Seismoelectric numerical simulation in 2D vertical transverse isotropic poroelastic medium

Seismoelectric coupling in an electric isotropic and elastic anisotropic medium is developed using a primary–secondary formulation. The anisotropy is of vertical transverse isotropic type and concerns only the poroelastic parameters. Based on our finite difference time domain algorithm, we solve the seismoelectric response to an explosive source. The seismic wavefields are computed as the primary field. The electric field is then obtained as a secondary field by solving the Poisson equation for the electric potential. To test our numerical algorithm, we compared our seismoelectric numerical results with analytical results obtained from Pride's equation. The comparison shows that the numerical solution gives a good approximation to the analytical solution. We then simulate the seismoelectric wavefields in different models. Simulated results show that four types of seismic waves are generated in anisotropic poroelastic medium. These are the fast and slow longitudinal waves and two separable transverse waves. All of these seismic waves generate coseismic electric fields in a homogenous anisotropic poroelastic medium. The tortuosity has an effect on the propagation of the slow longitudinal wave. The snapshot of the slow longitudinal wave has an oval shape when the tortuosity is anisotropic, whereas it has a circular shape when the tortuosity is isotropic. In terms of the Thomsen parameters, the radiation anisotropy of the fast longitudinal wave is more sensitive to the value of ε, while the radiation anisotropy of the transverse wave is more sensitive to the value of δ.     

Tutorial: unified 1D inversion of the acoustic reflection response

Acoustic inversion in one-dimension gives impedance as a function of travel time. Inverting the reflection response is a linear problem. Recursive methods, from top to bottom or vice versa, are known and use a fundamental wave field that is computed from the reflection response. An integral over the solution to the Marchenko equation, on the other hand, retrieves the impedance at any vertical travel time instant. It is a non-recursive method, but requires the zero-frequency value of the reflection response. These methods use the same fundamental wave field in different ways. Combining the two methods leads to a non-recursive scheme that works with finite-frequency bandwidth. This can be used for target-oriented inversion. When a reflection response is available along a line over a horizontally layered medium, the thickness and wave velocity of any layer can be obtained together with the velocity of an adjacent layer and the density ratio of the two layers. Statistical analysis over 1000 noise realizations shows that the forward recursive method and the Marchenko-type method perform well on computed noisy data.     

Fast and accurate three‐dimensional controlled source electromagnetic modelling†

We present a fast approximate method for three‐dimensional low frequency controlled source electro‐magnetic modeling. We apply the method to a synthetic model in a typical marine controlled source electromagnetic scenario, where conductivity and permittivity are different from the known background medium. For 3D configurations, fast computational methods are relevant for both forward and inverse modelling studies. Since this problem involves a large number of unknowns, it has to be solved efficiently to obtain results in a timely manner, without compromising accuracy. For this reason, the Born approximation, extended Born approximation and iterative extended Born approximation are implemented and compared with the full solution of the conjugate gradient fast Fourier transformation method. These methods are based on an electric field domain integral equation formulation. It is shown here how well the iterative extended Born approximation method performs in terms of both accuracy and speed with different configurations and different source positions. The improved accuracy comes at virtually no additional computational cost. With the help of this method, it is now possible to perform sensitivity analysis using 3D modelling in a timely manner, which is vital for controlled source electromagnetic applications. For forward modeling the solution at the sea‐bottom is of interest, because that is where the receivers are usually located. For inverse modeling, the accuracy of the solution in the target zone is important to obtain reasonably accurate conductivity values from the inversion using this approximate solution method. Our modelling studies show that the iterative extended Born approximation method is fast and accurate for both forward and inverse modelling. Sensitivity analysis as a function of the source position and different reservoir sizes validate the accuracy of the iterative extended Born approximation.     

Seismic and electromagnetic controlled-source interferometry in dissipative media

Seismic interferometry deals with the generation of new seismic responses by crosscorrelating existing ones. One of the main assumptions underlying most interferometry methods is that the medium is lossless. We develop an ‘interferometry‐by‐deconvolution’ approach which circumvents this assumption. The proposed method applies not only to seismic waves, but to any type of diffusion and/or wave field in a dissipative medium. This opens the way to applying interferometry to controlled‐source electromagnetic (CSEM) data. Interferometry‐by‐deconvolution replaces the overburden by a homogeneous half space, thereby solving the shallow sea problem for CSEM applications. We demonstrate this at the hand of numerically modeled CSEM data.     

Using multicomponent GPR to monitor cracks in a historical building

We tested the usefulness of acquiring multicomponent GPR data to detect cracks in a historical building, and to monitor their dynamics, caused by a slowly and irregularly moving landslide. We used 2 GHz bipolar antennas in a configuration that allows for acquiring the in-line and cross-line electric field components with x- and y-directed antennas. The 2 × 2 data matrix was collected on a floor in the building along transects at four different times over a period of one year. The data were processed with a standard 2D scalar algorithm and with the latest 3D single component vector algorithm that corrects for antenna effects. We have implemented a 3D single component vector migration algorithm in a 2.5D sense to produce 2D slices of a 3D vector migration image by applying the algorithm on line data. This procedure allows for migrating single component line data taking into account all vector effects as well as three-dimensional wave propagation. We show that the 2.5D vector migration images have a much better in-line resolution than the migration images obtained by applying a standard 2D scalar migration algorithm.The GPR profiles agree with the a priori information about the structure of the floor. In particular, we detected two different types of anomalies, only a few of which can be due to utilities and to metallic mesh. Some shallower anomalies agree well with the cracks visible on the tiling, suggesting that some cracks can be directly detected using GPR. Visually there were no changes in the cracks on the floor and no clear changes in the GPR data could be attributed to possible subsurface changes in the cracks. The variations in the GPR images seemed primarily caused by changes in the coupling of the antennas with the investigated structure (floor) depending on the season when the measurements were made. For this reason the monitoring aspect of the survey is not successful.     

Equipartitioning is not sufficient for Green's function extraction

The extraction of the Earth's Green's function from field fluctuations is a rapidly growing area of research.The principle of Green's function extraction is often related to the requirement of equipartitioning,which stipulates that the energy of field fluctuations is distributed evenly in some sense.We show the meaning of equipartitioning for a variety of different formulations for Green's function retrieval.We show that equipartitioning is not a sufficient condition,and provide several examples that illustrate this point.We discuss the implications of lack of equipartitioning for various schemes for the reconstruction of the Green's function in seismology.The theory for Green's function extraction is usually based on a statistical theory that relies on ensemble averages.Since there is only one Earth,one usually replaces the ensemble average with a time average.We show that such a replacement only makes sense when attenuation is taken into account,and show how the theory for Green's function extraction for oscillating systems can be extended to incorporate attenuation.     

The long-term fate of Cu, Zn, and Pb adsorption complexes at the calcite surface: An X-ray absorption spectroscopy study

In this study, the speciation of Zn²⁺, Pb²⁺, and Cu²⁺ ions sorbed at the calcite surface was monitored during a 2.5-year reaction period, using extended X-ray absorption spectroscopy to characterize metal speciation on the molecular scale. Experiments were performed using pre-equilibrated calcite-water suspensions of pH 8.3, at metal concentrations below the solubility of metal hydroxide and carbonate precipitates, and at constant metal surface loadings. The EXAFS results indicate that all three metals remained coordinated at the calcite surface as inner-sphere adsorption complexes during the 2.5-year ageing period, with no evidence to suggest slow formation of dilute metal-calcite solid solutions under the reaction conditions employed. All three divalent metals were found to form non-octahedral complexes upon coordination to the calcite surface, with Zn²⁺ adsorbing as a tetrahedral complex, Cu²⁺ as a Jahn-Teller distorted octahedral complex, and Pb²⁺ coordinating as a trigonal- or square-pyramidal surface complex. The non-octahedral configurations of these surface complexes may have hindered metal transfer from the calcite surface into the bulk, where Ca²⁺ is in octahedral coordination with respect to first-shell O. The use of pre-equilibrated calcite suspensions, with no net calcite dissolution or precipitation, likely prevented metal incorporation into the lattice as a result of surface recrystallization. The results from this study imply that ageing alone does not increase the stability of Zn²⁺, Pb²⁺, and Cu²⁺ partitioning to calcite if equilibrium with the solution is maintained during reaction; under these conditions, these metals are likely to remain available for exchange even after extended sorption times.