984], density in Preliminary Reference Earth Model (PREM) [Dziewonski and Anderson, 1981], and average Vp/Vs of garnet peridotites [Lee, 2003; Niu et al., 2004]. We can solve DT and D(Mg#) simultaneously by inverting d = Gm, where d = [D(Vp/Vs) Vs/Vs]T, G is the matrix containing the total derivatives of D(Vp/Vs) and DVs/Vs on T and Mg# [Fei, 1995; Lee, 2003; Niu et al., 2004], m = [DTD(Mg#)]T, and T denotes transpose. We obtain D(Mg#) 3.0 and DT 310°C (Figure 16, Figure 17). Allowing uncertainties of SF by

0.05 and DVs/Vs by 0.25% would effect our estimates of D(Mg#) and DT by about 0.5 units and 20°C, respectively. This estimate of D(Mg#) 3.0 ± 0.5 supports the argument that the slab-like anomaly was indeed part of the deep continental lithosphere and 310 ± 20°C colder than the mantle asthenosphere beneath the Rio Grande Rift. Our estimate of DT would be slightly higher if we adapt a lower attenuation (a higher Qs).

5. Buoyancy and Stability [19] An important issue is whether the fast dipping anomaly is indeed dense enough to sink as shown in the tomographic image and our model. We can address this issue by considering DrMg#/r due to increasing Mg# and DrT/r due to thermal contraction. The net density anomaly can be expressed as Dr/r = DrMg#/r + DrT/r. DrMg#/r can be estimated according to Table 5 in the study of Lee [2003] and DrT/r aDT, where a is the thermal expansion coefficient. The slab-like anomaly is more

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Figure 7. Deconvolved P and S record section of event 990915 from South America. The pulse widths for P and S record sections are both broadened by a factor of 2 or more at stations located towards the northwest (e.g., NM15).

likely to sink if jDrT/rj > jDrMg#/rj. For a depleted mantle with D(Mg#) 3.0, it suggested DrMg#/r 1.24% (Figure 18). Assuming a thermal expansion coefficient a 3.9 105 °C1 [Lee, 2003], we find that DT 310°C can produce DrT/r 1.2%, which is very close to DrMg#/r (Figure 18). [20] Note that our density estimate DrT/r is affected by the thermal expansion coefficient a. In addition, uncertainties exist in the derivatives (dlnVs/dMg#, dln(Vp/Vs) / dMg#, dlnr/dMg#) used to estimate D(Mg#) and density change Dr/r [Lee, 2003]. For example, a 10% difference in the derivative dln(Vp/Vs) / dMg# would effect our estimate of D(Mg#) by 0.3 units. A 10% increase in the derivative dlnVs/dMg# [Schutt and Lesher, 2006] would change our temperature estimate by about 25°C. More importantly, it is

essential to have appropriate estimate of dlnr/dMg#, which is critical to the estimate of DrMg#/r and the net buoyancy estimation of the slab-like anomaly. Note the estimate of dlnr/dMg# by Lee [2003] is obtained at STP conditions, and we have assumed it holds under ambient mantle condition. [21] Schutt and Lesher [2006] have shown that dlnr/ dMg# is pressure dependent and is about two-thirds of that estimated by Lee [2003] at the depth of about 200 km. Furthermore, Schutt and Lesher [2006] argued that the appropriate thermal expansion coefficient a for realistic upper mantle composition along the mantle adiabat would be a 3.5 4.9 105 °C1. If such a weak dependency of density on Mg# holds at deeper depth and a lower estimate of a 3.5 105 °C1 applies, the slab-like

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Figure 8. FD synthetics for Gao et al.’s [2004] P wave tomography model and amplified tomographic models. From left to right: dlnVp = dlnVp(Gao), dlnVp = 2 dlnVp(Gao), dlnVp = 3 dlnVp(Gao). The panel on the right shows the synthetics computed from model A, where we amplified the fast region by a factor of 2 and slow region by a factor of 4.

Figure 9. FD synthetics based on scaling of model A (see also Figure 1). From left to right: SF = 1.00, SF = 1.25, SF = 1.35, SF = 1.50, SF = 2.00. Using SFs of 1.0 – 1.25, we produce waveform shape and amplitude decay as observed in the data (Figure 10). 10 of 17

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Figure 10. Comparison of P wave travel time delays and amplitude ratio for event 990915 and synthetics (model A), with SF = 2, SF = 1.25 and SF = 1.00. Travel time delays and amplitude ratios are measured relative to reference station NM07. Travel time delay is measured by picking the onset of filtered wavelets at frequency range of 0.03 –0.3 Hz. The amplitude is computed by taking the envelope of the data and measuring its peak.

anomaly beneath the western Great Plains will be denser than the mantle asthenosphere beneath the Rio Grande Rift (Dr/r 0.2 0.5%) (Figure 18). If we assume that the dlnr/dMg# is 30% higher than that estimated by Lee [2003] and an even smaller a 3 105 °C, as initially proposed by Jordan [1988], the net Dr/r is negative, and the slab-like anomaly is positively buoyant (Figure 18). However, the effect of iron loss on density for the garnet peridotite is probably overpredicted by Jordan [1988], while thermal expansion coefficient a of 3 105 °C1 is likely too small for realistic upper mantle composition at elevated temperature [Lee, 2003; Schutt and Lesher, 2006]. [22] As discussed previously, we attribute observed D(Vp/ Vs) and DVs/Vs to Mg# and temperature. However, changes in orthopyroxene (opx#, volume fraction) and garnet (gnt#, volume fraction) are also observed in xenoliths data from deep continental lithosphere [Matsukage et al., 2005]. We would like to address these issues and give an estimate of how these components affect the above results. We use data reported in Table 2 of Matsukage et al. [2005] and Table 12 of Schutt and Lesher [2006] at high pressure (7 GPa) to compute compositional effects on D(Vp/Vs) and DVs/Vs. Since only dln(Vp/Vs) / dMg# exists [Lee, 2003], we assume dln(Vp/Vs) / dR = dlnVp/dR dlnVs/dR holds, where R is opx# or gnt#, so that we can evaluate compositional effects from these components in our estimates of D(Mg#) and DT. [23] Note that we can only simultaneously invert for two parameters with two observables. Assuming additional opx# of 10 in the sub-lithospheric detachment, we estimate D(Mg#) 2.6, DT of about 370°C, while there is no noticeable difference in Dr/r. If we allow additional gnt# of 5, we obtain DMg# 3.6, DT 250°C, and Dr/r is trivially modified because introducing additional garnet increases Vp/Vs and Vs, and it would lower the estimate of DT and increase the estimate of Mg#. In short, it seems that our inference is still valid even with variations in garnet and orthopyroxene. [24] Our result is compatible with the estimate of DrMg# /r using data reported by Schutt and Lesher [2006] even if we adapt a small thermal expansion

coefficient (Figure 18). Using our estimates of Dr/r and DVs/Vs, we obtain @lnr/@lnVs 0 0.1. It is smaller than the value estimated from thermal effect only [Karato, 1993; Shapiro et al., 1999b], and it is not inconsistent with inferences from mantle convection modeling of geoid and gravity data on continental lithospheres [Shapiro et al., 1999b; Forte and Perry, 2000; Deschamps et al., 2001, 2002; Perry et al., 2003]. Although the estimates of @lnr/ @lnVs from mantle convection flow models are consistent with our results, it is likely that global velocity models adapted to density models are too smooth, and the amplitude of seismic anomalies is underestimated, especially near the boundary. This could cause potential bias in estimating the depletion of continental lithospheres (D(Mg#)). For instance, if DVs/Vs and consequently Dr/ r are underestimated, the estimate of Mg# will be lower than the true value. This caveat probably provides one explanation why the estimated Mg# from mantle flow modeling is systematically lower than the one estimated from xenoliths data [Perry et al., 2003]. [25] As illustrated earlier, the magnitude of the velocity contrast across the western Great Plains and the Rio Grande Rift is an important issue. Song and Helmberger [2007] have demonstrated that the tomographic model is too smooth, and it is necessary to amplify the velocity anomaly at least by a factor of 2 to explain observed amplitude variations and waveform distortions. If we reduce our estimate of DVs/Vs by a factor of 2 (DVs/Vs 2%) and apply the same D(Vp/Vs), we obtain D(Mg#) 1.6 and DT 150 ± 20°C (Figure 17), and the slab-like anomaly is positively buoyant (Dr/r 0.2% 0.7%, Figure 18), which is less likely to promote sinking of the slab-like anomaly. We note that such an inconsistency

Table 2. Misfit of Event 990915: Model A Model

SF = 2.0

SF = 1.25

SF = 1.0

Misfit, Time Misfit, Amplitude

0.627 0.332

0.482 0.299

0.598 0.515

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Figure 11. FD synthetics based on scaling of model SD2 defined earlier. From left to right: SF = 1.00, SF = 1.25, SF = 1.35, SF = 1.50, SF = 2.00. Using SFs of 1.0 – 1.25, we observe comparable waveform shape and amplitude decay as observed in the data.

between seismological results and geodynamic consequences is reconciled by our analysis.

6. Discussions [26] In summary, we find that the slab-like seismic anomaly is depleted and sufficiently cold to sink and seems rather robust, especially with DrMg#/r estimated using data reported by Schutt and Lesher [2006]. Our estimate of D(Mg#) 3 in the deep upper mantle between the western Great Plains and the Rio Grande Rift is consistent with

xenoliths and xenocrysts analysis on variations in Mg# between the sub-continental lithosphere and the mantle asthenosphere [Lee et al., 2001; Griffin et al., 2004; O’Reilly and Griffin, 2006]. If the Mg# of the mantle asthenosphere is 0.88, the Mg# of the sub-lithospheric detachment we observed is 0.91, which is similar to the estimate for the deeper part of the old continental lithosphere, such as the Kaapvaal Craton, the Slave Craton, and the Colorado Plateau [Lee et al., 2001; Griffin et al., 1999; Lee, 2006; O’Reilly and Griffin, 2006].

Figure 12. Comparison of travel time delays and amplitude ratio between data and synthetics (model SD2) defined earlier, with scaling factor of SF = 2.00, SF = 1.25 and SF = 1.00. Travel time delays and amplitude ratios are measured relative to reference station NM07. Travel time delay is measured by picking the onset of filtered wavelets at frequency range of 0.03– 0.3 Hz. The amplitude is computed by taking the envelope of the data and measuring its peak. 12 of 17

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Figure 13. FD synthetics based on scaling of model SD4. From left to right: SF = 1.00, SF = 1.25, SF = 1.35, SF = 1.50, SF = 2.00. Using SFs of 1.0– 1.25, we observe comparable waveform shape and amplitude decay as observed in the data.

[27] Such a depleted continental lithosphere can be produced with a basalt extraction D 30% if (Mg#) is about 3 and dMg#/dD is about 0.1 (an average over 4 – 7 GPa in Table 12, Schutt and Lesher [2006]). If today’s crust of 45 km [Wilson et al., 2005] in the western Great Plains was generated at the same degree of melting, it would have produced a lithosphere reaching a depth of about 150 km, which is similar to recent seismic estimate of about 150 km beneath the western Great Plains (Figure 1, West et al. [2004]; Gao et al. [2004]). If we infer the melt fraction D

using a D(Mg#) of 1.6 as implied in the original tomographic model (see also earlier discussion), the melt fraction D is about 16%, which would suggest a much thicker lithosphere (280 km) that is not consistent with seismic estimates beneath the western Great Plains. [28] It appears that the slab-like structure discussed here was likely part of the sub-continental lithosphere beneath the western Great Plains, and it has been foundering and sinking. It is depleted with a higher Mg# (D(Mg#) 3), and its temperature is about 310°C lower than the nearby mantle

Figure 14. Comparison of travel time delays and amplitude ratio between data (990915) and synthetics (model SD4), with scaling factor of SF = 2.00, SF = 1.25 and SF = 1.00. Travel time delays and amplitude ratios are measured relative to reference station NM07. Travel time delay is measured by picking the onset of filtered wavelets at frequency range of 0.03– 0.3 Hz. The amplitude is computed by taking the envelope of the data and measuring its peak. 13 of 17

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Table 3. Misfit of Event 990915: SD-2 Model

SF = 2.0

SF = 1.25

SF = 1.0


0.672 0.375

0.587 0.308

0.803 0.519

asthenosphere beneath the Rio Grande Rift. Such a temperature contrast is probably sufficient to overcome the positive buoyancy due to increases in Mg# and promote lithosphere foundering or possibly edge-driven convection where the western Great Plains and the Rio Grande Rift are in contact. If we define the B DrMg#/DrT as the chemical buoyancy number, our study suggests that B is about 0.5– 1 for the sub-lithospheric detachment beneath the eastern edge of the Rio Grande Rift. It is therefore plausible that lateral variations in density across the Rio Grande Rift and the western Great Plains at depth is large enough to generate small-scale convection in the upper mantle [Doin et al., 1997; Shapiro et al., 1999a; King and Ritsema, 2000; Cottrel et al., 2004], although other factors such as the strength of the lithosphere, lateral variations in lithospheric thickness, or the existence of a weak zone are probably also important [Lenardic et al., 2003]. For a viscous lithosphere with a viscosity 5 1020 Pa s, we estimate Rayleigh number Ra rgaDTh3/kh of the lithosphere to be around 1020, where there is thermal expansion coefficient of 3 105 °C1, DT is 300°C, k is thermal diffusivity of 106 m2 s1, h is lithospheric thickness of 120 km, and g is gravitational acceleration of 9.8 ms2. This estimated Ra is likely large enough to generate Rayleigh-Beńard type of instability within the continental lithosphere even though the continental lithosphere is relatively depleted [Cottrel et al., 2004]. [29] King and Anderson [1998] and King and Ritsema [2000] have shown that a step in lithospheric thickness can generate large temperature and viscosity contrast and drive small-scale convections, whereas the down-welling velocity is estimated on the order of 2 cm/year. If we considered that the slab-like anomaly was initially part of the continental root at a depth 150 km, it would have taken about 20 My to reach depths of 550– 600 km. This timing coincides well with the first period of the major extension in the Rio Grande Rift region 30– 20 Ma [Baldridge et al., 1991]. Note that the magmatism in the Rio Grande Rift was very low 20– 10 Ma, and the second major extension started 10 Ma with volcanism concentrated to the west beneath the Jemez lineament. The down-welling lithosphere might have modified the regional stress field and changed the extent and focus of the extension and magmatism. [30] More recently, mechanical weakening of the lithosphere has been demonstrated to be effective in facilitating failures in the lithosphere [Lenardic et al., 2003; Pourhiet et al., 2006]. It is capable of peeling lithosphere off quickly in less than 5 My [Pourhiet et al., 2006] and is consistent

Table 4. Misfit of Event 990915: SD-4 Model

SF = 2.0

SF = 1.25

SF = 1.0


0.778 0.348

0.959 0.227

1.140 0.459

Figure 15. Comparison of amplitude ratio for events 990915, 000512, and 000423. Amplitude data of 000512 and 000423 are shifted for comparisons. Synthetics are computed with model A using SF = 2, SF = 1.25, and SF = 1.00, respectively.

with local gravity, topography, and seismic tomography [Boyd et al., 2004]. It is interesting to examine if such a mechanism is capable of explaining the location and timing of extension, the history of vertical motions [e.g., House et al., 2003] and geothermometry/geobarmometry data [e.g., Smith, 2000 and Kil and Wendlandt, 2004]. Note that the density anomaly Dr/r predicted in our model is relatively small, and a thin layer of dense eclogite incorporated in the

Figure 16. D(Vp/Vs) versus increases in Mg#, D(Mg#) (blue line). Estimated D(Vp/Vs) corresponds to D(Mg#) 3.0 (red line) with SF = 1.25 at DT 310°C. Estimates are also shown with SF = 1.2 (red dashed-dotted line) and SF = 1.3 (red dashed line).

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mechanical-weakening model [Pourhiet et al., 2006] can potentially further promote the sinking without modifying the bulk seismic anomalies estimated in this study. In short, our result suggests that the deeper part of the continental lithosphere beneath the western Great Plains and the eastern Rio Grande Rift is depleted, and it can be recycled into the mantle [Cooper et al., 2004; Lee et al., 2005; Lee, 2006]. However, as the sub-lithospheric detachment gets warmer, it will become positively buoyant and possibly rise at the time scale of 100 My [Lenardic et al., 2003].

7. Conclusions [31] We have demonstrated the usefulness of modeling broadband waveforms and amplitudes in constraining the lithospheric structure beneath the western edge of the Great Plains, where a 120-km-thick SE dipping slab-like fast anomaly is observed down to nearly 600-km depth. Broadband P and S waveforms are systematic distorted and broadened, while their amplitudes show a systematic decay. After amplifying the S wave tomographic image by Gao et al. [2004] and matching the S waveform distortions recorded at stations near the western edge of the Great Plains [Song and Helmberger, 2007], we model the P waveform distortions using the same source-receiver pairs and model geometry to obtain a preferred dlnVs/dlnVp 1.25, corresponding to D(Vp/Vs) 0.77% with DVs/Vs of 4%. [32] We use these observables to invert D(Mg#) and DT across the sub-lithospheric detachment and the adjoining mantle asthenosphere. We infer that the slab-like anomaly is depleted, and its Mg# is about 3 units higher than that of the mantle asthenosphere beneath the Rio Grande Rift. Temperature contrast DT reaches 310°C across the slab-

Figure 18. Computed density changes DrT/r (blue line) and DrMg#/r (blue dashed line) according to Lee [2003]. DrMg#/r and DrT/r estimated according to Schutt and Lesher [2006] are shown in red line and red dashed line. DrMg#/r and DrT/r estimated according to Jordan [1988] are shown in green line and green dashed line. Note that DT estimated in this study is shown in the yellow strip and while DT (Tomo) estimated with DVs/Vs 2% is shown in green strip for comparisons. DrMg#/r is reversed in sign.

like anomaly, and it is probably large enough to promote the observed continental sub-lithospheric detachment beneath the edge of the western Great Plain. The predicted @lnr/ @lnVs of 0 – 0.1 is generally not inconsistent with estimates from long wavelength dynamic mantle flow modeling. We believe that, with dense arrays such as the LA RISTRA Transect, broadband waveforms and amplitude systematic provide invaluable constraints on the sharpness, magnitude, and a better inference on the physical origin of seismic anomalies. [33] Acknowledgments. The authors would like to thank Mike Gurnis for pointing out the buoyancy issue and Don Anderson for reviewing an early version of this paper. We also appreciate comments from the editor Clifford Thurber, Eugene Humphreys, and an anonymous reviewer. This work was supported by the National Science Foundation, grant #EAR0639507 and contribution no. 9173 of the Division of Geological and Planetary Sciences, California Institute of Technology.

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Figure 17. DVs/Vs versus decreases in temperature, DT, and Mg#, D(Mg#). DT for DVs/Vs 4% is 310 ± 20°C shown in thick yellow bar while T for Vs/Vs 2% is 155 ± 20°C shown in thick green bar for comparisons.

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D. V. Helmberger, Division of Geological and Planetary Sciences, Seismo Lab, South Mudd, Pasadena, CA 91125, USA. T.-R. A. Song, Department of Terrestrial Magnetism, Carnegie Institution of Washington, NW Washington, DC 20015, USA. ([email protected]. edu)

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