Effect of 3-D viscoelastic structure on post-seismic relaxation from the 2004 M= 9.2 Sumatra earthquake

The 2004 M = 9.2 Sumatra–Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ∼1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress–strain relation; an aspherical perturbation in viscoelastic structure; a 'static' mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra–Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation.     

Post-seismic reloading and temporal clustering on a single fault

Geological studies show evidence for temporal clustering of large earthquakes on individual fault systems. Since post-seismic deformation due to the inelastic rheology of the lithosphere may result in a variable loading rate on a fault throughout the interseismic period, it is reasonable to expect that the rheology of the non-seismogenic lower crust and mantle lithosphere may play a role in controlling earthquake recurrence times. We study this phenomenon using a 2-D, finite element method continuum model of the lithosphere containing a single strike-slip fault. This model builds on a previous study using a 1-D spring-dashpot-slider analogue of a single fault system to study the role of Maxwell viscoelastic relaxation in producing non-periodic earthquakes. In our 2-D model, the seismogenic portion of the fault slips when a predetermined yield stress is exceeded; stress accumulated on the seismogenic fault is shed to the viscoelastic layers below and recycled back to the seismogenic fault through viscoelastic relaxation. We find that random variation of the fault yield stress from one earthquake to the next can cause the earthquake sequence to be clustered; the amount of clustering depends on a non-dimensional number, W , called the Wallace number defined as the standard deviation of the randomly varied fault yield stress divided by the effective viscosity of the system times the tectonic loading rate. A new clustering metric based on the bimodal distribution of interseismic intervals allows us to investigate clustering behaviour of systems over a wide range of model parameters and those with multiple viscoelastic layers. For models with   W ≥ 1  clustering increases with increasing W , while those with   W ≤ 1  are unclustered, or quasi-periodic.     

Temporal and spatial variations of post-seismic deformation following the 1999 Chi-Chi, Taiwan earthquake

We use GPS displacements collected in the 15 months after the 1999 Chi-Chi, Taiwan earthquake  ( M _w 7.6)  to evaluate whether post-seismic deformation is better explained by afterslip or viscoelastic relaxation of the lower crust and upper mantle. We find that all viscoelastic models tested fail to fit the general features in the post-seismic GPS displacements, in contrast to the satisfactory fit obtained with afterslip models. We conclude that afterslip is the dominant mechanism in the 15-month period, and invert for the space–time distribution of afterslip, using the Extended Network Inversion Filter. Our results show high slip rates surrounding the region of greatest coseismic slip. The slip-rate distribution remains roughly stationary over the 15-month period. In contrast to the limited coseismic slip on the décollement, afterslip is prominent there. Maximum afterslip of 0.57 m occurs downdip and to the east of the hypocentral region. Afterslip at hypocentral depths is limited to the southern part of the main shock rupture, with little or no slip on the northern section where coseismic slip was greatest. Whether this results from along strike variations in frictional properties or dynamic conditions that locally favour stable sliding is not clear. In general, afterslip surrounds the area of greatest coseismic slip, consistent with post-seismic slip driven by the main shock stress change. The total accumulated geodetic afterslip moment is  3.8 × 10¹⁹ N m  , significantly more than the seismic moment released by aftershocks,  6.6 × 10¹⁸ N m  . Afterslip and aftershocks appear to have different temporal evolutions and some spatial correlations, suggesting that aftershock rates may not be completely controlled by the rate of afterslip.     

A crack model of creep processes on deep sections of faults

A crack model in antiplane shear configuration is shown representing creep processes interpreted in terms of 'viscous' deformation of a narrow plastic layer, characterized by inhomogeneous rheological properties, embedded within a homogeneous elastic medium. The evolution in time of slip and stress over the crack plane is studied through a truncated expansion in Chebyshev polynomials, and convergence is proved to be fast in the simple examples considered. Finite-stress solutions are found which are compatible with constitutive relations of elasto-plastic materials and furthermore these allow us to simulate creep propagation and stress transfer between locked and unlocked fault segments. This model provides a simple interpretation of the shallow depth of the seismogenic layer observed in several areas of the world and lends itself to modelling creep processes during either post-seismic rebound or pre-seismic stress buildup. Stress transfer is accomplished mostly by the slow extension of the creeping section. During a seismic cycle it is envisaged that different regimes dominate over deep, intermediate and shallow sections of faults: (i) slow pre-seismic stress build-up accompanied by creep and stress migration toward intermediate depths; (ii) brittle fracture over shallow and intermediate sections of faults; (iii) post-seismic rebound over intermediate and deep sections of faults. The present crack model, while providing finite-stress solutions, allows a better understanding of how stress may accommodate at different depths over a fault plane during a seismic cycle.     

Stress transfer relations among the earthquakes that occurred in Kerman province, southern Iran since 1981

We explore the possible stress triggering relationship of the   M ≥ 6.4  earthquakes that occurred in Kerman Province, southern Iran since 1981. We calculated stress changes due to both coseismic sudden movement in the upper crust and the time-dependent viscous relaxation of the lower crust and/or upper mantle following the event. Four events of   M ≥ 6.4  occurred between 1981 and 2005, on and close to the Gowk fault, show a clear Coulomb stress load to failure relationship. The  2003 M = 6.5  Bam earthquake, however, which occurred approximately 95 km SW of the closest Gowk event, shows a very weak stress relation to preceding earthquakes. The coseismic static stress change at the hypocentre of the Bam earthquake is quite small (∼0.006 bars). The time-dependent post-seismic stress change could be 26 times larger or 7 times lower than that of coseismic static stress alone depending on the choice of viscoelastic crustal model and the effective coefficient of friction. Given the uncertainties in the viscoelastic earth models and the effective coefficient of friction, we cannot confidently conclude that the 2003 Bam event was brought closer to failure through coseismic or post-seismic stress loading. Interestingly, the southern Gowk segment with a similar strike to that of the Bam fault, experienced a stress load of up to 8.3 bars between 1981 and 2003, and is yet to have a damaging earthquake.     

Post-seismic relaxation following the great 2004 Sumatra-Andaman earthquake on a compressible self-gravitating Earth

The   M _w γ 9.0  2004 December 26 Sumatra-Andaman and   M _w = 8.7  2005 March 28 Nias earthquakes, which collectively ruptured approximately 1800 km of the Andaman and Sunda subduction zones, are expected to be followed by vigorous viscoelastic relaxation involving both the upper and lower mantle. Because of these large spatial dimensions it is desirable to fully account for gravitational coupling effects in the relaxation process. We present a stable method of computing relaxation of a spherically-stratified, compressible and self-gravitating viscoelastic Earth following an impulsive moment release event. The solution is cast in terms of a spherical harmonic expansion of viscoelastic normal modes. For simple layered viscoelastic models, which include a low-viscosity oceanic asthenosphere, we predict substantial post-seismic effects over a region several 100s of km wide surrounding the eastern Indian Ocean. We compare observed GPS time-series from ten regional sites (mostly in Thailand and Indonesia), beginning in 2004 December, with synthetic time-series that include the coseismic and post-seismic effects of the 2004 December 26 and 2005 March 28 earthquakes. A viscosity structure involving a biviscous (Burgers body) rheology in the asthenosphere explains the pattern and amplitude of post-seismic offsets remarkably well.     

Source history of the 1905 great Mongolian earthquakes (Tsetserleg, Bolnay)

Two great Mongolian earthquakes, Tsetserleg and Bolnay, occurred on 1905 July 9 and 23. We determined the source history of these events using body waveform inversion. The Tsetserleg rupture (azimuth N60°) correspond to a N60° oriented branch of the long EW oriented Bolnay fault.
Historical seismograms recorded by Wiechert instruments are digitized and corrected for the geometrical deformation due to the recording system. We use predictive filters to recover the signals lost at the minute marks.
The total rupture length for the Tsetserleg earthquake may reach up to 190 km, in order to explain the width of the recorded body waves. This implies adding 60 km to the previously mapped fault. The rupture propagation is mainly eastward. It starts at the southwest of the central subsegment, showing a left lateral strike-slip with a reverse component. The total duration of the modelled source function is 65 s. The seismic moment deduced from the inversion is 10²¹ N m, giving a magnitude   M _w = 8  .
The nucleation of the Bolnay earthquake was at the intersection between the main fault (375 km left lateral strike-slip) and the Teregtiin fault (N160°, 80 km long right lateral strike-slip with a vertical component near the main fault). The rupture was bilateral along the main fault: 100 km to the west and 275 km to east. It also propagated 80 km to the southeast along the Teregtiin fault. The source duration was 115 s. The moment magnitude Mw varies between 8.3 and 8.5.
The nucleation and rupture depths remain uncertain. We tested three cases: (1) nucleation and rupture depth limited to the seismogenic zone; (2) nucleation in the seismogenic zone and rupture propagation going to the base of the crust and (3) nucleation within the crust–upper mantle interface and rupture propagation within the upper mantle.     

Shallow earthquakes in a viscoelastic shear zone with depth-dependent friction and rheology

Summary. Most crustal earthquakes of the world are observed to occur within a seismogenic layer which extends from the Earth's surface to a depth of a few tens of kilometres at most. A model is proposed in which the shear zone along a transcurrent plate margin is represented as a viscoelastic medium with depth-dependent power-law rheology. A frictional resistance linearly increasing with depth is assumed on a vertical transcurrent fault within the shear zone. Such a model is able to reproduce a continuous transition from the brittle behaviour of the upper crust to the ductile behaviour at depth. Assuming that the shear zone is subjected to a constant strain rate from the opposite motions of the two adjacent plates, it is found that there exists a maximum depth H below which tectonic stress can never reach the frictional threshold: this may be identified as the maximum depth of earthquake nucleation. The value of H is consistent with observations for plausible values of the model parameters. The stress evolution in the shear zone is calculated in the linear approximation of the constitutive equation. A change in rigidity with depth, which is also introduced in the model, may reproduce the high vertical gradient of shear stress, which has been measured across the San Andreas fault, and the fact that most earthquakes are nucleated at some depth in the seismogenic layer. A crack which drops the ambient stress to the dynamic frictional level is then introduced in the model. To this aim, a crack solution is employed without a stress singularity at its edges, which is compatible with a frictional stress threshold criterion for fracture. A constraint on the vertical friction gradient is obtained if such cracks are assumed to be entirely confined within the seismogenic layer.     

Analytical approach for the toroidal relaxation of viscoelastic earth

This paper is concerned with post-seismic toroidal deformation in a spherically symmetric, non-rotating, linear-viscoelastic, isotropic Maxwell earth model. Analytical expressions for characteristic relaxation times and relaxation strengths are found for viscoelastic toroidal deformation, associated with surface tangential stress, when there are two to five layers between the core–mantle boundary and Earth's surface. The multilayered models can include lithosphere, asthenosphere, upper and lower mantles and even low-viscosity ductile layer in the lithosphere. The analytical approach is self-consistent in that the Heaviside isostatic solution agrees with fluid limit. The analytical solution can be used for high-precision simulation of the toroidal relaxation in five-layer earths and the results can also be considered as a benchmark for numerical methods. Analytical solution gives only stable decaying modes—unstable mode, conjugate complex mode and modes of relevant poles with orders larger than 1, are all excluded, and the total number of modes is found to be just the number of viscoelastic layers between the core–mantle boundary and Earth's surface—however, any elastic layer between two viscoelastic layers is also counted. This confirms previous finding where numerical method (i.e. propagator matrix method) is used. We have studied the relaxation times of a lot of models and found the propagator matrix method to agree very well with those from analytical results. In addition, the asthenosphere and lithospheric ductile layer are found to have large effects on the amplitude of post-seismic deformation. This also confirms the findings of previous works.     

Coseismic deformation revealed by inversion of strong motion and GPS data: the 2003 Chengkung earthquake in eastern Taiwan

A moderate earthquake of   M _w= 6.8  occurred on 2003 December 10. It ruptured the Chihshang Fault in eastern Taiwan which is the most active segment of the Longitudinal fault as a plate suture fault between the Luzon arc of the Philippine Sea plate and the Eurasian plate. The largest coseismic displacements were 13 cm (horizontal) and 26 cm (vertical). We analyse 40 strong motion and 91 GPS data to model the fault geometry and coseismic dislocations. The most realistic shape of the Chihshang fault surface is listric in type. The dipping angle of the seismic zone is steep (about 60°–70°) at depths shallower than 10 km and then gradually decreases to 40°–50° at depths of 20–30 km. Thus the polygonal elements in Poly3D are well suited for modelling complex surfaces with curving boundaries. Using the strong motion data, the displacement reaches 1.2 m dip-slip on the Chihshang Fault and decreases to 0.1 m near surface. The slip averages 0.34 m, releasing a scalar moment of 1.6E26 dyne-cm. For GPS data, our model reveals that the maximal dislocation is 1.8 m dip-slip. The dislocations decrease to 0.1 m near the surface. The average slip is 0.48 m, giving a scalar moment of 2.2E26 dyne-cm. Regarding post-seismic deformation, a displacements of 0.5 m were observed near the Chihshang Fault, indicating the strain had not been totally released, as a probable result of near-surface locking of the fault zone.     

Upper-crustal structure of the Benevento area (southern Italy): fault heterogeneities and potential for large earthquakes

The Benevento region is part of the southern Apennines seismogenic belt, which experienced large destructive seismic events both in historical and in recent times. The study area lies at the northern end of the Irpinia fault, which ruptured in 1980 with a M_s = 6.9 normal faulting event, which caused about 3000 casualties. The aims of this paper are to image lateral heterogeneities in the upper crust of the Benevento region, and to try to identify the fault segments that are expected to generate such large earthquakes. This work is motivated by the recognition that lithological heterogeneities along major fault zones, inferred from velocity anomalies, reflect the presence of fault patches that behave differently during large rupture episodes. In this paper, we define the crustal structure of the Benevento region by using the background seismicity recorded during 1991 and 1992 by a local seismic array. These data offer a unique opportunity to investigate the presence of structural discontinuities of a major seismogenic zone before the occurrence of the next large earthquake. The main result that we obtained is the delineation of two NW-trending high-velocity zones (HVZs) in the upper crust beneath the Matese limestone massif. These high velocities are interpreted as high-strength regions that extend for 30-40 km down to at least 12 km depth. The correspondence of these HVZs with the maximum intensity regions of historical earthquakes (1688 AD, 1805 AD) suggests that these anomalies delineate the extent of two fault segments of the southern Apenninic belt capable of generating M = 6.5⁻⁷ earthquakes. The lateral offset observed between the two segments from tomographic results and isoseismal areas is possibly related to transverse right-lateral faults.     

Modelling deformation rates in the western Gulf of Corinth: rheological constraints

The Gulf of Corinth is one of the most active extensional regions in the Mediterranean area characterized by a high rate of seismicity. However, there are still open questions concerning the role and the geometry of the numerous active faults bordering the basin, as well as the mechanisms governing the seismicity. In this paper, we use a 2-D plane strain finite element analysis to constrain the upper crust rheology by modelling the available deformation data (GPS and geomorphology). We consider a SSW–NNE cross-section of the rift cutting the main active normal faults (Aigion, West Eliki and Off-Shore faults). The models run for 650 Kyr assuming an elasto-viscoplastic rheology and 1.3 cm yr⁻¹ horizontal extension as boundary condition (resulting from GPS data). We model the horizontal and vertical deformation rates and the accumulation of plastic strain at depth, and we compare them with GPS data, with long term uplift rates inferred from geomorphology and with the distribution of seismicity, respectively. Our modelling results demonstrate that dislocation on high-angle normal faults in a plastic crustal layer plays a key role in explaining the extremely localized strain within the Gulf of Corinth. Conversely, the contribution of structures such as the antithetic Trizonia fault or the buried hypothetical subhorizontal discontinuity are not necessary to model observed data.     

Post-seismic rebound of a spherical Earth: new insights from the application of the Post–Widder inversion formula

The post-seismic response of a viscoelastic Earth to a seismic dislocation can be computed analytically within the framework of normal-modes, based on the application of propagator methods. This technique, widely documented in the literature, suffers from several shortcomings; the main drawback is related to the numerical solution of the secular equation, whose degree increases linearly with the number of viscoelastic layers so that only coarse-layered models are practically solvable. Recently, a viable alternative to the standard normal-mode approach, based on the Post–Widder Laplace inversion formula, has been proposed in the realm of postglacial rebound models. The main advantage of this method is to bypass the explicit solution of the secular equation, while retaining the analytical structure of the propagator formalism. At the same time, the numerical computation is much simplified so that additional features such as linear non-Maxwell rheologies can be simply implemented. In this work, for the first time, we apply the Post–Widder Laplace inversion formula to a post-seismic rebound model. We test the method against the standard normal-mode solution and we perform various benchmarks aimed to tune the algorithm and to optimize computation performance while ensuring the stability of the solution. As an application, we address the issue of finding the minimum number of layers with distinct elastic properties needed to accurately describe the post-seismic relaxation of a realistic Earth model. Finally, we demonstrate the potentialities of our code by modelling the post-seismic relaxation after the 2004 Sumatra–Andaman earthquake comparing results based upon Maxwell and Burgers rheologies.     

Evidence for underthrusting beneath the Queen Charlotte Margin, British Columbia, from teleseismic receiver function analysis

The Queen Charlotte Fault zone is the transpressive boundary between the North America and Pacific Plates along the northwestern margin of British Columbia. Two models have been suggested for the accommodation of the ∼20 mm yr⁻¹ of convergence along the fault boundary: (1) underthrusting; (2) internal crustal deformation. Strong evidence supporting an underthrusting model is provided by a detailed teleseismic receiver function analysis that defines the underthrusting slab. Forward and inverse modelling techniques were applied to receiver function data calculated at two permanent and four temporary seismic stations within the Queen Charlotte Islands. The modelling reveals a ∼10 km thick low-velocity zone dipping eastward at 28° interpreted to be underthrusting oceanic crust. The oceanic crust is located beneath a thin (28 km) eastward thickening (10°) continental crust.     

Geodetic evidence for conjugate faulting during the 1988 Tennant Creek, Australia earthquake sequence

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Repeat levelling measurements and detailed topographic profiles from the epicentral area of the 1988 January 22 Tennant Creek, Australia earthquakes are used to constrain the geometry of faulting associated with three M 6+ earthquakes. The observed elevation changes are modelled assuming elastic deformation and uniform slip on several faults. The vertical deformation data are poorly fit by a single-fault model, and require at least three distinct faults. In the preferred model, two faults on either end of the zone of surface rupture have similar orientations, but the central fault has an orientation conjugate to the flanking faults. This interpretation is consistent with the identification of the fault planes with well-defined, dipping zones of aftershock hypocentres determined with data from portable seismograph arrays. It is also consistent with the sense of surficial deformation documented by 75 topographic profiles across the scarps. However, a fourth fault associated with possible conjugate faulting in the central fault segment at the time of the second main shock is not required by the levelling data.     

A kinematic viscoelastic model of the San Francisco earthquake of 1906

Summary. We construct a model of the San Andreas fault zone based on a rectangular fault in an elastic layer overlying a viscoelastic half-space. We alllow both steady and episodic aseismic slip at depth on the fault as well as a large-scale relative plate driving force. We use the model to explain the aseismic changes in geodetic triangulation angles observed during the 40 years following the 1906 San Francisco earthquake. The most important results are that viscoelastic relaxation can explain the data very well, and that the driving force of relative plate motion can be characterized by a horizontal distance scale perpendicular to the plate boundary of hundreds of kilometres.     

Shear wave anisotropy in the crust around the San Andreas fault near Parkfield: spatial and temporal analysis

We systematically analysed shear wave splitting (SWS) for seismic data observed at a temporary array and two permanent networks around the San Andreas Fault (SAF) Observatory at Depth. The purpose was to investigate the spatial distribution of crustal shear wave anisotropy around the SAF in this segment and its temporal behaviour in relation to the occurrence of the 2004 Parkfield M 6.0 earthquake. The dense coverage of the networks, the accurate locations of earthquakes and the high-resolution velocity model provide a unique opportunity to investigate anisotropy in detail around the SAF zone. The results show that the primary fast polarization directions (PDs) in the region including the SAF zone and the northeast side of the fault are NW–SE, nearly parallel or subparallel to the SAF strike. Some measurements on the southwest side of the fault are oriented to the NNE–SSW direction, approximately parallel to the direction of local maximum horizontal compressive stress. There are also a few areas in which the observed fast PDs do not fit into this general pattern. The strong spatial variations in both the measured fast PDs and time delays reveal the extreme complexity of shear wave anisotropy in the area. The top 2–3 km of the crust appears to contribute the most to the observed time delays; however substantial anisotropy could extend to as deep as 7–8 km in the region. The average time delay in the region is about 0.06 s. We also analysed temporal patterns of SWS parameters in a nearly 4-yr period around the 2004 Parkfield main shock based on similar events. The results show that there are no appreciable precursory, coseismic, or post-seismic temporal changes of SWS in a region near the rupture of an M 6.0 earthquake, about 15 km away from its epicentre.     

Gravitational viscoelastic relaxation of eccentrically nested spheres

We present a semi-analytical solution to the 2-D forward modelling of viscoelastic relaxation in a heterogeneous model consisting of eccentrically nested spheres. Several numerical methods for 2-D and 3-D viscoelastic relaxation modelling have been applied recently, including finite-element and spectral-finite-difference schemes. The present semi-analytical approach provides a model response against which more general numerical algorithms can be validated. The eccentrically nested sphere solution has been tested by comparing it with the analytical solutions for viscoelastic relaxation in a homogeneous sphere and in two concentrically nested spheres, and good agreement was obtained.     

High-resolution structures of the Landers fault zone inferred from aftershock waveform data

High-frequency body waves recorded by a temporary seismic array across the surface rupture trace of the 1992 Landers, California, earthquake were used to determine fault-zone structures down to the seismogenic depth. We first developed a technique to use generalized ray theory to compute synthetic seismograms for arbitrarily oriented tabular low-velocity fault-zone models. We then generated synthetic waveform record sections of a linear array across a vertical fault zone. They show that both arrival times and waveforms of P and S waves vary systematically across the fault due to transmissions and reflections from boundaries of the low-velocity fault zone. The waveform characteristics and arrival-time patterns in the record sections allow us to locate the boundaries of the fault zone and to determine its P - and S -wave velocities independently as well as its depth extent. Therefore, the trade-off between the fault-zone width and velocities can be avoided. Applying the method to the Landers waveform data reveals a low-velocity zone with a width of 270–360 m and a 35–60 per cent reduction in P and S velocities relative to the host rock. The analysis suggests that the low-velocity zone extends to a depth of ∼7 km. The western boundary of the low-velocity zone coincides with the observed main surface rupture trace.     

East African earthquakes below 20 km depth and their implications for crustal structure

We report source parameters for eight earthquakes in East Africa obtained using a number of techniques, including (1) inversion of long-period P and SH waves for moment tensors and source-time functions, (2) forward modelling of first-motion polarities and P and pP amplitudes on short-period seismograms, and (3) determination of pP-P and sP-P differential traveltimes from short-period records. The foci of these earthquakes lie between depths of 24 and 34 km in Archean and Proterozoic lithosphere, and all but one fault-plane solution indicates normal faulting (primarily E-W extension), consistent with the regional stress regime in East Africa. Because many of these earthquakes occurred in areas where the crust may have been thinned by rifting, it is difficult to ascertain whether or not their foci lie within the lower crust or upper mantle. Some of them, however, occurred away from rift structures in Proterozoic crust that is possibly 35–40 km thick or thicker, and thus they probably nucleated within the lower crust. Strength profile calculations suggest that in order to account for seismogenic (i.e. brittle) behaviour at sufficient depths to explain lower crustal earthquakes in East Africa, the lower crust must not only be composed of mafic lithologies, as suggested by previous investigators, but also that significantly more heat (∼100 per cent) must come from the upper crust than predicted by the crustal heat source distribution obtained from a 1-D interpretation of the linear relationship between heat flow and heat production observed in Proterozoic terrains within eastern and southern Africa. Precambrian mafic dike swarms throughout East Africa provide evidence for magmatic events which could have delivered large amounts of mafic material to the lower crust over a very broad area, thus explaining why the lower crust in East Africa might be mafic away from the volcanogenic rift valleys.