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.     

Crustal structure in the Western Somali Basin

Summary. As part of integrated marine geophysical studies in the Western Somali Basin, we performed 118 sonobuoy experiments to define better the crustal structure of the margins and basin created by the separation of Madagascar and Africa. After using T ²/ X ², conventional slope-intercept methods, and slant-stacked t-p techniques to analyse the data, we combined our solutions with all previous velocity information for the area. Velocity functions were derived for the sediment coiumn, and we detected a high-velocity (4.58 ± 0.29 km s^–1) sediment layer overlying acoustic basement. We confirmed that the crust is indeed seismically oceanic, and that it may be considered either in terms of a layered model – layers 2B (5.42 ± 0.19 km s^–1), 2C (6.23 ± 0.22 km s^–1), 3 (7.03 ± 0.25 km s^–1), and mantle (7.85 ± 0.32 km s^–1) were identified – or a more complex gradient model in which layer 2 is marked by a steeper velocity gradient than underlying layer 3. Integrated igneous crustal thicknesses (1.62 ± 0.22 s, 5.22 ± 0.64 km) are significantly less than what is considered normal. We present a revised seismic transect across the East African margin, as well as total sediment thickness, depth to basement and crustal thickness maps.     

Elastic full-waveform inversion for earthquake source parameters

2-D full-waveform inversion of double-couple earthquake sources is implemented. Temporally and spatially extended sources are represented by superposition of double-couples. The source parameters solved for are the spatial location, origin time, amplitude and orientation of each double-couple. The velocity and density distribution and source time function are assumed to be known a priori but may be arbitrarily complicated. The non-linear inverse problem is solved by iterative linear approximation. The Jacobian matrix elements for source depth and rupture angle are computed by wavefield extrapolation forward in time, while those for origin time and amplitude are computed analytically. A smoothing technique that results in faster convergence and avoids local minima associated with cycle skipping is applied at each iteration. A spatial sampling interval, between discrete sources, of one-quarter wavelength of the dominant shear wave is optimal for inversion if high uniqueness of the result is desired. The presence of a fault is inferred from the spatial continuity of the rupture solution, rather than being imposed a priori. The method is illustrated by successful application to three synthetic source models: a single double-couple, a single extended rupture and a double extended rupture. The resolutions of the source depth and origin time are higher, and their posterior covariances are lower than those of the amplitude and rupture angle at each source point. Source depth, origin time and amplitude are primarily determined by the data; the rupture angle is more strongly influenced by the a priori information.     

Global crustal thickness from neural network inversion of surface wave data

We present a neural network approach to invert surface wave data for a global model of crustal thickness with corresponding uncertainties. We model the a posteriori probability distribution of Moho depth as a mixture of Gaussians and let the various parameters of the mixture model be given by the outputs of a conventional neural network. We show how such a network can be trained on a set of random samples to give a continuous approximation to the inverse relation in a compact and computationally efficient form. The trained networks are applied to real data consisting of fundamental mode Love and Rayleigh phase and group velocity maps. For each inversion, performed on a 2°× 2° grid globally, we obtain the a posteriori probability distribution of Moho depth. From this distribution any desired statistic such as mean and variance can be computed. The obtained results are compared with current knowledge of crustal structure. Generally our results are in good agreement with other crustal models. However in certain regions such as central Africa and the backarc of the Rocky Mountains we observe a thinner crust than the other models propose. We also see evidence for thickening of oceanic crust with increasing age. In applications, characterized by repeated inversion of similar data, the neural network approach proves to be very efficient. In particular, the speed of the individual inversions and the possibility of modelling the whole a posteriori probability distribution of the model parameters make neural networks a promising tool in seismic tomography.     

Joint inversion of receiver function and surface wave dispersion observations

We implement a method to invert jointly teleseismic P wave receiver functions and surface wave group and phase velocities for a mutually consistent estimate of earth structure. Receiver functions are primarily sensitive to shear wave velocity contrasts and vertical traveltimes, and surface wave dispersion measurements are sensitive to vertical shear wave velocity averages. Their combination may bridge resolution gaps associated with each individual data set. We formulate a linearized shear velocity inversion that is solved using a damped leastsquares scheme that incorporates a priori smoothness constraints for velocities in adjacent layers. The data sets are equalized for the number of data points and physical units in the inversion process. The combination of information produces a relatively simple model with a minimal number of sharp velocity contrasts. We illustrate the approach using noisefree and realistic noise simulations and conclude with an inversion of observations from the Saudi Arabian Shield. Inversion results for station SODA, located in the Arabian Shield, include a crust with a sharp gradient near the surface (shear velocity changing from 1.8 to 3.5 km s¹ in 3 km) underlain by a 5kmthick layer with a shear velocity of 3.5 km s¹ and a 27kmthick layer with a shear velocity of 3.8 km s¹, and an upper mantle with an average shear velocity of 4.7 km s¹. The crustmantle transition has a significant gradient, with velocity values varying from 3.8 to 4.7 km s¹ between 35 and 40 km depth. Our results are compatible with independent inversions for crustal structure using refraction data.     

Crustal P- and S-velocity structure of the Serbomacedonian Massif (Northern Greece) obtained by non-linear inversion of traveltimes

In the present study, the P - and S -velocity structure of the crust and uppermost mantle in the area of central Macedonia (northern Greece) is presented, as derived from the inversion of traveltimes of local events. An appropriate preconditioning of the final linearized system is used in order to reduce ray density effects on the results. The study focuses mainly on the structure of the broader area of the Serbomacedonian Massif. Interesting features and details of the crustal structure can be recognized in the final tomographic images. The crustal thickness shows strong variations. Under the Serbomacedonian and western Rhodope massifs the crust has a thickness that exceeds 30  km. On the other hand, the North Aegean Trough exhibits a fairly thin crust (25–27  km). Moreover, the Serbomacedonian Massif is bounded by two regions that trend parallel to the Axios river–Thermaikos gulf and the Strymon river–Orfanou gulf, respectively, which show significant crustal thinning (25–28  km). The observed match between the direction of this crustal thinning and the basins' axes indicates that they have been generated by the same extensional deformation episode.     

The three-dimensional shear wave structure in the mantle by overtone waveform inversion - I. Radial seismogram inversion

Summary. The three-dimensional (3-D) shear wave structure of the mantle, down to the depth of about 900 km, is obtained by inverting waveforms of radial component seismograms. Radial component seismograms contain large amplitude overtone signals which circle the Earth as wave packets and are sometimes called X1, X2, X3, … We use data which contain R1, X1 and X2 and filtered between 2 and 10mHz. It is shown that, unless each seismogram is weighted, all seismograms are not fitted uniformly. Only data from large earthquakes are fitted and the final velocity anomalies are biased by the small number of large earthquake data. Resolution is good at shallow depths, becomes worse in the intermediate depth range between about 400 and 500 km and then becomes better at greater depth ranges (600–900km). Even though we use only spheroidal mode data, velocity anomalies in the shallow structure show excellent correlation with the age of the surface rocks of the Earth. In the deeper regions, between about 600 and 900km, South America shows a fast velocity anomaly which may indicate the slab penetration beyond 700 km there. Another region which shows a fast velocity anomaly is the Mariana trench, but other subduction regions do not show such features.