地震波速度约束的大横向黏度变化的地幔对流研究

本文将横向黏度变化提高到3个量级,获得了地震波速度结构约束下的大横向黏度变化的地幔浅部的极型场和环型场对流图像.与小横向黏度变化下的结果相比,本文的结果具有显著的改善.对极型场对流图像,主要体现在本文结果能更清楚地解释太平洋板块、大洋洲和南美洲以及东太平洋洋中脊处的现今运动状态;对环型场对流图像,能更合理地解释北太平洋...     

S-Wave Velocities of the Lithosphere–Asthenosphere System in the Caribbean Region

An overview of the S-wave velocity (V _s) structural model of the Caribbean with a resolution of 2°?×?2° is presented. New tomographic maps of Rayleigh wave group velocity dispersion at periods ranging from 10 to 40?s were obtained as a result of the frequency time analysis of seismic signals of more than 400 ray-paths in the region. For each cell of 2°?×?2°, group velocity dispersion curves were determined and extended to 150?s by adding data from a larger scale tomographic study (Vdovin et al., Geophys. J. Int 136:324–340, 1999). Using, as independent a priori information, the available geological and geophysical data of the region, each dispersion curve has been inverted by the “hedgehog” non-linear procedure (Valyus, Determining seismic profiles from a set of observations (in Russian), Vychislitielnaya Seismologiya 4, 3–14. English translation: Computational Seismology (V.I. Keylis-Borok, ed.) 4:114–118, 1968), in order to compute a set of V _s versus depth models up to 300?km of depth. Because of the non-uniqueness of the solutions for each cell, a local smoothness optimization has been applied to the whole region in order to choose a three-dimensional model of V _s, satisfying this way the Occam's razor concept. Several known and some new main features of the Caribbean lithosphere and asthenosphere are shown on these models such as: the west directed subduction zone of the eastern Caribbean region with a clear mantle wedge between the Caribbean lithosphere and the subducted slab; the complex and asymmetric behavior of the crustal and lithospheric thickness in the Cayman ridge; the predominant oceanic crust in the region; the presence of continental type crust in Central America, and the South and North America plates; as well as the fact that the bottom of the upper asthenosphere gets shallower going from west to east.     

Effects of plate and slab viscosities on the geoid

The effects of plate rheology (strong plate interiors and weak plate margins) and stiff subducted lithosphere (slabs) on the geoid and plate motions, considered jointly, are examined with three-dimensional spherical models of mantle flow. Buoyancy forces are based on the internal distribution of subducted lithosphere estimated from the last 160 Ma of subduction history. While the ratio of the lower mantle/upper mantle viscosity has a strong effect on the long-wavelength geoid, as has been shown before, we find that plate rheology is also significant and that its inclusion yields a better geoid model while simultaneously reproducing basic features of observed plate motion. Slab viscosity can strongly affect the geoid, depending on whether a slab is coupled to the surface. In particular, deep, high-viscosity slabs beneath the northern Pacific that are disconnected from the surface as a result of subduction history produce significant long-wavelength geoid highs that differ from the observation. This suggests that slabs in the lower mantle may be not as stiff as predicted from a simple thermally activated rheology, if the slab model is accurate.     

Preliminary results of strong ground motion simulation for the Lushan earthquake of 20 April 2013, China

The earthquake occurred in Lushan County on 20 April, 2013 caused heavy casualty and economic loss. In order to understand how the seismic energy propagates during this earthquake and how it causes the seismic hazard, we simulated the strong ground motions from a representative kinematic source model by Zhang et al. (Chin J Geophys 56(4):1408–1411, 2013) for this earthquake. To include the topographic effects, we used the curved grids finite difference method by Zhang and Chen (Geophys J Int 167(1):337–353, 2006), Zhang et al. (Geophys J Int 190(1):358–378, 2012) to implement the simulations. Our results indicated that the majority of seismic energy concentrated in the epicentral area and the vicinal Sichuan Basin, causing the XI and VII degree intensity. Due to the strong topographic effects of the mountain, the seismic intensity in the border area across the northeastern of Boxing County to the Lushan County also reached IX degree. Moreover, the strong influence of topography caused the amplifications of ground shaking at the mountain ridge, which is easy to cause landslides. These results are quite similar to those observed in the Wenchuan earthquake of 2008 occurred also in a strong topographic mountain area.     

Possible effects of lateral viscosity variations induced by plate-tectonic mechanism on geoid inferred from numerical models of mantle convection

In a traditional analytical method, the convective features of Earth’s mantle have been inferred from surface signatures obtained by the geodynamic model only with depth-dependent viscosity structure. The moving and subducting plates, however, bring lateral viscosity variations in the mantle. To clarify the effects of lateral viscosity variations caused by the plate-tectonic mechanism, I have first studied systematically instantaneous dynamic flow calculations using new density-viscosity models only with vertical viscosity variations in a three-dimensional spherical shell. I find that the geoid high arises over subduction zones only when the vertical viscosity contrast between the upper mantle and the lower mantle is O(10³) to O(10⁴), which seems to be much larger than the viscosity contrast suggested by other studies. I next show that this discrepancy may be removed when I consider the lateral viscosity variation caused by the plate-tectonic mechanism using two-dimensional numerical models of mantle convection with self-consistently moving and subducting plates, and suggest that the observed geoid anomaly on the Earth’s surface is significantly affected by plate-tectonic mechanism as a first-order effect.     

Scaling Transition in Earthquake Sources: A Possible Link Between Seismic and Laboratory Measurements

We estimate the corner frequencies of 20 crustal seismic events from mainshock–aftershock sequences in different tectonic environments (mainshocks 5.7 < M _W < 7.6) using the well-established seismic coda ratio technique (Mayeda et al. in Geophys Res Lett 34:L11303, 2007; Mayeda and Malagnini in Geophys Res Lett, 2010), which provides optimal stability and does not require path or site corrections. For each sequence, we assumed the Brune source model and estimated all the events’ corner frequencies and associated apparent stresses following the MDAC spectral formulation of Walter and Taylor (A revised magnitude and distance amplitude correction (MDAC2) procedure for regional seismic discriminants, 2001), which allows for the possibility of non-self-similar source scaling. Within each sequence, we observe a systematic deviation from the self-similar \( M_{0} \propto \mathop f\nolimits_{\text{c}}^{ - 3} \) line, all data being rather compatible with \( M_{0} \propto \mathop f\nolimits_{\text{c}}^{ - (3 + \varepsilon )} \) , where ε > 0 (Kanamori and Rivera in Bull Seismol Soc Am 94:314–319, 2004). The deviation from a strict self-similar behavior within each earthquake sequence of our collection is indicated by a systematic increase in the estimated average static stress drop and apparent stress with increasing seismic moment (moment magnitude). Our favored physical interpretation for the increased apparent stress with earthquake size is a progressive frictional weakening for increasing seismic slip, in agreement with recent results obtained in laboratory experiments performed on state-of-the-art apparatuses at slip rates of the order of 1 m/s or larger. At smaller magnitudes (M _W < 5.5), the overall data set is characterized by a variability in apparent stress of almost three orders of magnitude, mostly from the scatter observed in strike-slip sequences. Larger events (M _W > 5.5) show much less variability: about one order of magnitude. It appears that the apparent stress (and static stress drop) does not grow indefinitely at larger magnitudes: for example, in the case of the Chi–Chi sequence (the best sampled sequence between M _W 5 and 6.5), some roughly constant stress parameters characterize earthquakes larger than M _W ~ 5.5. A representative fault slip for M _W 5.5 is a few tens of centimeters (e.g., Ide and Takeo in J Geophys Res 102:27379–27391, 1997), which corresponds to the slip amount at which effective lubrication is observed, according to recent laboratory friction experiments performed at seismic slip velocities (V ~ 1 m/s) and normal stresses representative of crustal depths (Di Toro et al. in Nature in press, 2011, and references therein). If the observed deviation from self-similar scaling is explained in terms of an asymptotic increase in apparent stress (Malagnini et al. in Pure Appl Geophys, 2014, this volume), which is directly related to dynamic stress drop on the fault, one interpretation is that for a seismic slip of a few tens of centimeters (M _W ~ 5.5) or larger, a fully lubricated frictional state may be asymptotically approached.     

Geoid and topography of Venus in various thermal convection models

Important though indirect information about the internal structure of Venus is provided by its topography and geoid. In the last decades this information has been used to constrain the Venus mantle viscosity structure and its dynamic regime. Recently, the geodynamic inversion of the Venus?? geoid and topography resulted in a group of best fitting viscosity profiles. We use these viscosity models here as an input to our mantle convection code. We carry out simulations of the Venus?? mantle evolution in a 3D spherical shell with depth dependent viscosity and check whether the character of the dynamic topography and the geoid represented by their power spectra fits the observed quantities. We compare the results with several other models obtained for different viscosity stratifications (constant, constant with highly viscous lithosphere, linear increase of viscosity). Further, we estimate the effect of other factors such as internal heating and varying Rayleigh number. We use a 2D spherical axisymmetric convection code to study the effect of lateral viscosity variations. In these 2D models we monitor the topography and the geoid developing above the axisymmetric plume and compare them with the observed elevations of Venus?? geoid and topography in several Regia. Though none of the models fits observed data perfectly, we can generally conclude, that the best fit between the observed and predicted quantities is reached for viscosity profiles with 200 km thick lithosphere followed by a gradual increase of viscosity with depth and with the upper mantle viscosity of 2 × 10 ²¹ Pa s. For all viscosity profiles the predicted geoid and topography spectra match the observed ones only up to the degree 40, thus indicating other than dynamic origin of these quantities for higher degrees.     

Basin patterns of upper ocean warming for 1993–2009

A previous study (Lyman et al., Nature 465:334–337, 2010) showed a robust warming signal of the global upper ocean (0–700 m). They examined several sources of uncertainty that contribute to differences among heat content estimations. However, their focus was limited to globally averaged estimation. This study presents the spatial pattern of the global heat content change based on observed gridded datasets (Levitus et al., Geophys Res Lett 36:L07608, 2009). The western Pacific, Atlantic, and Indian Oceans showed significant warming trends, whereas eastern Pacific and some areas of the Gulf Stream experienced negative trends during 1993–2009. Steady warming trend was obtained from the first EOF mode when El Nino and Southern Oscillation (ENSO)-related signals were removed. This result implies that the rapid increase in heat content of the upper ocean around 2000–2005 is not related to a sampling transition from XBT to Argo observations but is associated with a natural variability dominated by strong ENSO-related signals.     

The mechanical state of the lithosphere in the Altiplano-Puna segment of the Andes

Information about topography, the shape of the geoid, seismicity, Neogene deformation and volcanism in the region of Altiplano-Puna of western South America is used to analyse the state of stress across the convergent plate margin in terms of the effects of topography and simple models of its compensation. An average elevation near 4 km is consistent with compensation by a yet unresolved combination of crustal root and hot uppermost mantle producing a geoid high of 22–27 meters, average horizontal compressive stress (in excess of a reference sea level lithostatic value) of 390 bars in a 150 km thick lithosphere, and an average shear stress of 170 bars along a 30° dipping interplate boundary. The basis for these estimates is evidence for a neutral to extensional stress regime within the high plateau contrasted with a compressional regime on the eastern slopes and along the interplate boundary itself. Comparison with other plateaus in a convergent plate tectonic setting suggests an evolutionary sequence from compressional to extensional tectonics as elevation of the plateau increases.     

Gradual Fault Weakening with Seismic Slip: Inferences from the Seismic Sequences of L’Aquila, 2009, and Northridge, 1994

We estimate seismological fracture energies from two subsets of events selected from the seismic sequences of L’Aquila (2009), and Northridge (1994): 57 and 16 selected events, respectively, including the main shocks. Following Abercrombie and Rice (Geophys J Int 162: 406–424, 2005), we postulate that fracture energy (G) represents the post-failure integral of the dynamic weakening curve, which is described by the evolution of shear traction as a function of slip. Following a direct-wave approach, we compute mainshock-/aftershock-source spectral ratios, and analyze them using the approach proposed by Malagnini et al. (Pure Appl. Geophys., this issue, 2014) to infer corner frequencies and seismic moment. Our estimates of source parameters (including fracture energies) are based on best-fit grid-searches performed over empirical source spectral ratios. We quantify the source scaling of spectra from small and large earthquakes by using the MDAC formulation of Walter and Taylor (A revised Magnitude and Distance Amplitude Correction (MDAC2) procedure for regional seismic discriminants, 2001). The source parameters presented in this paper must be considered as point-source estimates representing averages calculated over specific ruptured portions of the fault area. In order to constrain the scaling of fracture energy with coseismic slip, we investigate two different slip-weakening functions to model the shear traction as a function of slip: (i) a power law, as suggested by Abercrombie and Rice (Geophys J Int 162: 406–424, 2005), and (ii) an exponential decay. Our results show that the exponential decay of stress on the fault allows a good fit between measured and predicted fracture energies, both for the main events and for their aftershocks, regardless of the significant differences in the energy budgets between the large (main) and small earthquakes (aftershocks). Using the power-law slip-weakening function would lead us to a very different situation: in our two investigated sequences, if the aftershock scaling is extrapolated to events with large slips, a power law (a la Abercrombie and Rice) would predict unrealistically large stress drops for large, main earthquakes. We conclude that the exponential stress evolution law has the advantage of avoiding unrealistic stress drops and unbounded fracture energies at large slip values, while still describing the abrupt shear-stress degradation observed in high-velocity laboratory experiments (e.g., Di Toro et al., Fault lubrication during earthquakes, Nature 2011).     

Interseismic Strain Localization in the San Jacinto Fault Zone

We investigate interseismic deformation across the San Jacinto fault at Anza, California where previous geodetic observations have indicated an anomalously high shear strain rate. We present an updated set of secular velocities from GPS and InSAR observations that reveal a 2–3 km wide shear zone deforming at a rate that exceeds the background strain rate by more than a factor of two. GPS occupations of an alignment array installed in 1990 across the fault trace at Anza allow us to rule out shallow creep as a possible contributor to the observed strain rate. Using a dislocation model in a heterogeneous elastic half space, we show that a reduction in shear modulus within the fault zone by a factor of 1.2–1.6 as imaged tomographically by Allam and Ben-Zion (Geophys J Int 190:1181–1196, 2012) can explain about 50 % of the observed anomalous strain rate. However, the best-fitting locking depth in this case (10.4 ± 1.3 km) is significantly less than the local depth extent of seismicity (14–18 km). We show that a deep fault zone with a shear modulus reduction of at least a factor of 2.4 would be required to explain fully the geodetic strain rate, assuming the locking depth is 15 km. Two alternative possibilities include fault creep at a substantial fraction of the long-term slip rate within the region of deep microseismicity, or a reduced yield strength within the upper fault zone leading to distributed plastic failure during the interseismic period.     

Imaging heterogeneity of the crust adjacent to the Dead Sea fault using ambient seismic noise tomography

For the purpose of studying the Earth’s crust by means of tomography, we investigated cross-correlation functions emerging from long-term observations of propagating ambient seismic noise at pairs of broadband stations in Israel and Jordan. The data was provided by the eight permanent broadband stations of the Israel Seismic Network evenly distributed over Israel and the 30 stations of the DESERT2000 experiment distributed across the Arava Fault (South of the Dead Sea basin). To eliminate the influence of earthquakes and explosions, we have applied the methodology of Bensen et al. (Geophys J Int 169:1239–1260, 2007), including bandpass filtering and amplitude normalization in time and frequency domain. The cross-correlation functions estimated from continuous recordings of a few months were used to extract Rayleigh waves group velocity dispersion curves using automatic version of the frequency–time analysis procedure. Subsequently, these curves have been converted into the Rayleigh wave group velocity maps in the period range 5–20 s and S waves velocity maps in the depth range 5–15 km. In these maps, four velocity anomalies are prominent. Two of them are outlined by the previous reflection-refraction profiles and body wave tomography studies, i.e. a low velocity anomaly corresponds to the area of the extremely deep (down to 14 km) sedimentary infill in the Southern Dead Sea Basin and a high velocity anomaly in the Southern Jordan corresponds to the area of the Precambrian crystalline rocks of the Nubian Shield on the flanks of the Red Sea. The two other anomalies have not been reported before - the high velocity zone close to the Beersheba city and the low velocity anomaly in the region of Samaria-Carmel mountains - Southern Galilee. They have relatively low resolution and hence need further investigations for approving and contouring. The highest contrast between the average Rayleigh wave group velocity (2.7 km/s) and the anomalies is 10–13 %, comparable, however, to the level of noise in the data. The results have been verified by modeling the revealed anomalies which showed that all the four zones mentioned above could be detected by the tomography study.     

On the origin of compressional intraplate stresses in South America

Intraplate stresses in middle South America are not negligible. We report thrust-faulting mechanisms for five intraplate earthquakes, which indicate a dominant horizontal deviatoric compressional stress oriented in a NW-SE direction. We conclude that this state of stress is due to forces connected with spreading on the Mid Atlantic Ridge and resistive forces exerted by the Caribbean plate to the north and the Nazca plate to the west. The existence and nature of the resistive forces is inferred from earthquake mechanisms and geological evidence presented in other studies. All the available intraplate stress data for Nazca and South America indicate that both plates are under deviatoric compression generated at spreading centers. The absence of tensional earthquake focal mechanisms, particularly in the Nazca plate near the trench, suggests that the forces associated with the gravitational sinking of subducted lithosphere are locally compensated. We present a simple numerical calculation of a non-subducting plate to show how the compressional deviatoric stresses in middle South America can be used to estimate an upper bound of about 10²¹ P for the viscosity of the mantle.     

Stability analyses and numerical simulations of the single degree of freedom spring-slider system obeying the revised rate- and state-dependent friction law

The linear and nonlinear stabilities of the single degree of freedom spring-slider system which accords to the revised rate- and state-dependent friction law (RSF) (Nagata et al. J Geophys Res 117 (B2):B2314, 2012) are analyzed. The revised ageing law obtained by Nagata et al. (J Geophys Res 117 (B2):B2314, 2012) incorporates the effects of changes in shear stress. Numerical simulations on the cyclic stick–slip motions of the system are developed and compared with the results of the systems according to the original ageing law or the slip law. From the insight of the stability analyses and numerical simulations, it is found that the revised ageing law integrates the “healing effect” feature of the original ageing law and the dynamic slip features of the slip law. In the stick–slip cycles, the velocity decreases with non-constant states during the dynamic overshoot for the revised ageing law, which is different from both the original ageing law and the slip law. Although the revised ageing law concluded from the low velocity friction experiments cannot account for the earthquake-like high velocity friction experiments, it can be used in earthquake nucleation with low velocity. The stability analyses and the results of numerical simulations are helpful to understanding the implications of the revised ageing law.     

Analysis of STCC eddies using the Okubo–Weiss parameter on model and satellite data

The North Pacific Subtropical Counter Current (STCC) is a weak zonal current comprising of a weak eastward flow near the surface (with speeds of less than 0.1 m/s and a thickness of approximately 50–100 m) and westward flow (the North Equatorial Current) beneath. Previous studies (e.g., Qiu J Phys Oceanogr 29: 2471–2486, 1999) have shown that the STCC is baroclinically unstable. Therefore, despite its weak mean speeds, nonlinear STCC eddies with diameters ~300 km or larger and rotational speeds exceeding the eddy propagation speeds develop (Samelson J Phys Oceanogr 27: 2645–2662, 1997; Chelton et al. Prog Oceanogr 91: 167–216, 2011). In this study, the authors present numerical experiments to describe and explain the instability and eddy-generation processes of the STCC and the seasonal variation. Emphasis is on finite-amplitude eddies which are analyzed based on the parameter of Okubo (Deep-Sea Res 17: 445–454, 1970) and Weiss (Physica D 48: 273–294, 1991). The temperature and salinity distribution in March and April offer the favorable condition for eddies to grow, while September and October are unfavorable seasons for the generation of eddies. STCC is maintained not only by subsurface front but also by the sea surface temperature (SST) front. The seasonal variation of the vertical shear is dominated by the seasonal surface STCC velocity. The SST front enhances the instability and lead to the faster growth of STCC eddies in winter and spring. The near-surface processes are therefore crucial for the STCC system.     

Comparison of ground motions from the 2010 Mw 7.2 El Mayor–Cucapah earthquake with the next generation attenuation ground motion prediction equations

A total of 144 free-field ground motions with closest site-to-rupture distances (R_rup) less than 200 km recorded during the 2010 M_w 7.2 El Mayor–Cucapah earthquake are used to investigate predictive capabilities of the next generation attenuation (NGA) ground-motion prediction equations (GMPE). The NGA GMPEs underpredict observed spectral accelerations at sites with shear wave velocity in the upper 30 m of the site (V_s30) between 180 and 366 m/s with R_rup from about 10 to 50 km and overpredict at sites with R_rup from about 50 to 200 km. Intra-event residuals of the NGA GMPEs exhibit a noticeable negative trend for peak ground acceleration and 0.3, 1.0, and 2.0 s periods. Comparison of the inter-event residual between the 2010 M_w 7.2 El Mayor–Cucapah earthquake and the NGA dataset reveals that short-period inter-event residuals from the 2010 M_w 7.2 El Mayor–Cucapah earthquake is within the scatter of inter-event residuals from the NGA dataset but long-period inter-event residuals do not appear within of the scatter of inter-event residuals from the NGA dataset. Spectral accelerations predicted by the NGA GMPEs are generally unbiased against V_s30 and periods of less than 4.0 s. Observed spectral accelerations show a stronger V_s30 dependence for both short and long periods compared with the NGA GMPEs. The Boore and Atkinson (Earthq Spectra 24(1):99–138, 2008) and Chiou and Youngs (Earthq Spectra 24(1):173–215, 2008) GMPEs perform better in predicting observed short-period spectral accelerations at the sites with V_s30 between 180 and 250 m/s than the Abrahamson and Silva (Earthq Spectra 24(1):67–97, 2008) and Campbell and Bozorgnia (Earthq Spectra 24(1):139–171, 2008) GMPEs.     

罗斯海海域大地水准面异常的成因研究

本文利用数值法求解瞬时地幔对流问题以模拟大地水准面异常.利用两个较新的S波速度异常层析模型SEMUCB_WM1和TX2019slab,将其转换为密度异常作为控制方程的浮力驱动项;采取的黏度结构模型中,上下地幔的黏度比为1∶50.为了研究地幔不同结构对罗斯海海域大地水准面异常的影响,分别提取上、下地幔的密度异常正/负值,作为对流控制方程的输入项,计算相应的模拟大地水准面异常.将模拟大地水准面异常与观测值进行对比,发现罗斯海海域的大地水准面异常主要来自下地幔及上地幔的负密度(波速)异常,下地幔正密度异常对该区域大地水准面负异常也有一定的贡献.本文认为,地幔密度负异常在罗斯海海域大地水准面异常的形成中占据主导作用,地幔对流的动力学效应对该区域大地水准面异常的形成影响较弱.     

Rheology of the mantle and tectonics of the oceanic lithospheric plates

The modern concepts of the rheology of viscous mantle and brittle lithosphere, as well as the results of the numerical experiments on the processes in a heated layer with a viscosity dependent on pressure, temperature, and shear stress, are reviewed. These dependences are inferred from the laboratory studies of olivine and measurements of postglacial rebound (glacial isostatic adjustment) and geoid anomalies. The numerical solution of classical conservation equations for mass, heat, and momentum shows that thermal convection with a highly viscous rigid lithosphere develops in the layer with the parameters of the mantle with the considered rheology under a temperature difference of 3500 K, without any special additional conditions due to the self-organization of the material. If the viscosity parameters of the lithosphere correspond to dry olivine, the lithosphere remains monolithic (unbroken). At a lower strength (probably due to the effects of water), the lithosphere splits into a set of separate rigid plates divided by the ridges and subduction zones. The plates submerge into the mantle, and their material is involved in the convective circulation. The results of the numerical experiment may serve as direct empirical evidence to validate the basic concepts of the theory of plate tectonics; these experiments also reveal some new features of the mantle convection. The probable structure of the flows in the upper and lower mantle (including the asthenosphere), which shows the primary role of the lithospheric plates, is demonstrated for the first time.     

Can We Improve Estimates of Seismological Q Using a New “Geometrical Spreading” Model?

Precise measurements of seismological Q are difficult because we lack detailed knowledge on how the Earth’s fine velocity structure affects the amplitude data. In a number of recent papers, Morozov (Geophys J Int 175:239–252, 2008; Seism Res Lett 80:5–7, 2009; Pure Appl Geophys, this volume, 2010) proposes a new procedure intended to improve Q determinations. The procedure relies on quantifying the structural effects using a new form of geometrical spreading (GS) model that has an exponentially decaying component with time, e ^?γt·γ is a free parameter and is measured together with Q. Morozov has refit many previously published sets of amplitude attenuation data. In general, the new Q estimates are much higher than previous estimates, and all of the previously estimated frequency-dependence values for Q disappear in the new estimates. In this paper I show that (1) the traditional modeling of seismic amplitudes is physically based, whereas the new model lacks a physical basis; (2) the method of measuring Q using the new model is effectively just a curve fitting procedure using a first-order Taylor series expansion; (3) previous high-frequency data that were fit by a power-law frequency dependence for Q are expected to be also fit by the first-order expansion in the limited frequency bands involved, because of the long tails of power-law functions; (4) recent laboratory measurements of intrinsic Q of mantle materials at seismic frequencies provide independent evidence that intrinsic Q is often frequency-dependent, which should lead to frequency-dependent total Q; (5) published long-period surface wave data that were used to derive several recent Q models inherently contradict the new GS model; and (6) previous modeling has already included a special case that is mathematically identical to the new GS model, but with physical assumptions and measured Q values that differ from those with the new GS model. Therefore, while individually the previous Q measurements have limited precision, they cannot be improved by using the new GS model. The large number of Q measurements by seismologists are sufficient to show that Q values in the Earth are highly laterally variable and are often frequency dependent.     

Middle Mantle Seismic Structure of the African Superplume

I present the results of statistical hypothesis testing of Grand’s (2002) global tomography model of three-dimensional shear velocity variations for the middle mantle underneath eastern and southern Africa. I apply an F test to evaluate the validity of a model where a tilted, slow-velocity anomaly in the deepest mantle under southern Africa, known as the African superplume, is continuous with a slow-velocity anomaly in the upper mantle under eastern Africa. This null hypothesis is tested against alternative hypotheses, in which various “obstruction volumes” in the middle mantle are constrained to zero perturbation from the one-dimensional reference velocity during the tomographic inversion. I find that there is an equal probability of accepting an alternative hypothesis with a thin “obstruction volume” at 850–1,000 km depth, whereas volumes at other depths are rejected. But the alternative hypothesis, where a connection is forced at 850–1,000 km depth, is rejected. I conclude that the African superplume rises to at least 1,150 km depth, and that the upper mantle slow-velocity anomaly continues from the surface to below the mantle transition zone. I interpret the “obstruction volume” as a weakening of the superplume in the middle mantle.