ALBERT

Description: Lying below Vatnajökull ice cap in Iceland, Bárðarbunga stratovolcano began experiencing wholesale caldera collapse in 2014 August 16, one of the largest such events recorded in the modern instrumental era. Simultaneous with this collapse is the initiation of a plate boundary rifting episode north of the caldera. Observations using the international constellation of radar satellites indicate rapid 50 cm d –1 subsidence of the glacier surface overlying the collapsing caldera and metre-scale crustal deformation in the active rift zone. Anomalous earthquakes around the rim of the caldera with highly nondouble-couple focal mechanisms provide a mechanical link to the dynamics of the collapsing magma chamber. A model of the collapse consistent with available geodetic and seismic observations suggests that the majority of the observed subsidence occurs aseismically via a deflating sill-like magma chamber.

Description: Deformation experiments on partially molten rocks in simple shear form melt bands at 20° to the shear plane instead of at the expected 45° principal compressive stress direction. These melt bands may play an important role in melt focusing in mid-ocean ridges. Such shallow bands are known to form for two-phase media under shear if strongly non-Newtonian power-law creep is employed for the solid phase, or anisotropy imposed. However laboratory experiments show that shallow bands occur regardless of creep mechanism, even in diffusion creep, which is nominally Newtonian. Here we propose that a couple of forms of two-phase damage allow for shallow melt bands even in diffusion creep.

Description: Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystallographic preferred orientation or CPO) whose observable signatures include shear-wave splitting and azimuthal dependence of surface wave speeds. Comparison of these signatures with mantle flow models thus allows mantle dynamics to be unraveled on global and regional scales. However, existing self-consistent models of CPO evolution are computationally expensive when used with 3-D and/or time-dependent convection models. Here we propose a new method, called ANPAR, which is based on an analytical parametrization of the crystallographic spin predicted by the second-order (SO) self-consistent theory. Our parametrization runs 2–6  x  10 4 times faster than the SO model and fits its predictions for CPO and crystallographic spin with a variance reduction 〉99 per cent. We illustrate the ANPAR model predictions for the deformation of olivine with three dominant slip systems, (010)[100], (001)[100] and (010)[001], for three uniform deformations (uniaxial compression, pure shear and simple shear) and for a corner-flow model of a spreading mid-ocean ridge.

Description: We investigate the capability of Time Reversal Mirror (TRM) algorithm to image local acoustic sources (〈3.5 km) associated with complex, sustained volcanic eruptions. Accurate source localization for volcano infrasound (low-frequency acoustic waves) is often challenging due to pronounced volcanic topography and emergent arrivals of infrasound signals. While the accuracy of the conventional approaches (e.g. triangulation and semblance method) can be severely compromised by the complex volcanic settings, a TRM-based method may have the potential to properly image acoustic sources by the use of full waveform information and numerical modelling of the time-reversed wavefield. We apply the TRM algorithm to a pyroclastic-laden eruption (sustained for ~60 s) at Santiaguito Volcano, Guatemala, and show that an ordinary TRM operation can undergo significant reduction of its focusing power due to strong topographic propagation effects (e.g. reflection and diffraction). We propose a weighted imaging condition to compensate for complicated transmission loss of the time-reversed wavefield and demonstrate that the presented condition significantly improves the focusing quality of TRM in the presence of complex topography. The consequent TRM source images exhibit remarkable agreement with the visual observation of the eruption implying that the TRM method with a proper imaging condition can be used to localize and track acoustic sources associated with complex volcanic eruptions.

Description: We present a strategy to thoroughly investigate the effects of prominent topography on the surface tilt due to a spherical pressure source. We use Etna's topography as a case of study and, for different source positions, we compare the tilt fields calculated through (i) a 3-D boundary element method and (ii) analytical half-space solutions. We systematically determine (i) the source positions leading to the strongest tilt misfits when numerical and analytical results are compared and (ii) the surface areas where the strongest distortions in the tilt field are most likely to be observed. We also demonstrate that, under critical circumstances, in terms of respective positions of pressure source and observation points, results of inversion procedures aimed at retrieving the source parameters can be misleading, if tilt data are analysed using models that do not account for topography.

Description: The agreement between shear wave velocities for the Earth's inner core observed from seismology with those derived from mineral physics is considerably worse than for any other region of the Earth. Furthermore, there is still debate as to the phase of iron present in the inner core, particularly when alloying with nickel and light elements is taken into account. To investigate the extent to which the mismatch between seismology and mineral physics is a function of either crystal structure and/or the amount of nickel present, we have used ab initio molecular dynamics simulations to calculate the elastic constants and seismic velocities ( V p and V s ) of face centred cubic (fcc) iron at Earth's inner core pressures (360 GPa) and at temperatures up to ~7000 K. We find that V p for fcc iron (fcc-Fe) is very similar to that for hexagonal close packed (hcp) iron at all temperatures. In contrast, V s for fcc-Fe is significantly higher than in hcp-Fe, with the difference increasing with increasing temperature; the difference between V s for the core (from seismology) and V s for fcc-Fe exceeds 40 per cent. These results are consistent with previous work at lower temperatures. We have also investigated the effect of 6.5 and 13 atm% Ni in fcc-Fe. We find that Ni only slightly reduces V p and V s (e.g. by 2 per cent in V s for 13 atm% Ni at 5500 K), and cannot account for the difference between the velocities observed in the core and those of pure fcc-Fe. We also tried to examine pre-melting behaviour in fcc-Fe, as reported in hcp-Fe by extending the study to very high temperatures (at which superheating may occur). However, we find that fcc-Fe spontaneously transforms to other hcp-like structures before melting; two hcp-like structures were found, both of hexagonal symmetry, which may most easily be regarded as being derived from an hcp crystal with stacking faults. That the structure did not transform to a true hcp phase is likely as a consequence of the limited size of the simulation box (108 atoms). At 360 GPa, in pure fcc-Fe, we find that the transition from fcc to the hcp-like structure occurs at 7000 K, whereas in the Ni bearing system, the transition occurs at higher temperature (7250 K). This reinforces previous work showing that fcc-Fe might transform to hcp-Fe just before melting, and that Ni tends to stabilize the fcc structure with respect to hcp.

Description: Viscoelastic behaviour of materials in nature is observed in post-event deformations due to seismic or volcanic activities. In this paper, by adopting the correspondence principle, we propose an inelastic model to predict first the Laplace-domain response of a transversely isotropic viscoelastic half-space due to a shear or tensile fault of polygonal shape. The displacement and stress fields in the time domain are then obtained using an efficient and accurate algorithm for the inverse Laplace transform. Numerical examples are presented to validate the proposed solution and to show the viscoelastic displacement and stress fields due to a strike-slip, dip-slip and tensile fault of rectangular shape. The obtained results indicate that both viscoelasticity and transverse isotropy play significant roles in the viscoelastic response of the half-space due to faults, which could be used as benchmarks for the future numerical analysis of realistic post-seismic or volcanic event.

Description: One of the unresolved questions concerning fault deformation is the degree and cause of localization of shear at depth beneath a fault. Geologic observations of exhumed shear zones indicate that while the motion is no longer planar, it can still be localized near the down-dip extension of the fault; however, the degree of localization is uncertain. We employ simple analytic and numerical models to investigate the structural form of distributed shear beneath a strike-slip fault, and the relative importance of the physical mechanisms that have the potential to localize a shear zone. For a purely depth dependent viscosity, = 0 exp (– z / z 0 ), we find that a shear zone develops with a half-width $\delta _w\sim \sqrt{z_0}$ for small z 0 at the base of the layer, where lengths are non-dimensionalized by the layer thickness ( d km). Including a non-linear stress–strain-rate relation ( $\dot{\epsilon }\propto \sigma ^n$ ) scales w by $1/\sqrt{n}$ , comparable to deformation length scales in thin viscous sheet calculations. We find that the primary control on the shear-zone width is the depth dependence of viscosity that arises from the temperature dependence of viscosity and the increase in temperature with depth. As this relationship is exponential, scaling relations give a dimensional half-width that scales approximately as $$ \tilde{\delta }_w\approx T_{\frac{1}{2}}\sqrt{\frac{Rd}{nQ\beta }}\text{ km}, $$ where $T_{\frac{1}{2}}$ (K) is the temperature at the midpoint of the layer, R (J mol –1 K –1 ) the gas constant, Q (J mol –1 ) the activation energy and β (K km –1 ) the geothermal gradient. This relation predicts the numerical results for the parameter range consistent with continental rheologies to within 2–5 per cent and shear-zone half-widths from 2 to 6 km. The inclusion of shear-stress heating reduces w by only an additional 5–25 per cent, depending on the initial width of the shear zone. While the width of the shear zone may not decrease significantly, local temperature increases from shear-stress heating range from 50 to 300 °C resulting in a reduction in viscosities beneath the fault of several orders of magnitude and a concomitant reduction in the stresses needed to drive the motion.

Description: The equation that relates pressure, temperature and volume and is described by parameters that are function of temperature at 1 bar (hereafter called thermal equation of state, TEOS), has practical computational advantages for petrological and geophysical applications over the equation that considers explicitly a thermal pressure. Some considerations that justify the use of the TEOS are discussed here. (1) The assumption that the parameters are function of temperature is perhaps better understood by looking at the Helmholtz energy function that is implicitly assumed in the case of an equation of state (EOS) derived from interatomic potentials. A test case shows that the Helmholtz energy related to the Vinet EOS and the Helmholtz energy from the Debye model are very similar. (2) The TEOS should be able to reproduce thermal expansion (α), isothermal bulk modulus ( K T ) and heat capacity ( C p and C v ) at high P , T computed from a lattice vibration model. The generalized Rydberg EOS applied to MgO is able to fit reasonably well the properties computed using Jacobs’ lattice dynamics formulation ( T range = 300–3000 K, P range = 1 bar–1500 kbar). (3) It is shown that in the case of MgO, the TEOS can be used quite successfully for extrapolation that goes beyond the P , T range of the measured/given data. Some physical constraints need to be applied to the derivation of the volume, bulk modulus and derivative of the bulk modulus with pressure at 1 bar. (4) The pressure dependence of the reference parameters in the TEOS that was inferred several decades ago is only apparent. A numerical computation demonstrates that the combined pressure effect in the terms defining the partial derivative of the reference V and K (and K') over temperature cancels out, making the reference parameters independent of pressure at any condition.

Description: The equation that relates pressure, temperature and volume and is described by parameters that are function of temperature at 1 bar (hereafter called thermal equation of state, TEOS), has practical computational advantages for petrological and geophysical applications over the equation that considers explicitly a thermal pressure. Some considerations that justify the use of the TEOS are discussed here. (1) The assumption that the parameters are function of temperature is perhaps better understood by looking at the Helmholtz energy function that is implicitly assumed in the case of an equation of state (EOS) derived from interatomic potentials. A test case shows that the Helmholtz energy related to the Vinet EOS and the Helmholtz energy from the Debye model are very similar. (2) The TEOS should be able to reproduce thermal expansion (α), isothermal bulk modulus ( K T ) and heat capacity ( C p and C v ) at high P , T computed from a lattice vibration model. The generalized Rydberg EOS applied to MgO is able to fit reasonably well the properties computed using Jacobs’ lattice dynamics formulation ( T range = 300–3000 K, P range = 1 bar–1500 kbar). (3) It is shown that in the case of MgO, the TEOS can be used quite successfully for extrapolation that goes beyond the P , T range of the measured/given data. Some physical constraints need to be applied to the derivation of the volume, bulk modulus and derivative of the bulk modulus with pressure at 1 bar. (4) The pressure dependence of the reference parameters in the TEOS that was inferred several decades ago is only apparent. A numerical computation demonstrates that the combined pressure effect in the terms defining the partial derivative of the reference V and K (and K') over temperature cancels out, making the reference parameters independent of pressure at any condition.

Description: A knowledge of subsurface temperatures in sedimentary basins, fault zones, volcanic environments and polar ice sheets is of interest for a wide variety of geophysical applications. However, the process of drilling deep boreholes in these environments to provide access for temperature and other measurements invariably disturbs the temperature field around a newly created borehole. Although this disturbance dissipates over time, most temperature measurements are made while the temperature field is still disturbed. Thus, the measurements must be ‘corrected’ for the drilling-disturbance effect if the undisturbed temperature field is to be determined. This paper provides compact analytical solutions for the thermal drilling disturbance based on 1-D (radial) and 2-D (radial and depth) Green's functions (GFs) in cylindrical coordinates. Solutions are developed for three types of boundary conditions (BCs) at the borehole wall: (1) prescribed temperature, (2) prescribed heat flux and (3) a prescribed convective condition. The BC at the borehole wall is allowed to vary both with depth and time. Inclusion of the depth dimension in the 2-D solution allows vertical heat-transfer effects to be quantified in situations where they are potentially important, that is, near the earth's surface, at the bottom of a well and when considering finite-drilling rates. The 2-D solution also includes a radial- and time-dependent BC at the earth's surface to assess the impact of drilling-related infrastructure (drilling pads, mud pits, permanent shelters) on the subsurface temperature field. Latent-heat effects due to the melting and subsequent refreezing of interstitial ice while drilling a borehole through ice-rich permafrost can be included in the GF solution as a moving-plane heat source (or sink) located at the solid–liquid interface. Synthetic examples are provided illustrating the 1-D and 2-D GF solutions. The flexibility of the approach allows the investigation of thermal drilling effects in rock or ice for a wide variety of drilling technologies. Numerical values for the required radial GFs G R are available through the Advanced Cooperative Arctic Data and Information Service at doi:10.5065/D64F1NS6.

Description: Tarim Craton is a Precambrian block situated in northwest China, just north of the Tibetan Plateau, where a large sedimentary basin with abundant hydrocarbon potential has developed. Accurate heat flow data for Tarim is vital for understanding the lithospheric evolution and hydrocarbon generation in this area; however, there were unavailable until now, due to a lack of high quality steady-state temperature logging data. Here, we report 10 new heat flow values derived from steady-state temperature logging and measured thermal conductivity data. New heat flow values range from 40.1 to 49.4 mW m –2 , with a mean of 43.1 ± 3.0 mW m –2 . In addition, radiogenic heat production from the sediments accounts for 20 per cent of the observed surface heat flow, whilst the mantle heat flow is estimated to be as low as 6–15 mW m –2 ; this indicates a dominant contribution from crustal heat, to the observed heat flow. The average heat flow and crustal temperature in the Tarim Craton are markedly lower than those in the Tibetan Plateau, whilst the calculated rheological strength of the lithosphere, beneath Tarim, is sufficiently large to resist the elevation-induced gravitational potential energy difference between Tarim and Tibet. This inherited thermal and rheological contrast, between the craton and Plateau, can be traced back to before the India–Asia collision; this accounts for the differential active deformation pattern in the Tarim Craton and adjacent areas.

Description: In this study, equations are developed that predict for synthetic sedimentary rocks (clastics, carbonates and evapourates) thermal properties comprising thermal conductivity, specific heat capacity and thermal diffusivity. The rock groups are composed of mineral assemblages with variable contents of 15 major rock-forming minerals and porosities of 0–30 per cent. Petrophysical properties and their well-logging-tool-characteristic readings were assigned to these rock-forming minerals and to pore-filling fluids. Relationships are explored between each thermal property and other petrophysical properties (density, sonic interval transit time, hydrogen index, volume fraction of shale and photoelectric absorption index) using multivariate statistics. The application of these relations allows computing continuous borehole profiles for each rock thermal property. The uncertainties in the prediction of each property vary depending on the selected well-log combination. Best prediction is in the range of 2–8 per cent for the specific heat capacity, of 5–10 per cent for the thermal conductivity, and of 8–15 for the thermal diffusivity, respectively. Well-log derived thermal conductivity is validated by laboratory data measured on cores from deep boreholes of the Danish Basin, the North German Basin, and the Molasse Basin. Additional validation of thermal conductivity was performed by comparing predicted and measured temperature logs. The maximum deviation between these logs is 〈3 °C. The thermal-conductivity calculation allowed an evaluation of the depth range in which the palaeoclimatic effect on the subsurface temperature field can be observed in the North German Basin. This effect reduces the surface heat-flow density by 25 mW m –2 .

Description: It is important to know the electrokinetic properties of crustal rocks for interpreting the conductivity mechanisms and seismoelectric phenomena during earthquakes and seismoelectric well logging. In this study, electrokinetic experiments are conducted using a special core-holder by employing an AC lock-in technique. A series of experiments are conducted on 10 sandstone samples to measure the streaming potentials and streaming currents, and the experiments on each sample are done at six different salinities. The streaming potential coefficient and streaming current coefficient are calculated from the measured streaming potentials and streaming currents. The experimental results show that streaming potential coefficient and streaming current coefficient decrease as the salinity increases. The dependence of these two coefficients on permeability and pore radius are analysed and compared with previous works. At low salinities, the streaming potential coefficient and streaming current coefficient increase with the increasing permeability and pore radius. At high salinities, the streaming potential coefficient (streaming current coefficient) almost share a same value for 10 different samples. This conclusion indicates that the differences of rock parameters can only be well recognized at lower salinities, and the electrokinetic signals are invalid at high salinities, which offers a restrictive condition for using the amplitude of electrokinetic signals to estimate rock parameters. The zeta-potential have also been estimated through combined measurements of streaming potential and streaming current. The surface conductivity and its contribution to electrokinetic effects are determined from a comparison of zeta-potentials by two different methods, and then the validation of the Helmholz–Smoluchowski equation for a capillary tube is tested in rocks. We also compare our date with theoretical and experimental works, and set up an expression about the relationship between zeta potential and salinity, which fits the experimental data well.

Description: We used ab initio molecular dynamics to calculate the elastic constants of MgSiO 3 , FeSiO 3 and (Fe 0.5 Mg 0.5 )SiO 3 perovskite under lower-most mantle conditions (136 GPa, 2000–4000 K). At 0 K, V p and V s for FeSiO 3 perovskite are 12 and 18 per cent lower, respectively than those for MgSiO 3 , in agreement with previous work. The difference in velocity, however, increases with temperature for high spin (but not low spin) states and at 4000 K, V p and V s for the end-member FeSiO 3 are, respectively, 19 and 34 per cent lower than those of MgSiO 3 . We find that (dln V s /dln V p ) T,P of Fe x Mg 1- x O 3 remains below 2 for all relevant iron concentrations and lower than the value of 3 seen in most ultralow velocity zones (ULVZ). Moreover, we are unable to match simultaneously the observed density increase and shear wave velocity reduction shown by ULVZs by increasing the ferrous iron content in perovskite except for the largest density increases and the smallest shear wave decreases observed in ULVZs. Assuming that current seismic estimates of ULVZ properties are accurate, our results suggest that ferrous iron enrichment alone cannot explain ULVZs.