ALBERT

Description: The Fisher distribution is central to palaeomagnetism but presents several problems when used to characterize geomagnetic field directions as observed in sequences of volcanic rocks. First, it introduces a shallowing effect when used to define the mean of any group of directional unit vectors. This is problematic because it can suggest the presence of persistent non-axial dipole components when none are present. More importantly, it fails to capture the observed ‘long tail’ in distributions of both directions and associated virtual geomagnetic poles in terms of angular distance from a central direction. To achieve a good fit to data, it therefore requires the introduction of a second distribution (and therefore the estimation of additional parameters) or the arbitrary removal of data. Here we present a new distribution to describe palaeomagnetic directions and demonstrate that it overcomes both of these problems, generating robust indicators of both the central direction (or pole position) and the spread of palaeomagnetic data as defined by unit vectors. Starting from the assumption that poles (or directions) have an expected colatitude, rather than a mean location, we derive the spherical exponential distribution. We demonstrate that this new distribution provides a good fit to palaeomagnetic data sets from seven large igneous provinces between 15 and 65 Ma and also those produced by numerical dynamo models. We also use it to derive a new shape parameter which may be used as a diagnostic tool for testing goodness of fit of models to data and use this to argue for a shift in geomagnetic behaviour between 5 and 15 Ma. Furthermore, we point out that this new statistic can be used to determine the most appropriate distribution to be used when constructing confidence limits for poles.

Description: We develop an singular value decomposition-based compression of the Green's function matrix of an electromagnetic integral equation forward solver for global geomagnetic induction, on top of an fast Fourier transform reduction of the system to a block-diagonal form. With this approach, the memory usage and CPU time of Krylov subspace iterative solutions are significantly reduced at a very small cost of accuracy, making the accelerated forward solver well suited for 3-D inversions as well as forward simulations with multiple sources.

Description: Fifteen sites of lava flows from Martinique Island (FWI) have been selected to document the geomagnetic field in the Caribbean area over the past 2.5 Ma and further constrain the time-averaged field during this period. Identical characteristic directions were isolated using both AF and thermal stepwise demagnetization techniques in all flows. Nine mean-site directions have a normal polarity, while three others are reversed. The mean geomagnetic pole position obtained after reducing all directions to the same polarity is indistinguishable from the present north geographic pole. The dispersion is at least 8° larger than the values derived from the time-averaged field models and remains unexplained otherwise than resulting from the relatively small number of directions. The other three flows are characterized by large deviations from the expected north–south direction. One lava flow dated at 1.69 Ma (±0.02 Ma) is likely associated with a transitional field during the Gilsà subchron. The lava flow dated at 770 ka (±11 ka) coincides with the age of the Brunhes-Matuyama geomagnetic reversal and is also coeval with another intermediate flow of the same age found at Guadeloupe Island. The 617 ka (±52 ka) old unit is characterized by reversed directions that are evidently not related to the last reversal, but with other reversed polarity and transitional lava flows of the same age recorded, respectively at Mexico and La Palma island. We infer that the presence of reversed directions with the same age at distinct localities confirms that a short episode of reversed polarity has occurred during this period.

Description: We demonstrate that first differences of polar orbiting satellite magnetic data in the along-track direction can be used to obtain high resolution models of the lithospheric field. Along-track differences approximate the north–south magnetic field gradients for non-polar latitudes. In a test case, using 2 yr of low altitude data from the CHAMP satellite, we show that use of along-track differences of vector field data results in an enhanced recovery of the small scale lithospheric field, compared to the use of the vector field data themselves. We show that the along-track technique performs especially well in the estimation of near zonal spherical harmonic coefficients. Moreover, lithospheric field models determined using along-track differences are found to be less sensitive to the presence of unmodelled external field contributions and problems associated with the polar gap are ameliorated. Experiments in modelling the Earth's lithospheric magnetic field with along-track differences are presented here as a proof of concept. We anticipate that use of such along-track differences in combination with east–west field differences, as are now provided by the Swarm satellite constellation, will be important in building the next generation of lithospheric field models.

Description: Surface nuclear magnetic resonance (surface-NMR) is a promising technique for exploring shallow subsurface aquifer structures. Surface-NMR can be applied in environments that are characterized as a 1-D layered Earth. The technique utilizes a single loop and is referred to as magnetic resonance sounding. The technique referred to as magnetic resonance tomography (MRT) allows complex 2-D aquifer structures to be explored. Currently, MRT requires multiple loops and a roll along measurement scheme, which causes long survey time. We propose a loop layout using an elongated transmitter and an in-loop receiver arrays (ETRA) to conduct a 2-D survey with just one measurement. We present a comprehensive comparison between the new layout and the common approaches based on sensitivity and resolution analyses and show synthetic and field data. The results show that ETRA generates subsurface images at sufficient resolution with significantly lower survey times than other loop layouts.

Description: According to field observations, electromagnetic (EM) signals accompanying seismic waves can be recorded. The orders of magnitude of observed coseismic electric and magnetic signals associated with earthquakes are usually around 1 to 10 1 mV km –1 and 10 –2 to 1 nT, respectively. In this paper, we carry out numerical simulation of coseismic EM signals associated with seismic waves due to electrokinetic effect and compare with field observations. The seismic source is represented by a finite fault measuring 15 x 9 km 2 with a max slip displacement 1.5 m, corresponding to a M w 5.9 earthquake. While using the EM surface boundary condition of continuous horizontal EM components, the magnetic signals only accompany the late-arriving S waves at receiver near the ground surface. This is obviously different from field observations. Thus, we adopt another EM surface boundary condition which assumes the ground surface carries surface charge. For the used half-space model, a surface-charge density magnitude | Q sc | in excess of 10 –4 C m –2 is sufficient to make horizontal magnetic components clearly show up at the whole time duration of seismic waves. When | Q sc | increases, the contribution of surface-charge density to coseismic EM signals becomes more and more dominant comparing with that of the seismically induced streaming-current. We estimate the Q sc expected at the Earth's surface might be a value between –5 x 10 –4 and –0.1 C m –2 by the comparison between numerical results and field observations. The vertical magnetic signals only accompany the late-arriving seismic waves, because they are theoretically only induced by SH wave. The field observation results of vertical magnetic signals may be resulted from the scattering effect or the seismic dynamo effect. We conclude that electrokinetic effect combined with surface-charge assumption is one possible generation mechanism of the observed coseismic EM signals.

Description: We present a rigorous method for interpolation of electric and magnetic fields close to an interface with a conductivity contrast. The method takes into account not only a well-known discontinuity in the normal electric field, but also discontinuity in all the normal derivatives of electric and magnetic tangential fields. The proposed method is applied to marine 3-D controlled-source electromagnetic modelling (CSEM) where sources and receivers are located close to the seafloor separating conductive seawater and resistive formation. For the finite-difference scheme based on the Yee grid, the new interpolation is demonstrated to be much more accurate than alternative methods (interpolation using nodes on one side of the interface or interpolation using nodes on both sides, but ignoring the derivative jumps). The rigorous interpolation can handle arbitrary orientation of interface with respect to the grid, which is demonstrated on a marine CSEM example with a dipping seafloor. The interpolation coefficients are computed by minimizing a misfit between values at the nearest nodes and linear expansions of the continuous field components in the coordinate system aligned with the interface. The proposed interpolation operators can handle either uniform or non-uniform grids and can be applied to interpolation for both sources and receivers.

Description: We studied ionospheric responses to the 2012 April 11 M w 8.6 North Sumatra earthquake using total electron content (TEC) measurements with the regional Global Navigation Satellite System network. This earthquake ruptured the oceanic lithosphere off the Indian Ocean coast of North Sumatra, and is known as the largest strike-slip earthquake ever recorded. Coseismic ionospheric disturbances (CIDs) with rapid TEC enhancement of a few TEC units propagated northward with a speed of acoustic waves (~1 km s –1 ). Resonant atmospheric oscillation with a frequency ~4 mHz have been found as monochromatic oscillation of TEC lasting for an hour after the main shock and the largest aftershock. We compared CID amplitudes of 21 earthquakes world-wide with moment magnitudes ( M w ) 6.6–9.2. They roughly obeyed a law such that CID amplitude increases by two orders of magnitude for the M w increase of three. The 2012 North Sumatra earthquakes slightly deviated negatively from the trend possibly reflecting their strike-slip mechanisms, that is small vertical crustal movements for their magnitudes.

Description: We investigate polarity reversals in the geodynamo using a rotating, convection-driven dynamo model. As the flow in rapidly rotating convection is dominated by columns aligned with the axis of rotation, the focus is on the dynamics of columnar vortices. By studying the growth of a seed magnetic field to a stable axial dipole field, we show that the magnetic field acts in ways that significantly enhance the relative helicity between cyclonic and anticyclonic vortices. This flow asymmetry is the hallmark of a dipolar dynamo. Strong buoyancy, on the other hand, offsets the effect of the magnetic field, establishing parity between positive and negative vortices. As the dipole field is deprived of the helicity required to support itself, the dynamo is pushed into a reversing state. This is a likely regime for polarity reversals in the Earth's core. The integral lengthscale at which buoyancy injects energy is not significantly different from the convective flow lengthscale, which implies that buoyancy does not feed vortices at the small scales where non-linear inertia is present. The lengthscale at which the Lorentz force acts in the reversing dynamo is small, which may allow the passive presence of non-linear inertia in the small scales.

Description: We illustrate a new imaging method to estimate the depth to the sources of potential fields and the structural index. The method consists of applying the Depth from EXtreme Point (DEXP) transformation to the ratio (R) between two different-order partial derivatives of the field. While the scaling function of the potential field depends on the structural index, we show that the scaling function of R merely depends on the difference between the two used orders of differentiation. This allows three main features to be established for the DEXP transformation of R: (1) it is independent from the structural index; (2) the estimation of the source depths is fully automatic, simply consisting in the search of position of the extreme points of the DEXP image and (3) the structural index of each source is finally determined from the scaling function or the extreme points using the estimated depth. Besides the well-known characteristics of the DEXP transformation, such as high-resolution and stability, the DEXP transformation of R enjoys one more relevant feature: it can be applied to multisource cases, yielding simultaneously correct estimations of structural index and depth for each source in the same image. However, while the DEXP transformation is a linear transformation of the field, the DEXP transformation of R is non-linear, and a procedure is described to circumvent the non-linear effects. The method is tested with synthetic examples and the estimated source parameters show a good agreement with the true values. The method was applied also to real magnetic data from the Pima copper mine, Arizona, USA, Hamrawien area, Egypt and Cataldere, Bala district of Turkey. The results are consistent with the known information about the causative sources.