Local earthquake data from a dense temporary seismological network in the southern Dead Sea area have been analysed within the project DESIRE (Dead Sea Integrated Research Project). Local earthquakes are used for the first precise image of the distribution of the P-wave velocity and the v_P/v_S ratios. 65 stations registered 655 local events within 18 months of observation time. A subset of 530 well-locatable events with 26 730 P- and S-arrival times was used to calculate a tomographic model for the v_P and v_P/v_S distribution. Since the study area is at first-order 2-D, a gradual approach was chosen, which compromised a 2-D inversion followed by a 3-D inversion. The sedimentary basin fill is clearly imaged through high v_P/v_S ratios and low v_P. The basin fill shows an asymmetric structure with average depth of 7 km at the western boundary and depth between 10 and 14 km at the eastern boundary. This asymmetry is reflected by the vertical strike-slip eastern border fault, and the normal faulting at the western boundary, caused by the transtensional deformation within the last 5 Myr. Within the basin fill the Lisan salt diapir is imaged through low v_P/v_S ratios, reflecting its low fluid content. The extensions were determined to 12 km in E–W and 17 km in N–S direction while its depth is 5–6 km. The thickness of the pre-basin sediments below the basin fill cannot be derived from the tomography data—it is estimated to less than 3 km from former investigations. Below the basin, down to 18 km depth very low P-wave velocities and low v_P/v_S ratios are observed—most likely caused by fluids from the surrounding crust or the upper mantle.

Interferometric synthetic aperture radar (InSAR) measurements, field observations and elastic modelling of the 2009–2010 Karonga (northern Malawi) earthquake swarm reveal widespread coseismic and localized post-seismic deformation. In a period of about 1.5 months starting on November 5, 29 M ≥ 4 earthquakes struck the region, culminating in an M_w 6 peak event on December 19. The next few months were characterized by significant localized deformation with a very low seismic moment release. We find a very good agreement between InSAR and field observations of surface ruptures. Our best fitted coseismic models indicate dip-slip displacements on a fault dipping 40° to the southwest with maximum slip of about 120 cm at 3–5 km depth. Fault activity continued until 2010 August as shallow aseismic afterslip mostly above the maximum coseismic slip patches. Although the swarm occurred within a coastal plain covered by porous Quaternary sediments and a high water table, the effect of poroelastic relaxation on the post-seismic deformation was found to be negligibly small. In contrast with other recent earthquake swarms along the East African Rift, the Karonga swarm shows no evidence for dike intrusion.

Laboratory experiments with rock samples show that transient creep, at which strain grows with time and strain rate decrease at constant stress, occurs while creep strains are sufficiently small. The transient creep at high temperatures is described by the Andrade rheological model. Since plate tectonics allows only small deformations in lithospheric plates, creep of the lithosphere plates is transient whereas steady-state creep, described by non-Newtonian power-law rheological model, takes place in the underlying mantle. At the transient creep, the effective viscosity, found in the study of postglacial flows, differs significantly from the effective viscosity, which characterizes convective flow, since timescales of these flows are very different. Besides, the transient creep changes the elastic crust thickness estimated within the power-law rheology of the lithosphere. Two problems of convective stability for the lithosphere with the Andrade rheology are solved. The solution of the first problem shows that the state, in which large-scale convective flow in the mantle occurs under lithospheric plates, is unstable and must bifurcate into another more stable state at which the lithospheric plates become mobile and plunge into the mantle at subduction zones. If the lithosphere had the power-law fluid rheology, the effective viscosity of the stagnant lithospheric plates would be extremely high and the state, in which large-scale convection occurs under the stagnant plates, would be stable that contradicts plate tectonics. The mantle convection forms mobile lithospheric plates if the effective viscosity of the plate is not too much higher than the effective viscosity of the underlying mantle. The Andrade rheology lowers the plate effective viscosity corresponding to the power-law fluid rheology and, thus, leads to instability of the state in which the plates are stagnant. The solution of the second stability problem shows that the state, in which the lithospheric plate moves as a whole with constant velocity, is stable but small-amplitude oscillations are imposed on this motion in regions of thickened lithosphere beneath continental cratons (subcratonic roots) where the thickness of the lithosphere is about 200 km. These oscillations create small-scale convective cells (the horizontal dimensions of the cells are of the order of the subcratonic lithosphere thickness). Direction of motion within the cells periodically changes (the period of oscillations is of the order of 10⁸ yr). The small-amplitude convective oscillations cause small strains and do not destroy the thickening of the lithosphere beneath cratons. Thus, the transient creep of the lithosphere explains not only mobility of the lithospheric plates but longevity of subcratonic roots as well.

The space–time–size distributions of seismicity during the last four decades (1973–2010) are used to identify megathrust asperities, the degree of plate coupling (hence potential future large earthquakes) and slab dehydration below the Andean margin (15°–48°S). This seismicity displays globally a typical magnitude distribution with a b value of 1.04 ± 0.024, for a magnitude of completeness of 4.5 and without considering aftershock sequences. However, this unitary b value of the entire catalogue masks large variations (0.6–1.7) in space and time, interpreted as related to different tectonics contexts or different states of the seismic cycle. The study has been performed for different regions (upper continental plate, upper and lower parts of the subducting oceanic plate) with respect to a 3-D slab geometry model all along the Andean margin. Low b values (0.6–0.8) are observed in areas that were ruptured by large M_w≥ 7.5 megathrust earthquakes. A temporal analysis of these features show that b values where low before these earthquakes and remain low after the relaxation of the aftershock phase, suggesting that they are related to time-persistent asperities within the seismogenic zone of the megathrust. Interestingly, a persistently low b value was observed from 2001 to the end 2009 within the southern limit of the Maule M_w= 8.8 earthquake, 2010 February 27. Our results also identify other low b asperities below the Chilean margin that have not ruptured during the last 40 yr and are places of potentially large megathrust earthquakes in the future. In contrast, large b values (1.1–1.7) are observed at seismicity clusters occurring inside the subducted slab beneath the Central Volcanic Zone (CVZ) of the Andes and below the forearc near the subduction point of aseismic ridges and fracture zones. Clusters below the CVZ are spatially related to relative large intermediate-depth earthquakes (like the M_w= 7.8 Tarapaca 2005 earthquake) and may reveal extensive thermally-driven dehydration of the oceanic lithosphere that favours wet mantle melting and therefore magmagenesis feeding the volcanic chain.

Upper-mantle structure between 100 and 300 km depth below the northern Antarctic Peninsula is imaged by modelling P-wave traveltime residuals from teleseismic events recorded on the King Sejong Station (KSJ), the Argentinean/Italian stations (JUBA and ESPZ), an IRIS/GSN Station (PMSA) and the Seismic Experiment in Patagonia and Antarctica (SEPA) broad-band stations. For measuring traveltime residuals, we applied a multichannel cross-correlation method and inverted for upper-mantle structure using VanDecar's method. The new 3-D velocity model reveals a subducted slab with a ∼70° dip angle at 100–300 km depth and a strong low-velocity anomaly confined below the SE flank of the central Bransfield Basin. The low velocity is attributed to a thermal anomaly in the mantle that could be as large as 350–560 K and which is associated with high heat flow and volcanism in the central Bransfield Basin. The low-velocity zone imaged below the SE flank of the central Bransfield Basin does not extend under the northern Bransfield Basin, suggesting that the rifting process in that area likely involves different geodynamic processes.

The overall picture of Mount Etna deformation emerging since a couple of decades of geodetic surveys shows effects of magma accumulation, characterized by inflation/deflation cycle, accompanied by a sliding instability of the southeast flank, whose manifestation is an increase in the horizontal deformation away from the volcano summit. This is a very interesting case to test whether advanced models, taking into account topography, internal structure and frictional rheology, may contribute to a better understanding of the complex interplay among mechanical response, magmatic activity and gravitational load occurring in a volcanic system. Using finite element numerical models we make predictions of surface displacements associated with a simple expansion source and with a dike-like vertical discontinuity. A new methodology is developed to initialize the lithostatic stress field according to the material and geometrical complexities of the models considered. Our results show that, while an amplification of the horizontal displacement can be easily obtained up to a maximum distance of 10 km from the source, we have not been able to find any configuration to extend further this signal. For the case of Mount Etna this suggests that the large horizontal displacements observed in the east flank along the coast cannot be directly related to magma accumulation below the volcano’s summit.

Natural rocks and synthetic analogues can contain extremely small scaled magnetic minerals varying in shape from approximately equidimensional nanoparticles to lower dimensionally shaped lamellae resembling thin films or whiskers.

The magnetic ordering temperatures of such nanomagnetic structures can significantly depend on their size and shape. Here, a general method for detailed numerical or analytical calculations of these ordering temperatures is developed. Based on a modified mean-field approach, the result proves a refined version of a known scaling law that links atomic-layer number to the Curie temperatures of nanostructures. An analytic expression for the dependence of the Curie temperature on the atomic-layer number is obtained for thin films and rectangular nanostructures. It is confirmed by comparison to experimental results.

The global 3-D electrical conductivity distribution in the mantle (in the depth range between 400 and 1600 km) is imaged by inverting C-responses estimated on a global net of geomagnetic observatories.

Very long time-series (up to 51 years; 1957–2007) of hourly means of three components of the geomagnetic field from 281 geomagnetic observatories are collected and analysed. Special attention is given to data processing in order to obtain unbiased C-responses with trustworthy estimates of experimental errors in the period range from 2.9 to 104.2 d. After careful inspection of the obtained C-responses the data from 119 observatories are chosen for the further analysis. Squared coherency is used as a main quality indicator to detect (and then to exclude from consideration) observatories with a large noise-to-signal ratio. During this analysis we found that—along with the C-responses from high-latitude observatories (geomagnetic latitudes higher than 58°)—the C-responses from all low-latitude observatories (geomagnetic latitudes below 11°) also have very low squared coherencies, and thus cannot be used for global induction studies.

We found that the C-responses from the selected 119 mid-latitude observatories show a huge variability both in real and imaginary parts, and we investigated to what extent the ocean effect can explain such a scatter. By performing the systematic model calculations we conclude that: (1) the variability due to the ocean effect is substantial, especially at shorter periods, and it is seen for periods up to 40 d or so; (2) the imaginary part of the C-responses is to a larger extent influenced by the oceans; (3) two types of anomalous C-response behaviour associated with the ocean effect can be distinguished; (4) to accurately reproduce the ocean effect a lateral resolution of 1°× 1° of the conductance distribution is needed, and (5) the ocean effect alone does not explain the whole variability of the observed C-responses.

We also detected that part of the variability in the real part of the C-responses is due to the auroral effect. In addition we discovered that the auroral effect in the C-responses reveals strong longitudinal variability, at least in the Northern Hemisphere. Europe appears to be the region with smallest degree of distortion compared with North America and northern Asia. We found that the imaginary part of the C-responses is weakly affected by the auroral source, thus confirming the fact that in the considered period range the electromagnetic (EM) induction from the auroral electrojet is small. Assuming weak dependence of the auroral signals on the Earth’s conductivity at considered periods, and longitudinal variability of the auroral effect, we developed a scheme to correct the experimental C-responses for this effect.

With these developments and findings in mind we performed a number of regularized 3-D inversions of our experimental data in order to detect robust features in the recovered 3-D conductivity images. Although differing in details, all our 3-D inversions reveal a substantial level of lateral heterogeneity in the mantle at the depths between 410 and 1600 km. Conductivity values vary laterally by more than one order of magnitude between resistive and conductive regions. The maximum lateral variations of the conductivity have been detected in the layer at depths between 670 and 900 km. By comparing our global 3-D results with the results of independent global and semi-global 3-D conductivity studies, we conclude that 3-D conductivity mantle models produced so far are preliminary as different groups obtain disparate results, thus complicating quantitative comparison with seismic tomography or/and geodynamic models. In spite of this, our 3-D EM study and most other 3-D EM studies reveal at least two robust features: reduced conductivity beneath southern Europe and northern Africa, and enhanced conductivity in northeastern China.

A detailed magnetostratigraphic and rock-magnetism study of two Late Palaeozoic rhythmite exposures (Itu and Rio do Sul) from the Itararé Group (Paraná Basin, Brazil) is presented in this paper. After stepwise alterning-field procedures and thermal cleaning were performed, samples from both collections show reversed characteristic magnetization components, which is expected for Late Palaeozoic rocks. However, the Itu rocks presented an odd, flat inclination pattern that could not be corrected with mathematical methods based on the virtual geomagnetic pole (VGP) distributions. Correlation tests between the maximum anisotropy of the magnetic susceptibility axis (K1) and the magnetic declination indicated a possible mechanical influence on the remanence acquisition. The Rio do Sul sequence displayed medium to high inclinations and provided a high-quality palaeomagnetic pole (after shallowing corrections of f = 0.8) of 347.5°E 63.2°S (N = 119; A95 = 3.3; K = 31), which is in accordance with the Palaeozoic apparent wander pole path of South America.

The angular dispersion (S_b) for the distribution of the VGPs calculated on the basis of both the 45° cut-off angle and Vandamme method was compared to the best-fit Model G for mid-latitudes. Both of the S_b results are in reasonable agreement with the predicted (palaeo) latitudinal S-λ relationship during the Cretaceous Normal Superchron (CNS), although the S_b value after the Vandamme cut-off has been applied is a little lower than expected. This result, in addition to those for low palaeolatitudes during the Permo-Carboniferous Reversed Superchron (PCRS) previously reported, indicates that the low secular variation regime for the geodynamo that has already been discovered in the CNS might have also been predominant during the PCRS.

In this study we analyse the error distribution in regional models of the geomagnetic field. Our main focus is to investigate the distribution of errors when combining two regional patches to obtain a global field from regional ones. To simulate errors in overlapping patches we choose two different data region shapes that resemble that scenario. First, we investigate the errors in elliptical regions and secondly we choose a region obtained from two overlapping circular spherical caps. We conduct a Monte-Carlo simulation using synthetic data to obtain the expected mean errors. For the elliptical regions the results are similar to the ones obtained for circular spherical caps: the maximum error at the boundary decreases towards the centre of the region. A new result emerges as errors at the boundary vary with azimuth, being largest in the major axis direction and minimal in the minor axis direction. Inside the region there is an error decay towards a minimum at the centre at a rate similar to the one in circular regions. In the case of two combined circular regions there is also an error decay from the boundary towards the centre. The minimum error occurs at the centre of the combined regions. The maximum error at the boundary occurs on the line containing the two cap centres, the minimum in the perpendicular direction where the two circular cap boundaries meet. The large errors at the boundary are eliminated by combining regional patches. We propose an algorithm for finding the boundary region that is applicable to irregularly shaped model regions.

Paper II of this series described the chemical and microstructural evolution of ferri-ilmenite solid solutions during high-T quench and short-term annealing. Here we explore consequences of these Fe–Ti ordering-induced microstructures and show how they provide an explanation for both self-reversed thermoremanent magnetization and room-T magnetic exchange bias. The dominant antiferromagnetic interactions between (001) cation layers cause the net magnetic moments of ferrimagnetic ordered phases to be opposed across chemical antiphase domain boundaries. Magnetic consequences of these interactions are explored in conceptual models of four stages of microstructure evolution, all having in common that A-ordered and B-anti-ordered domains achieve different sizes, with smaller domains having higher Fe-content, lesser Fe–Ti order, and slightly higher Curie T than larger domains. Stage 1 contains small Fe-rich domains and larger Ti-rich domains separated by volumes of the disordered antiferromagnetic phase. Magnetic linkages in this conceptual model pass through disordered host, but self-reversed TRM could occur. In stage 2, ordered domains begin to impinge, but some disorder remains, creating complex magnetic interactions. In stages 3 and 4, all disordered phase is eliminated, with progressive shrinkage of Fe-rich domains, and growth of Ti-rich domains. Ordered and anti-ordered phases meet at chemical antiphase and synphase boundaries. Strong coupling across abundant antiphase boundaries provides the probable configuration for self-reversed thermoremanent magnetization. Taking the self-reversed state into strong positive fields provides a probable mechanism for room-temperature magnetic exchange bias.

In this work, numerical simulations of the atmospheric and ionospheric anomalies are performed for the Tohoku-Oki tsunami (2011 March 11). The Tsunami–Atmosphere–Ionosphere (TAI) coupling mechanism via acoustic gravity waves (AGWs) is explored theoretically using the TAI-coupled model. For the modelled tsunami wave as an input, the coupled model simulates the wind, density and temperature disturbances or anomalies in the atmosphere and electron density/magnetic anomalies in the F region of the ionosphere. Also presented are the GPS-total electron content (TEC) and ground-based magnetometer measurements during the first hour of tsunami and good agreements are found between modelled and observed anomalies. At first, within 6 min from the tsunami origin, the simulated wind anomaly at 250 km altitude and TEC anomaly appear as the dipole-shaped disturbances around the epicentre, then as the concentric circular wave fronts radially moving away from the epicentre with the horizontal velocity ∼800 m s⁻¹ after 12 min followed by the slow moving (horizontal velocity ∼250 m s⁻¹) wave disturbance after 30 min. The detailed vertical–horizontal propagation characteristics suggest that the anomalies appear before and after 30 min are associated with the acoustic and gravity waves, respectively. Similar propagation characteristics are found from the GPS-TEC and magnetic measurements presented here and also reported from recent studies. The modelled magnetic anomaly in the F region ionosphere is found to have similar temporal variations with respect to the epicentre distance as that of the magnetic anomaly registered from the ground-based magnetometers. The high-frequency component ∼10 min of the simulated wind, TEC and magnetic anomalies in the F region develops within 6–7 min after the initiation of the tsunami, suggesting the importance of monitoring the high-frequency atmospheric/ionospheric anomalies for the early warning. These anomalies are found to maximize across the epicentre in the direction opposite to the tsunami propagation suggesting that the large atmospheric/ionospheric disturbances are excited in the region where tsunami does not travel.

During the last three decades, at least 30 independent estimates of the secular global mean sea level rise (GMSLR) have been published, based on sufficiently long tide gauge (TG) records. Despite its apparent simplicity, the problem of GMSLR is fraught with a number of difficulties, which make it one of the most challenging questions of climate change science. Not surprisingly, published estimates show considerable scatter, with rates ranging between 1 and 2 mm yr⁻¹ for observations on the century timescale. In previous work, the importance of Glacial Isostatic Adjustment (GIA) upon the assessment of the GMSLR has been clearly demonstrated. In particular, starting from the 1980s, GIA models have been routinely employed to decontaminate TG observations from the effects of melting of the late-Pleistocene ice sheets, to fully highlight the sea level variations driven by climate change. However, uncertainties associated with the Earth’s rheological profile and the time history of the past continental ice sheets can propagate into the GIA corrections. After revisiting previous work and estimates, we suggest a significant modification of the criteria for the selection of the TGs which are most suitable for the robust assessment of the secular GMSLR. In particular, we seek a set of TGs for which GIA corrections are essentially independent of the parametrization of the rheological profile of the Earth’s mantle and of the detailed time chronology of surface loading. This insensitivity is established by considering predictions based upon three GIA models widely employed in the recent literature (namely, ICE–3G, ICE–5G and the one developed at the Research School of Earth Sciences of the National Australian University). Applying this approach and selection criteria previously proposed in the literature, we identify a set of 22 sufficiently evenly distributed TGs. By simple statistical methods, these records yield a ‘preferred’, GIA-independent GMSLR estimate since 1880, namely 1.5 ± 0.1 mm yr⁻¹ (rms = 0.4 mm yr⁻¹, wrms = 0.3 mm yr⁻¹). This value is consistent with various previous estimates based on secular TG observations and with that proposed, for the 20th century, by the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (1.7 ± 0.5 mm yr⁻¹).

A novel, multidimensional small baseline subset (MSBAS) methodology is presented for integration of multiple interferometric synthetic aperture radar (InSAR) data sets for computation of 2- or 3-D time-series of deformation. The proposed approach allows the combination of all possible air-borne and space-borne SAR data acquired with different acquisition parameters, temporal and spatial sampling and resolution, wave-band and polarization. The produced time-series have improved temporal resolution and can be enhanced by applying either regularization or temporal filtering to remove high-frequency noise. We apply this methodology to map 2003–2010 ground deformation of the Virunga Volcanic Province (VVP), North Kivu, Democratic Republic of Congo. The horizontal and vertical time-series of ground displacement clearly identify lava compaction areas, long-term deformation of Mt Nyamuragira and 2004, 2006 and 2010 pre- and coeruptive deformation. Providing that enough SAR data is available, the method opens new opportunities for detecting ground motion in the VVP and elsewhere.

It has been demonstrated that the Gravity Recovery And Climate Experiment (GRACE) spaceborne gravimetry data are capable of observing coseismic gravity changes resulting from great earthquakes, such as the 2004 December 26 Sumatra–Andaman event (M_w 9.1–9.3). Here, we show for the first time that refined deformation signals from the 2004 December 26 Sumatra–Andaman Earthquake (M_w 9.1–9.3) together with the 2005 March 28 Nias earthquake (M_w 8.6) can be revealed by deriving the full gravitational gradient tensor from GRACE monthly gravitational field. The GRACE-inferred coseismic gravitational gradient changes agree well with coseismic slip model predictions. Since the high-frequency contents in gravitational field variation can be amplified by deriving the gravitational gradients, the GRACE-derived coseismic gravitational gradient changes clearly delineate the fault lines, locate significant slips, and better define the extent of the coseismic deformation.

The Pearl River Delta (PRD) is one of the most important economic regions with the highest population densities in China. With its dramatic increasing population and economy, hazards associated with land subsidence frequently occur here that amplify the negative effect of sea level rise. However, land subsidence has not been regularly measured in this region. Here, we use interferometric synthetic aperture radar (InSAR) to investigate the rate and extent of land subsidence in the PRD region. Assuming purely vertical displacements, multi-track interferograms from different viewing geometries are combined to estimate the linear rate map and time series at a higher resolution in time than is possible with a single track. The results show apparent subsidence along the coastal region of Shenzhen associated with rapid urban development in recent years. The average subsidence rate within 500 m of the coast is about 2.5 mm yr⁻¹, and the maximum is up to about 6 mm yr⁻¹ with respect to the central part of the city. Much of the land surface in the PRD is less than 2 m above mean sea level; high-precision geodetic measurements throughout the PRD region are therefore critical for conducting risk assessments, considering the rate of about 2–3 mm yr⁻¹ of current global sea level rise.

The precession and obliquity frequencies of the Earth’s rotational motion are functions of the dynamic ellipticity of the Earth’s gravitational figure, and this connection has provided a novel bridge between studies of palaeoclimate and geodynamics. In particular, analyses of tuned climate proxy records have yielded bounds on the mean relative perturbation in dynamic ellipticity over both the last 3 Myr and 25 Myr that are less than ∼3 per cent of the non-hydrostatic component of the ellipticity. We demonstrate that this apparent consistency actually defines an important geophysical enigma. Over the last 3 Myr, changes in the Earth’s figure are likely dominated by ice age forcings—in this case, a small perturbation to dynamic ellipticity implies significant isostatic compensation of the ice-ocean surface mass loads and, hence, a relatively low mantle viscosity. In contrast, over the last 25 Myr, changes in the Earth’s long-wavelength gravitational form are likely dominated by mantle convective flow, and in this case, the small perturbation to dynamic ellipticity implies sluggish convection and a relatively high mantle viscosity. There are at least four possible routes to resolving this enigma: The viscosity in the Earth’s mantle is transient (i.e. dependent on the timescale of the applied forcing), tidal dissipation changed in a manner between the last 3 Myr and 25 Myr that was sufficient to resolve the issue, the observationally inferred bounds are unrealistically restrictive, or earth models exist in which the ice age and convection effects approximately cancel leading to no net perturbation. In this paper, we compute a suite of numerical predictions of ice age and convection-induced perturbations to the dynamic ellipticity to illustrate the enigma described above.

The posterior distribution of earth models that fit observed geophysical data convey information on the uncertainty with which they are resolved. From another perspective, the non-uniqueness inherent in most geophysical inverse problems of interest can be quantified by examining the posterior model distribution converged upon by a Bayesian inversion. In this work we apply a reversible jump Markov chain Monte Carlo method to sample the posterior model distribution for the anisotropic 1-D seafloor conductivity constrained by marine controlled source electromagnetic data. Unlike conventional gradient based inversion approaches, our algorithm does not require any subjective choice of regularization parameter, and it is self parametrizing and trans-dimensional in that the number of interfaces with a resistivity contrast at depth is variable, as are their positions. A synthetic example demonstrates how the algorithm can be used to appraise the resolution capabilities of various electromagnetic field components for mapping a thin resistive reservoir buried beneath anisotropic conductive sediments. A second example applies the method to survey data collected over the Pluto gas field on the Northwest Australian shelf. A benefit of our Bayesian approach is that subsets of the posterior model probabilities can be selected to test various hypotheses about the model structure, without requiring further inversions. As examples, the subset of model probabilities can be viewed for models only containing a certain number of layers, or for models where resistive layers are present between a certain interval as suggested by other geological constraints such as seismic stratigraphy or nearby well logs.

Energy dissipation is observed on seismic data when a wave propagates through a porous medium, involving different frequency regimes depending on the nature of rock and fluid types. We focus here on the role of partial fluid saturation in unconsolidated porous media, looking in particular at P-wave phase velocity and attenuation. The study consists in running an experiment in a sand-filled tank partially saturated with water. Seismic propagation in the tank is generated in the kHz range by hitting a steel ball on a granite plate. Seismic data are recorded by buried accelerometers and injecting or extracting water controls the partial saturation. Several imbibition/drainage cycles were performed between the water and gas residual saturations. A Continuous Wavelet Transform applied on seismic records allowed us to extract the direct P wave at each receiver. We observe an hysteresis in phase velocities and inverse quality factors between imbibition and drainage. Phase velocities and inverse quality factors are then jointly inverted to get a final poro-viscoelastic model of the partially saturated sand that satisfactorily reproduces the data. The model formulation consists in generalizing the Biot theory to effective properties of the fluid and medium (permeability and bulk modulus) to properly explain the phase velocity variation as a function of the saturation. The strong level of attenuation measured experimentally is further explained by an anelastic effect due to grain to grain sliding, adding to Biot’s losses. This study shows that fluid distribution at microscopic scale has strong influence on the attenuation of direct P waves at macroscopic scale and confirms that seismic prospection may be a powerful tool for the characterization of transport phenomena in porous media.

Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

Fractures are common in the Earth’s crust due to different factors, for instance, tectonic stresses and natural or artificial hydraulic fracturing caused by a pressurized fluid. A dense set of fractures behaves as an effective long-wavelength anisotropic medium, leading to azimuthally varying velocity and attenuation of seismic waves. Effective in this case means that the predominant wavelength is much longer than the fracture spacing. Here, fractures are represented by surface discontinuities in the displacement u and particle velocity v as , where the brackets denote the discontinuity across the surface, is a fracture stiffness and is a fracture viscosity.

We consider an isotropic background medium, where a set of fractures are embedded. There exists an analytical solution—with five stiffness components—for equispaced plane fractures and an homogeneous background medium. The theory predicts that the equivalent medium is transversely isotropic and viscoelastic. We then perform harmonic numerical experiments to compute the stiffness components as a function of frequency, by using a Galerkin finite-element procedure, and obtain the complex velocities of the medium as a function of frequency and propagation direction, which provide the phase velocities, energy velocities (wavefronts) and quality factors. The algorithm is tested with the analytical solution and then used to obtain the stiffness components for general heterogeneous cases, where fractal variations of the fracture compliances and background stiffnesses are considered.

Volcanic explosions are accompanied by strong acoustic pressure disturbances in the atmosphere. With a proper source model, these acoustic signals provide invaluable information about volcanic explosion dynamics. Far-field solutions to volcanic infrasound radiation have been derived above a rigid half-space boundary, and a simple inversion method was developed based on the half-space model. Acoustic monopole and dipole sources were estimated simultaneously from infrasound waveforms. Stability of the inversion procedure was assessed in terms of variances of source parameters, and the procedure was reliable with at least three stations around the infrasound source. Application of this method to infrasound observations recorded at Tungurahua volcano in Ecuador successfully produced a reasonable range of source parameters with acceptable variances. Observed strong directivity of infrasound radiation from explosions at Tungurahua are successfully explained by the directivity of a dipole source model. The resultant dipole axis, in turn, shows good agreement with the opening direction of the vent at Tungurahua, which is considered to be the origin of the dipole source. The method is general and can be utilized to study any monopole, dipole or combined sources generated by explosions.

Acoustic wavefields produced using sources appropriately delayed in time can be focused at known positions and times in a heterogeneous medium. Seismoelectric conversion occurs if the acoustic focus point coincides with a discontinuity in electrical and hydrological medium properties, thus generating a current density. The current generates a potential difference, which can be observed at a distance by an array of monitoring electrodes. Since the acoustic wavefield is precisely located at a position and time, this electrical source behaves like a controlled virtual electrode whose properties depend on the strength of the acoustic wavefield and on the medium properties. This procedure can be used to increase the robustness and resolutions of electrical resistivity tomography and to identify hydrological parameters at various points in the medium by scanning the medium by changing the position of the acoustic focus point.

The mechanisms of seismo-electromagnetic phenomena remain largely unexplained. To address this issue, we introduce a fault model that takes account of a coupled interaction between earthquake nucleation and deep Earth gases. This interaction causes a negatively electrified gas flow due to an exo-electron attachment reaction, as the gases pass through fractured asperities. This transient activity may be regarded to be a pressure-impressed electric current generator. In the model, the current and frequency are formulated as functions of earthquake parameters. The estimated current is sufficient to explain the seismic electromagnetic signals observed at ground level. A physical model of how current generation is coupled with ionospheric electromagnetic disturbances is explained in terms of magnetic induction coupling for strong offshore earthquakes, which may provide a plausible explanation of observed ionospheric electron enhancement prior to some recent offshore earthquakes. The model also suggests that geomagnetic observations close to an epicentre of a strong offshore earthquake may provide an effective means of detecting clear and identifiable precursor signals.

The goal of this study is to investigate the spatial variability of the seismic radiation spectral content of the Sumatra–Andaman 2004 earthquake. We determine the integral estimates of source geometry, duration and rupture propagation given by the stress glut moments of total degree 2 of different source models. These models are constructed from a single or a joint use of different observations including seismology, geodesy, altimetry and tide gauge data. The comparative analysis shows coherency among the different models and no strong contradictions are found between the integral estimates of geodetic and altimetric models, and those retrieved from very long period seismic records (up to 2000–3000 s). The comparison between these results and the integral estimates derived from observed surface wave spectra in period band from 500 to 650 s suggests that the northern part of the fault (to the north of 8°N near Nicobar Islands) did not radiate long period seismic waves, that is, period shorter than 650 s at least. This conclusion is consistent with the existing composite short and long rise time tsunami model: with short rise time of slip in the southern part of the fault and very long rise time of slip at the northern part. This complex space-time slip evolution can be reproduced by a simple dynamic model of the rupture assuming a crude phenomenological mechanical behaviour of the rupture interface at the fault scales combining an effective slip-controlled exponential weakening effect, related to possible friction and damage breakdown processes of the fault zone, and an effective linear viscous strengthening effect, related to possible interface lubrication processes. While the rupture front speed remains unperturbed with initial short slip duration, a slow creep wave propagates behind the rupture front in the case of viscous effects accounting for the long slip duration and the radiation characteristics in the northern segment.

Simultaneous estimation of origin time, location and moment tensor of seismic events is critical for automatic, continuous, real-time monitoring systems. Recent studies have shown that such systems can be implemented via waveform fitting methods based on pre-computed catalogues of Green’s functions. However, limitations exist in the number and length of the recorded traces, and the size of the monitored volume that these methods can handle without compromising real-time response. This study presents numerical tests using a novel waveform fitting method based on compressive sensing, a field of applied mathematics that provides conditions for sampling and recovery of signals that admit a sparse representation under a known base or dictionary. Compressive sensing techniques enable us to determine source parameters in a compressed space, where the dimensions of the variables involved in the inversion are significantly reduced. Results using a hypothetical monitoring network with a dense number of recording stations show that a compressed catalogue of Green’s functions with 0.004 per cent of its original size recovers the exact source parameters in more than 50 per cent of the tests. The gains in processing time in this case drop from an estimated 90 days to browse a solution in the uncompressed catalogue to 41.57 s to obtain an estimation using the compressed catalogue. For simultaneous events, the compressive sensing approach does not appear to influence the estimation results beyond the limitations presented by the uncompressed case. The main concern in the use of compressive sensing is detectability issues observed when the amount of compression is beyond a minimum value that is identifiable through numerical experiments. Tests using real data from the 2002 June 18 Caborn Indiana earthquake show that the presence of noise and inaccurate Green’s functions require a smaller amount of compression to reproduce the solution obtained with the uncompressed catalogue. In this case, numerical simulation enables the assessment of the amount of compression that provides a reasonable rate of detectability. Overall, the numerical experiments demonstrate the effectiveness of our compressed domain inversion method in the real-time monitoring of seismic sources with dense networks of receivers. As an added benefit of the compression process, the size of the monitored volume can also be increased under specific restrictions while maintaining the real-time response.

This paper evaluates a forecasting procedure, which was based on the data for the period 1926–1993, in and around Japan. The period of the experiment is from 1994 to April 2011. According to the procedure, the probability that the first earthquake will be a foreshock varies in a range between 1 and 10-odd per cent, depending on its location. This location-dependent forecasting performed significantly better than the unconditional foreshock probability (3.7 per cent average) throughout the Japan region. Furthermore, when multiple earthquakes were observed as a cluster, the foreshock forecast probabilities varied in a much wider range, depending on the space–time distances and magnitude increments, between the earthquakes. Such forecasts performed better than the average foreshock probability, and the forecast probabilities were basically consistent with the outcomes. The improvements of the forecasts were objectively evaluated by using the log likelihood score. It is also shown that the forecasting procedure was robust enough and can be adopted for automatically determined earthquakes in real-time.

We explore a recently developed procedure for kinematic inversion based on an elliptical subfault approximation. In this method, the slip is modelled by a small set of elliptical patches, each ellipse having a Gaussian distribution of slip. We invert near-field strong ground motion for the 2004 September 28 M_w 6.0 Parkfield, California, earthquake. The data set consists of 10 digital three-component 18-s long displacement seismograms. The best model gives a moment of 1.21 × 10¹⁸ N m, with slip on two distinct ellipses, one with a high-slip amplitude of 0.91 m located 20 km northwest of the hypocentre. The average rupture speed of the rupture process is ∼2.7 km s⁻¹. We find no slip in the top 5 km. At this depth, a lineation of small aftershocks marks the transition from creeping above to locked below, in the interseismic period. The high-slip patch coincides spatially with the hypocentre of the 1966 M_w6.0 Parkfield, California, earthquake. The larger earthquakes prior to the 2004 Parkfield earthquake and the aftershocks of the 2004 earthquake (M_w > 3) also lie around this high-slip patch, where our model images a sharp slip gradient. This observation suggests the presence of a permanent asperity that breaks during large earthquakes, and has important implications for the slip deficit observed on the Parkfield segment, which is necessary for reliable seismic hazard assessment.

The M_w 7.8 2006 July 17 earthquake off the southern coast of Java, Indonesia, has been responsible for a very large tsunami causing more than 700 casualties. The tsunami has been observed on at least 200 km of coastline in the region of Pangandaran (West Java), with run-up heights from 5 to more than 20 m. Such a large tsunami, with respect to the source magnitude, has been attributed to the slow character of the seismic rupture, defining the event as a so-called tsunami earthquake, but it has also been suggested that the largest run-up heights are actually the result of a second local landslide source. Here we test whether a single slow earthquake source can explain the tsunami run-up, using a combination of new detailed data in the region of the largest run-ups and comparison with modelled run-ups for a range of plausible earthquake source models.

Using high-resolution satellite imagery (SPOT 5 and Quickbird), the coastal impact of the tsunami is refined in the surroundings of the high-security Permisan prison on Nusa Kambangan island, where 20 m run-up had been recorded directly after the event. These data confirm the extreme inundation lengths close to the prison, and extend the area of maximum impact further along the Nusa Kambangan island (about 20 km of shoreline), where inundation lengths reach several hundreds of metres, suggesting run-up as high as 10–15 m.

Tsunami modelling has been conducted in detail for the high run-up Permisan area (Nusa Kambangan) and the PLTU power plant about 25 km eastwards, where run-up reached only 4–6 m and a video recording of the tsunami arrival is available. For the Permisan prison a high-resolution DEM was built from stereoscopic satellite imagery. The regular basin of the PLTU plant was designed using photographs and direct observations. For the earthquake's mechanism, both static (infinite) and finite (kinematic) ruptures are investigated using two published source models. The models account rather well for the sea level variation at PLTU, showing a better agreement in arrival times with the finite rupture, and predict the Permisan area to be one of the regions where tsunami waves would have focussed. However, the earthquake models that match the data at PTLU do not predict that the wave heights at Permisan are an overall maximum, and do not predict there more than 10 m of the 21 observed. Hence, our results confirm that an additional localized tsunami source off Nusa Kambangan island, such as a submarine landslide, may have increased the tsunami impact for the Permisan site. This reinforces the importance for hazard assessment of further mapping and understanding local potential for submarine sliding, as a tsunami source added to usual earthquake sources.

A methodology for the interpolation of peak ground acceleration (PGA) from discrete array stations is developed. Limited number of accelerometers or difficulty of monitoring at unreachable locations often has a negative impact on the generation of the maps of shaking after an earthquake. In locations with no recordings, PGA is inferred from interpolation of recorded PGA. The presented methodology estimates PGA at an arbitrary set of closely spaced points, in a way that is statistically compatible with known or prescribed PGA at other locations. The observed data recorded by strong motion stations of Istanbul Earthquake Rapid Response System are used for the development and validation of the new numerical method. The estimated and recorded PGAs are compared. Biased ground motion prediction equations are also considered at the comparisons. Ground motion prediction equations underestimated both observed and estimated PGAs. It has been found that the methodology is very effective for highly vulnerable mega-cities and urban areas.

We present S receiver functions and SKS splitting measurements from the China Seismograph Network located in the Qinghai and Gansu provinces. Teleseismic data are used to interpret the structure of the lithosphere–asthenosphere boundary (LAB) and upper-mantle deformation beneath the northeastern Tibetan Plateau (NETP) in regions north of the east Kunlun Fault. Based on our observations, the LAB lies at a depth of 125–135 km beneath the northeastern Songpan–Ganzi block and the west Qinling orogen, between 145 and 175 km beneath the Kunlun and Qilian orogen, and deepens below the Qaidam Basin (175–190 km), Ordos Craton (170 km) and Alashan platform (200 km). The NETP is characterized by a nearly uniform fast NW–SE S-wave direction. These observations are different from those to the south of the Kunlun Fault where fast S directions are rotating clockwise from the inner plateau. The change in fast directions across the Kunlun Fault implies a sudden variation of upper-mantle deformation. Shear wave splitting delay times vary from 0.8 to 1.9 s. Data from beneath regions north of the Kunlun–Ayimaqin suture showed that delay time was positively correlated with lithospheric thickness with an increase of 0.7 s per 100 km. This indicates that the anisotropy may develop in the uppermost mantle, such as the lithosphere, beneath the NETP.

The Chamoli region, within the ∼700 km seismic gap of the seismically active region of the Central Himalaya, has been site of moderate sized earthquakes in recent past, viz. 1999 March 29 (M_b 6.3), 2005 December 14 (M_b 5.3), and very recently 2011 June 20 (M 4.6). To understand the process of earthquake generation in the region, we constrain earthquake distribution pattern and determine the crustal seismic wave velocity variation using local earthquake data recorded by the Kumaon-Garhwal Himalaya seismic network that was operated during 2005–2008. Also, we included aftershocks data from the 1999 Chamoli earthquake. We infer that the earthquakes are mainly clustered near the Munsiary Thrust marking the southern part of the Main Central Thrust zone and in depth, above the Main Himalayan Thrust. The Chamoli earthquake source region is characterized by low P-wave velocity (V_P) and high V_P/V_S. This could be expression of possible presence of fluids because of metamorphic dehydration reaction by the underthrusting Indian crust. The released fluid percolates upwards into the brittle portion of the crust, reducing the fault zone friction leading to generation of crustal earthquakes.

We propose a forward wavefield simulation based on a particle continuum model to simulate seismic waves travelling through a complex subsurface structure with arbitrary topography. The inclusion of arbitrary topography in the numerical simulation is a key issue not only for scientific interests but also for disaster prediction and mitigation purposes. In this study, a Hamiltonian particle method (HPM) is employed. It is easy to introduce traction-free boundary conditions in HPM and to refine the particle density in space. Any model with complex geometry and velocity structure can be simulated by HPM because the connectivity between particles is easily calculated based on their relative positions and the free surfaces are automatically introduced. In addition, the spatial resolution of the simulation could be refined in a simple manner even in a relatively complex velocity structure with arbitrary surface topography. For these reasons, the present method possesses great potential for the simulation of strong ground motions.

In this paper, we first investigate the dispersion property of HPM through a plane wave analysis. Next, we simulate surface wave propagation in an elastic half space, and compare the numerical results with analytical solutions. HPM is more dispersive than FDM, however, our local refinement technique shows accuracy improvements in a simple and effective manner. Next, we introduce an earthquake double-couple source in HPM and compare a simulated seismic waveform obtained with HPM with that computed with FDM to demonstrate the performance of the method. Furthermore, we simulate the surface wave propagation in a model with a surface of arbitrary topographical shape and compare with results computed with FEM. In each simulation, HPM shows good agreement with the reference solutions. Finally, we discuss the calculation costs of HPM including its accuracy.

We investigated the temporal changes in the seismic attenuation of a fault zone using near-source recordings of S waves from repeating microearthquakes that occurred both before and after M ∼ 2 earthquakes in the Bambanani gold mine, South Africa. Because the source locations and the mechanisms of repeating earthquakes can be regarded as identical, the attenuation change can be estimated using the spectral ratios for repeating earthquake pairs. We found an increase in the S-wave attenuation parameter on the vertical component which is positively correlated with frequency, corresponding to times before and after the M ∼ 2 earthquakes. This increase can be explained by scattering attenuation, with a typical scale of damage in the fault zone of ∼3 m.

We discuss results associated with 2-D numerical simulations of in-plane dynamic ruptures on a fault governed by slip-weakening and rate-and-state friction laws with off-fault yielding. The onset of yielding is determined by a Mohr–Coulomb-type criterion whereas the subsequent inelastic response is described by a Duvaut-Lions-type viscoplastic rheology. The study attempts to identify key parameters and conditions that control the spatial distribution and the intensity variation of off-fault yielding zones, the local orientation of the expected microfractures, and scaling relations or correlations among different quantities that can be used to characterize the yielding zones. In this paper, we present example results for crack and pulse ruptures, along with calculations of energy partition and characteristics of the simulated off-fault yielding zones. A companion follow-up paper provides a comprehensive parameter-space study of various examined features. In agreement with previous studies, the location and shape of the off-fault yielding zones depend strongly on the angle of the background maximum compressive stress relative to the fault and the crack versus pulse mode of rupture. Following initial transients associated with nucleation of ruptures, the rate of various energy components (including off-fault dissipation) linearly increases with time for cracks, while approaching a constant level for pulse-like ruptures. The local angle to the fault of the expected microfractures is generally shallower and steeper than in the compressional and extensional quadrants, respectively. The scalar seismic potency density decays logarithmically with increasing fault normal distance, with decay slope and maximum value that are influenced by the operating stress field.

We perform a detailed parameter-space study on properties of yielding zones generated by 2-D in-plane dynamic ruptures on a planar fault with different friction laws and parameters, different initial stress conditions, different rock cohesion values, and different contrasts of elasticity and mass density across the fault. The focus is on cases corresponding to large strike-slip faults having high angle () to the maximum compressive background stress. The simulations and analytical scaling results show that for crack-like ruptures (1) the maximum yielding zone thickness T_max linearly increases with rupture distance L and the ratio T_max/L is inversely proportional to (1 +S)² with S being the relative strength parameter; (2) the potency density decays logarithmically with fault normal distance at a rate depending on the stress state and S; (3) increasing rock cohesion reduces T_max/L, resulting in faster rupture speed and higher inclination angle of expected microfractures on the extensional side of the fault. For slip pulses in quasi-steady state, T is approximately constant along strike with local values correlating with the maximum slip velocity (or final slip) at a location. For a bimaterial interface with , the energy dissipation to yielding contributes to developing macroscopically asymmetric rupture (at the scale of rupture length) with the same preferred propagation direction predicted for purely elastic cases with Coulomb friction. When , representative for thrust faulting, the energy dissipation to yielding leads to opposite preferred rupture propagation. In all cases, is higher on average on the compliant side. For both crack and pulse ruptures with , T decreases and increases for conditions representing greater depth. Significant damage asymmetry of the type observed across several large strike-slip faults likely implies persistent macroscopic rupture asymmetry (unilateral cracks, unilateral pulses or asymmetric bilateral pulses). The results on various features of yielding zones expected from this and other studies are summarized in a table along with observations from the field and laboratory experiments.

Stacks of SS precursors have been widely used in the past two decades to investigate the existence and characteristics of upper mantle discontinuities on a global scale as well as in several regional cases. Here, we present observations of SS precursors from an M_b 6.7 earthquake recorded at the US Transportable Array in 2010. In this particular case, the S₆₆₀S precursors on the transverse component are strong enough to be identified on individual seismograms across the array without any stacking procedures. Two S₆₆₀S precursors are observed, seeming to suggest double discontinuities around 660 km depth in the bounce point region. Through careful analysis of 1-D and 3-D synthetic seismograms, we however discover that, although they have arrival times and slownesses that are very close to the theoretical values of SS precursors, the apparent ‘double precursors’ are artefacts because of mantle heterogeneity in the upper mantle near the receivers away from the bounce point region. This suggests that caution must be taken about appropriate azimuthal coverage at the SS bounce point, before interpreting double SS or PP precursors in terms of complex mineralogical transitions.

Basin response depends on the soil properties (site geometry, impedance contrast), on the constitutive model and on the input motion. Numerical modelling is a useful tool to understand the role and the influence of these different parameters governing site effects. In this study, we focus on the 2-D P–SV seismic wave propagation in a simple asymmetric basin model. We assess the influence of the material constitutive model (elastic, viscoelastic, elastoplastic and viscoelastoplastic) on the wave propagation as well as the importance of the input motion on the development of material non-linearity. We also show that both viscoelasticity and material non-linearity strongly modify the ground motion on a broad range of frequencies, yet they have a stronger effect in some particular frequency bands. We advise that realistic simulations should couple both viscoelasticity accounting for energy dissipation at small strains and non-linear soil behaviour taking into account hysteresis energy dissipation and shear modulus degradation at higher strain levels. In addition, we study the influence of the source frequency content, intensity and complexity on the Fourier and response spectra of horizontal acceleration time histories, and the maximum shear stresses and strains computed within the non-linear material filling the basin. We show that the complexity and amplitude of the source determines whether damping or reduction of the S-wave velocity dominates the wave propagation in the non-linear media. Indeed, for a simple impulsive input the high frequencies are damped whereas for a complex input motion, such a real earthquake, high frequency damping comes together with frequency shift to lower frequency values. For this reason, the use of the source peak ground acceleration (PGA) only is not a good indicator to characterize soil non-linear effects because of the simultaneous influence of input motion intensity and complexity, impedance contrast, and material strength. However, testing other ground motion indicators is beyond the scope of this paper. At last, we test the importance of dynamic soil properties on the wave propagation and show that shear modulus and damping ratio curves that are relatively close, regarding uncertainties associated to such curves measurements, may lead to notable variations in the acceleration fields. Simulations should take into account this variability to assess the uncertainties on computed ground motion.

Wavelets are extremely powerful to compress the information contained in finite-frequency sensitivity kernels and tomographic models. This interesting property opens the perspective of reducing the size of global tomographic inverse problems by one to two orders of magnitude. However, introducing wavelets into global tomographic problems raises the problem of computing fast wavelet transforms in spherical geometry. Using a Cartesian cubed sphere mapping, which grids the surface of the sphere with six blocks or ‘chunks’, we define a new algorithm to implement fast wavelet transforms with the lifting scheme. This algorithm is simple and flexible, and can handle any family of discrete orthogonal or bi-orthogonal wavelets. Since wavelet coefficients are local in space and scale, aliasing effects resulting from a parametrization with global functions such as spherical harmonics are avoided. The sparsity of tomographic models expanded in wavelet bases implies that it is possible to exploit the power of compressed sensing to retrieve Earth’s internal structures optimally. This approach involves minimizing a combination of a ℓ₂ norm for data residuals and a ℓ₁ norm for model wavelet coefficients, which can be achieved through relatively minor modifications of the algorithms that are currently used to solve the tomographic inverse problem.

The comparison of seismograms plays a central role in seismology in diverse ways such as relative time-shifts, propagation effects between stations for a common source, and inversion for source or structural studies. Different measures for comparison have been used in the various situations, but all can be linked by the use of the concept of a transfer operator between a reference seismogram and a comparator trace. Transfer operators are implicit in various methods of phase velocity estimation, receiver functions and anisotropy studies, and measures for estimating arrival times and amplitude variations.

Such transfer operators have a number of important roles; first they allow a visual assessment of the similarities of seismograms, secondly they provide a useful description of propagation effects for a common source in terms of the evolution from a reference station, and thirdly the transfer operator provides a means of representing seismogram differences in inversion without dominance by the largest amplitude arrivals.

Whereas many time-domain measures of the degree of fit between an observed seismogram and the corresponding synthetic seismogram depend on the difference between the traces, which can be readily disturbed by minor misalignment, the transfer operator can readily represent a time offset while retaining a suitable measure of the similarities between the traces.

The transfer operator concept can be applied with weighting or windowing of seismograms, and can be expressed in the time and frequency domains, or even in frequency time. This approach provides a means of representing and quantifying differences in the character of two seismograms that are visually apparent, in the time or frequency domain, but which get suppressed in any single measure of fit.

We show how transfer operators can be usefully employed in many aspects of seismology with emphasis on frequency-domain representations at low frequency, and the time domain for higher frequency applications. We can express the general goal of inversion as the reduction of the transfer operator between observed and synthetic seismograms to the identity, thereby avoiding dominance by the largest arrivals and enhancing the influence of the full range of propagation processes. Broad classes of measures for comparison of times of arrival and amplitudes with quasi-linear properties can be constructed from the transfer operators through the use of a simple weighting function. This versatility highlights the unifying character of the transfer operator; and greatly simplifies the design of measurements targeted at specific aspects of the Earth’s structure.

A new technique is presented to jointly invert the teleseismic and Interferometric Synthetic Aperture Radar (InSAR) data by simultaneously searching for the hypocentre and the relative weight of InSAR data. In this technique, the parameters of causative fault is determined by using InSAR data first, and then the hypocentre is searched for by jointly inverting teleseismic and InSAR data with the assumption that each subfault on the fault is a potential hypocentre. With this technique, we investigated the source rupture process of the 2009 April 6 L’Aquila M_W 6.3 earthquake without the use of the existing hypocentre locations. Our estimated hypocentre is 42.366°N, 13.385°E, depth 6.9 km, with an uncertainty of 1∼2 km, similar to the hypocentre (42.348°N, 13.380°E, depth 9.5 km) determined by National Institute of Geophysics and Volcanology (INGV) using arrival time data within the epicentral distance of 50 km. Our joint inversion suggests a scalar moment of 3.5 × 10¹⁸ Nm, equivalent to a moment magnitude of M_W 6.3. The source process consists of two subevents with a total duration of 7.7 s. The first event (0∼3 s) corresponds to the slip patch near the hypocentre and the second (in the next 4.7 s) ruptured the other slip patch at 4∼16 km along the strike direction. These unilateral rupture characteristics of the L’Aquila earthquake are confirmed by the apparent source time functions (ASTFs) analysis. In addition, two resolution tests are performed to check the reliability of this work, clarifying the differences between the inversion results with teleseismic data only, InSAR data only and joint inversion, indicating that a higher resolution can be achieved through the joint inversion.

Angle of incidence amplitude variations of acoustic waves reflected from an interface is increasingly important in acoustic sea floor imaging and seismological studies. Such observations are almost solely interpreted assuming elastic wave theory. However, wave propagation through, and hence reflectivity from, liquid-saturated porous solids is complicated by the presence of the slow longitudinal (P2) wave. There have only been limited quantitative experimental tests of porous media reflectivity as a function of angle of incidence. Here, the acoustic reflectivity from a water-saturated porous plate is measured as a function of the angle of incidence using a specially developed ultrasonic reflectometer. The observed reflectivity agrees with that predicted using the Biot-type poroelastic theory; this work confirms the use of boundary conditions that allow fluid transfer across the reflecting interface. It is found that simpler elastic expressions based on equivalent-elastic solid cannot be reconciled with the observations.

We use ambient seismic noise and earthquake recordings on a temporary regional network in southern Norway to produce Rayleigh and Love wave phase velocity maps from 3 to 67 s period. Local dispersion curves are then jointly inverted for a 3-D shear wave velocity model of the region. We perform a two-step inversion approach. First, a direct search, Monte Carlo algorithm is applied to find best fitting isotropic velocity depth profiles. Those profiles are then used as initial models for a linearised inversion which takes into account radial anisotropy in the shear wave structure. Results reveal crustal as well as uppermost mantle structures in the studied region. Velocity anomalies in the upper crust are rather small in amplitude and can in most parts be related to surface geology in terms of rock densities. Old tectonic units like the Oslo Graben (300–240 Ma) and the Caledonian nappes (440–410 Ma) are clearly imaged. Furthermore, we find clear indications for localized crustal anisotropy of about 3 per cent. Despite generally poor resolution of interface depths in surface wave inversion, we find lateral variation of crustal thickness in agreement with previous studies. We are able to confirm and locate the transition from a slow lithospheric upper mantle underneath southern Norway to a fast shield-like mantle towards Sweden.

A fault made of two segments or asperities having different strengths and subject to a constant strain rate is considered. The fault is modelled by a discrete dynamical system made of two blocks coupled by a spring and pulled at constant velocity on a rough plane. We give a complete analytical solution for the evolution of the system. The long-term behaviour of the fault is studied by calculating the orbits of the system in the phase space. The dynamics of the system has four different modes and produces a variety of behaviours: the asperities may slip one at a time, originating a medium-size earthquake, or simultaneously, originating a large earthquake. In the latter case, the focus may be at one asperity or at the other. In some cases, the weaker asperity may slip twice, both before and after the failure of the stronger asperity. The time pattern of the seismic events generated by the fault is controlled by the stress distribution on the asperities and may include many different behaviours. We devise suitable correspondence rules allowing application of the discrete model to real fault systems. As an example, the model is applied to the 1964 great Alaska earthquake, which was originated by the failure of two asperities, and a possible evolution of this fault system is discussed.