Dipping Anisotropy Research Articles

Reproducing complex anisotropy patterns at subduction zones from splitting intensity analysis and anisotropy tomography

SUMMARYMeasurements of seismic anisotropy provide a lot of information on the deformation and structure as well as flows of the Earth's interior, in particular of the upper mantle. Even though the strong and heterogeneous seismic anisotropic nature of the upper mantle has been demonstrated by a wealth of theoretical and observational approaches , most of standard teleseismic body-wave tomography studies overlook P- and S-wave anisotropy, thus producing artefacts in tomographic models in terms of amplitude and localization of heterogeneities. Conventional methods of seismic anisotropy measurement have their limitations regarding lateral and mainly depth resolution. To overcome this problem much effort has been done to develop tomographic methods to invert shear wave splitting data for anisotropic structures, based on finite-frequency sensitivity kernels that relate model perturbations to splitting observations. A promising approach to image the upper mantle anisotropy is the inversion of splitting intensity (SI). This seismic observable is a measure of the amount of energy on the transverse component waveform and, to a first order, it is linearly related to the elastic perturbations of the medium through the 3-D sensitivity kernels, that can be therefore inverted, allowing a high-resolution image of the upper mantle anisotropy. Here we present an application of the SI tomography to a synthetic subduction setting. Starting from synthetic SKS waveforms, we first derived high-quality SKS SI measurements; then we used the SI data as input into tomographic inversion. This approach enables high-resolution tomographic images of upper-mantle anisotropy through recovering vertical and lateral changes in anisotropy and represents a propaedeutic step to the real cases of subduction settings. Additionally this study was able to detect regions of strong dipping anisotropy by allowing a 360° periodic dependence of the splitting vector.

The influence of anisotropic electrical resistivity on surface magnetotelluric responses and the design of two new anisotropic inversions

Using the 3-D axial anisotropy, the dipping anisotropy, and the azimuthal anisotropy as case studies, we investigated the influence of each anisotropic resistivity element on the magnetotelluric surface responses. To justify the strong and weak influence and edge effect, we have introduced the influence indices for the impedance components, and the edge effect indices for the tipper components. Interestingly, for decoupled modes, we found that {rho }_{xx} has a strong influence on Zxy, Zyy, and Ty, while {rho }_{yy} strongly affects Zyx, Zxx, and Tx. The three elements {rho }_{zz}, {rho }_{xz}, and {rho }_{yz} have only a very weak influence on all types of responses. For the coupled mode, {rho }_{xx}, {rho }_{yy}, and {rho }_{xy} display a strong influence on all responses. Based on our studies on the influence of the anisotropic resistivity elements, we design and propose two practical processes to replace the conventional axial, dipping, azimuthal, and general anisotropic inversions. First, the axial or dipping inversion can be approximately decoupled into {rho }_{x}-mode and {rho }_{y}-mode inversions. The decoupled mode inversions can be performed either independently and in parallel, or as a joint inversion. Second, since the three resistivity elements always show a weak influence, the general anisotropic inversion can be simplified to just the reduced coupled azimuthal anisotropic inversion with only three resistivity elements as outputs. Both proposed techniques can save a lot of the computational resources. Criteria to choose either the decoupled or coupled modes depend greatly on the magnitudes and distributions of the Zxx and/or Zyy, and Tx and/or Ty responses.Graphical

Simulation of diffusive solute transport in heterogeneous porous media with dipping anisotropy

Dipping anisotropy is a common feature in heterogeneous porous media that can substantially affect solute transport. For problems with complex geometry the influence of dipping anisotropy must be analyzed using numerical models, since suitable analytical solutions are not available. The most straightforward approach is to use a Cartesian coordinate system aligned with the material coordinate system. However, this approach is usually not practical, especially in 3D simulation domains with dipping layers and heterogeneous material properties. Furthermore, in the case of diffusion-dominated transport, the effect of anisotropy is often neglected. In this research, a general-purpose, fully 3-D unstructured grid code was developed to simulate diffusion-dominated solute transport in systems with dipping anisotropy, while accounting for complex geometry. The code has been verified against both 2-D and 3-D analytical solutions and has then been applied to two anisotropic diffusion problems, including an in-situ diffusion experiment and a hypothetical deep geologic repository, respectively. The simulation results indicate that consideration of anisotropy is required if the solute distribution in the rock matrix is of importance, in particular for assessing long-term evolution in layered systems. The formulation presented provides a versatile method for assessing diffusion-dominated solute transport in systems with dipping anisotropy subject to complex geometry.

Magnetotelluric Responses of an Anisotropic 1-D Earth with a Layer of Exponentially Varying Conductivity

The magnetotelluric (MT) sounding of a layered Earth model involving a transitional layer has been widely studied, and MT responses of the model with dipping anisotropic conductivity have also been treated. However, a model incorporating both a transitional layer and dipping anisotropy has seldom been considered. The analytical solution of such a geoelectrical model including three layers was derived in this study. The middle layer was a transitional layer with conductivity exponentially varying with depth, which was covered by a homogeneous layer and underlaid by a dipping anisotropic half-space. The electromagnetic (EM) fields in the transitional layer were explicitly solved with modified Bessel functions. The surface impedance was calculated recursively. The dependence of the apparent resistivity and impedance phase as well as the EM fields on different model parameters were investigated in detail. We believe that our analytical solution provides a useful complement to the theory of the one-dimensional (1D) inversion and interpretation based on the layered model with fixed conductivity.

Understanding the effect of 1-D dipping anisotropic conductivity on the response and interpretation of magnetotelluric data

SUMMARY Anisotropy in geological settings has been shown to be able to have a significant effect on data and to result in different interpretations when anisotropy is not taken into account. Recent work in inversion of electromagnetic data has emphasized the need for greater accuracy in interpretations where anisotropic effects dominate in data. We focus on how effectively inversions can extract anisotropic characteristics from magnetotelluric (MT) data for the 1-D dipping anisotropy case. We assess the sensitivity of 1-D MT data to each electrical conductivity component by examining the variability of polar plot eccentricity between analytic cases and by examining how sensitivity varies with increasing anisotropic dip angle. We apply a Tikhonov regularized inversion to both synthetic and experimental data using both an L2 norm and an Ekblom norm to approximate an L1 norm to identify the extent to which all model parameters associated with the 1-D dipping anisotropy case are recovered. We find that the application of an L1 norm aids in recovering the true depth extent and horizontal conductivities of an anisotropic layer when compared to the results from a standard L2 norm.

Shear-wave splitting beneath Fennoscandia — evidence for dipping structures and laterally varying multilayer anisotropy

SUMMARYThe geodynamic evolution of Fennoscandia in northern Europe (Finland, Sweden and Norway) is coined by ca. 3 Ga history of tectonic processes including continental growth in its central and eastern parts and Neogene uplift processes of the Scandinavian mountains (Scandes) located along its western edge. Many details are still under debate and we contribute with new findings from studying deep-seated seismic anisotropy. Using teleseismic waveforms of more than 260 recording stations (long-running permanent networks, previous temporary experiments and newly installed temporary stations) in the framework of the ScanArray experiment, we present the most comprehensive study to date on seismic anisotropy across Fennoscandia. The results are based on single and multi-event shear-wave splitting analysis of core refracted shear waves (SKS, SKKS, PKS and sSKS). The splitting measurements indicate partly complex, laterally varying multilayer anisotropy for individual areas. Consistent measurements at permanent and temporary recording stations over several years and for seismic events of specific source regions allow us to robustly constrain dipping anisotropic structures by adding systematic forward modelling. Although the data coverage is partly limited to only few source regions, our findings support concepts of continental growth due to individual episodes of (paleo-) subduction, each affecting a plunging of the anisotropic fast axis direction due to collisional deformation. Along the northern Scandes the fast axis direction (ϕ) is parallel to the mountain range (NE-SW), whereas an NNW-SSE trend dominates across the southern Scandes. In the south, across the Sorgenfrei–Tornquist Zone, a NW-SE trend of ϕ dominates which is parallel to this suture zone. The Oslo Graben is characterized by an NNE-SSW trend of ϕ. In northern Norway and Sweden (mainly Paleoproterozoic lithosphere), a dipping anisotropy with ϕ towards NE prevails. This stands in contrast to the Archean domain in the NE of our study region where ϕ is consistently oriented NNE-SSW. In the Finnish part of the Svecofennian domain, a complex two-layer anisotropy pattern is found which may be due to lateral variations around the seismic stations and which requires a higher data density than ours for a unique model building. Based on these findings our study demonstrates the importance of long recording periods (in the best case > 10 yr) to obtain a sufficient data coverage at seismic stations, especially to perform meaningful structural modelling based on shear-wave splitting observations.

Adaptive finite element modelling of three-dimensional magnetotelluric fields in general anisotropic media

We present a goal-oriented adaptive finite element (FE) modelling algorithm for 3-D magnetotelluric fields in generally anisotropic conductivity media. The model consists of a background layered structure, containing anisotropic blocks. Each block and layer might be anisotropic by assigning to them 3×3 conductivity tensors. The second-order partial differential equations are solved using the adaptive finite element method (FEM). The computational domain is subdivided into unstructured tetrahedral elements, which allow for complex geometries including bathymetry and dipping interfaces. The grid refinement process is guided by a global posteriori error estimator and is performed iteratively.The system of linear FE equations for electric field E is solved with a direct solver MUMPS. Then the magnetic field H can be found, in which the required derivatives are computed numerically using cubic spline interpolation. The 3-D FE algorithm has been validated by comparisons with both the 3-D finite-difference solution and 2-D FE results. Two model types are used to demonstrate the effects of anisotropy upon 3-D magnetotelluric responses: horizontal and dipping anisotropy. Finally, a 3D sea hill model is modelled to study the effect of oblique interfaces and the dipping anisotropy.

3D anisotropic modeling for airborne EM systems using finite-difference method

Abstract Most current airborne EM data interpretations assume an isotropic model, which is sometimes inappropriate, especially in regions with distinct dipping anisotropy due to strong layering and stratifications. In this paper, we investigate airborne EM modeling and interpretation for a 3D earth with arbitrarily electrical anisotropy. We implement the staggered finite-difference algorithm to solve the coupled partial differential equations for the scattered electrical fields. Whereas the current density that is connected to the diagonal elements of the anisotropic conductivity tensor is discretized by using the volume weighted average, the current density that is connected to the non-diagonal elements is discretized by using the volume current density average. Further, we apply a divergence correction technique designed specifically for 3D anisotropic models to speed up the modeling process. For numerical experiments, we take both VMD and HMD transmitting dipoles for two typical anisotropic cases: 1) anisotropic anomalous inhomogeneities embedded in an isotropic half-space; and 2) isotropic anomalous inhomogeneities embedded in an anisotropic host rock. Model experiments show that our algorithm has high calculation accuracy, the divergence correction technique used in the modeling can greatly improve the convergence of the solutions, accelerating the calculation speed up to 2 times for the model presented in the paper. The characteristics inside the anisotropic earth, like the location of the anomalous body and the principal axis orientations, can also be clearly identified from AEM area surveys.

Numerical modeling of contaminant transport in a stratified heterogeneous aquifer with dipping anisotropy

The combined influence of dip angle and adsorption heterogeneity on solute transport mechanisms in heterogeneous media can be understood by performing simulations of steady-state flow and transient transport in a heterogeneous aquifer with dipping anisotropy. Reactive and non-reactive contaminant transport in various types of heterogeneous aquifer is studied by simulations. The hydraulic conductivity (K) of the heterogeneous aquifer is generated by HYDRO_GEN with a Gaussian correla- tion spectrum. By considering the heterogeneity of the adsorption distribution coefficient (Kd), a perfect negative correlation between lnK and lnKd is obtained by using the spherical grains model. The generated K and Kd are used as input to groundwater flow and transport models to investigate the effects of dipping sedimentary heterogene- ity on contaminant plume evolution. Simulation results showed that the magnitude of the dip angle strongly controls the plume evolution in the studied anisotropic and heterogeneous aquifer. The retarded average pore-water velocity (v/R) of the adsorption model significantly controls the horizontal spreading of the plume. The bottom plume is intensively retarded in the zones between the dipping lenses of lower hydraulic conductivity and the no-flow bottom boundary. The implications of these findings are very important for the management of contaminated heterogeneous aquifers.

Adaptive finite element modeling of marine controlled-source electromagnetic fields in two-dimensional general anisotropic media

In this paper, we extend the scope of numerical simulations of marine controlled-source electromagnetic (CSEM) fields in a particular case of anisotropy (dipping anisotropy) to the general case of anisotropy by using an adaptive finite element approach. In comparison to a dipping anisotropy case, the first order spatial derivatives of the strike-parallel components arise in the partial differential equations for generally anisotropic media, which cause a non-symmetric linear system of equations for finite element modeling. The adaptive finite element method is employed to obtain numerical solutions on a sequence of refined unstructured triangular meshes, which allows for arbitrary model geometries including bathymetry and dipping layers. Numerical results of a 2D anisotropic model show both anisotropy strike and dipping angles have great influence on the marine CSEM responses.

Two triaxial induction tools: sensitivity to radial invasion profile‡

I study the responses of two different triaxial induction tools to invaded dipping anisotropic formations. I show that the triaxial measurements have generally higher sensitivity to the radial invasion profile, compared to the conventional induction measurements. This enables accurate interpretation of both the anisotropic formation properties and the invasion parameters. Multi-spacing and single-spacing multifrequency triaxial induction tools can both be used for this purpose. Failure to take the invasion properties into account may lead to misinterpretation of the vertical formation resistivity. Symmetrization of the apparent conductivity matrix opens ways for a visual interpretation of triaxial induction logs for the formation and the invasion zone properties. This technique enables simpler and faster inversion algorithms. I study how the effect of a conductive annulus forming around the invasion zone couples with effects of the dipping anisotropy and the dipping boundaries and show when these effects are additive. Thus, a visual detection of log parts affected by a conductive annulus becomes possible. The key tool for interpretation in complex 3D scenarios is efficient modelling software. I use a 3D finite-difference modelling approach to simulate responses of induction logging tools of the new generation. Its high efficiency enables simultaneous multi-spacing and multi-frequency computing of the tool responses to arbitrary 3D anisotropic formations that made the study possible.

Separation of azimuthal effects for new-generation resistivity logging tools — Part I

A symmetrization approach used in new-generation logging-while-drilling (LWD) resistivity tools separates the dipping anisotropy and dipping boundary effects. It deals with couplings between axial transmitters and tilted or transverse receivers. I have investigated the performance of two symmetrization schemes in full 3D scenarios for LWD and rigorously extended them to triaxial induction logging, including couplings between transverse transmitters and transverse receivers. Thus, I apply similar principles of data processing to new-generation wireline and LWD tools. The method enables separation of the formation response from the borehole eccentricity effect, which cannot be ignored for triaxial induction. The technique can accelerate and improve existing methods of formation interpretation by directly determining bed boundary positions, formation anisotropy azimuth, and tool eccentricity direction and by improving visual interpretation of raw tool data. The second objective of my investigation was a brief review of previously published work on a 3D finite-difference (FD) modeling approach, its latest development and its ability to simulate responses of new-generation resistivity tools in general 3D formations. This approach, based on the Lebedev staggered FD grid, handles arbitrary resistivity anisotropy effectively. Its high efficiency encourages its routine use for modeling. In addition, the method enables simultaneous multispacing and multifrequency computing at no cost. It makes the detailed investigation and further development of the separation technique possible.

AutomatedSKSsplitting and upper-mantle anisotropy beneath Canadian seismic stations

SUMMARY We have developed an automated method for measuring shear wave splitting and applied it to SKS phases recorded at permanent broad-band stations in Canada. Our method performs two measurements, one seeking to minimize the energy on the transverse component, the other minimizing the smaller of two eigenvalues calculated from the covariance matrix of particle motion. A short-term-average/long-term-average (STA/LTA) phase picker is used to identify SKS arrivals and successive splitting measurements are made on incrementally larger windows around the SKS arrival. The final result is derived from the longest series of windows over which the splitting parameters remain constant. In this study we have processed over 20 000 station/event combinations from 34 stations and 1540 events. Roughly 2 per cent of the data produce reliable estimates of splitting, due to the stringent quality controls applied. We find good correlation between our results and previously published results from the same stations. At some stations we find significant differences in results between the two methods, an observation that has been verified using manual measurements. In each case, eigenvalue derived measurements are consistent with a single layer of anisotropy but transverse-energy derived results require a more complex interpretation. This discrepancy can be explained by misalignment of horizontal components. Tests with synthetic seismograms show that component misalignment can lead to false interpretations of multilayer or dipping anisotropy using the transverse-energy method. The quality of results at individual stations is variable, being influenced both by the volume of available data (determined by station deployment date and the distribution of natural seismicity), and the performance of the STA/LTA picker used to define the start of the SKS window. We compare the orientation of the inferred anisotropy at each station with local tectonic features and directions of absolute plate motion (APM); there is no consistent correlation. Many stations give results that agree with both, while some agree better with local geology and others agree better with APM directions. Results are available through a dedicated website and provide a potential aid to other studies of anisotropy in the deep Earth.

Effects of anisotropy on the two-dimensional inversion procedure

Summary In this paper we show some of the effects that appear in magnetotelluric measurements over 2-D anisotropic structures, and propose a procedure to recover the anisotropy using 2-D inversion algorithms for isotropic models. First, we see how anisotropy affects the usual interpretation steps: dimensionality analysis and 2-D inversion. Two models containing general 2-D azimuthal anisotropic features were chosen to illustrate this approach: an anisotropic block and an anisotropic layer, both forming part of general 2-D models. In addition, a third model with dipping anisotropy was studied. For each model we examined the influence of various anisotropy strikes and resistivity contrasts on the dimensionality analysis and on the behaviour of the induction arrows. We found that, when the anisotropy ratio is higher than five, even if the strike is frequency-dependent it is possible to decide on a direction close to the direction of anisotropy. Then, if the data are rotated to this angle, a 2-D inversion reproduces the anisotropy reasonably well by means of macro-anisotropy. This strategy was tested on field data where anisotropy had been previously recognized.

The modelling of mise-à-la-masse anomalies in an anisotropic half-space by the integral equation method

An integral equation method is described for solving the mise-à-la-masse potential problem in a linear, homogeneous, and anisotropic half-space in which there are embedded equipotential conductors. The integral equation is Fredholm's equation of the first kind developed for the potential of the electric field. The unknown function is the normal component of the current density on the surfaces of the conductors. The unknown constant potential values of the various conductors can be determined using supplementary equations derived from the equation of continuity for each conductor. The kernel of the integral equation is Green's function of the single-layer potential for the linear, homogeneous, and anisotropic half-space. Numerical applications show that the mise-à-la-masse anomaly peaks are shifted to the up-dip direction from over the conductor. It is also difficult to discriminate between the effects caused by the dipping anisotropy or by the dip of the conductor using only the potential values on the ground surface.

Electrical potential due to a point current source over a layered conducting earth with dipping anisotropy

A compact analytical expression for the potential due to a point current source on a horizontally stratified earth with an overburden having dipping anisotropy has been obtained by using the Hankel transform technique and the principle of rotation of axes. The sounding curves for two configurations, Wenner and Schlumberger, are presented. It has been shown that if the depth of the anisotropic overburden is known, the inclination of the axis of anisotropy can be determined from the resistivity sounding curves.

MAGNETOTELLURIC EFFECT OF DIPPING ANISOTROPIES*

AbstractReddy, I. K., D. Rankin, 1971, Magnetotelluric Effect of Dipping Anisotropies, Geophysical Prospecting 19, 84–97.A solution is obtained for the magnetotelluric effect in the case of multi‐layered earth, each layer containing dipping anisotropy, with the strike of anisotropy oriented at an arbitrary angle to the measuring directions. A technique to compute tensor impedances and tensor apparent resistivities is presented and the importance of anisotropies in magnetotelluric interpretation is discussed.