Chester J. Weiss

Mapping thin resistors and hydrocarbons with marine EM methods : Insights from 1D modeling

The use of marine controlled-source electromagnetic EM (CSEM) sounding to detect thin resistive layers at depths below the seafloor has been exploited recently to assess the resistivity of potential hydrocarbon reservoirs before drilling. We examine the sensitivity of the CSEM method to such layers with forward and inverse modeling in one and three dimensions. The 3D modeling demonstrates that if both source and receivers are over a tabular 3D target, 1D modeling predicts the observed response to very high accuracy. Experimental design can thus be based on 1D analysis in which hundreds of range and frequency combinations can be computed to find the optimal survey parameters for a given target structure. Modeling in three dimensions shows that the vertical electric-field response is largest over the edges of a 3D target. The 3D modeling also suggests that a target body needs to have a diameter twice the burial depth to be reliably seen by CSEM sounding. A simple air-wave model (energy propagating from source to receiver via the atmosphere) allows the effects of the target layer and atmosphere to be separated and shows where sensitivity to the target is diminished or lost because of finite water depth as a function of range, frequency, and seafloor resistivity. Unlike DC resistivity sounding, the marine CSEM method is not completely T-equivalent and, in principle, can resolve resistivity and thickness separately. Smooth inversion provides an estimate of the method’s resolving power and highlights the fact that although the radial CSEM fields contain most of the sensitivity to the thin resistive target, inverted alone they produce only increasing resistivity with depth. Inclusion of the radial mode CSEM data forces the recovery of the thin resistor, but magnetotelluric data can be used more effectively to achieve the same result.

Mapping thin resistors and hydrocarbons with marine EM methods, Part II — Modeling and analysis in 3D

The electromagnetic fields surrounding a thin, subseabed resistive disk in response to a deep-towed, time-harmonic electric dipole antenna are investigated using a newly developed 3D Cartesian, staggered-grid modeling algorithm. We demonstrate that finite-difference and finite-volume methods for solving the governing curl-curl equation yield identical, complex-symmetric coefficient matrices for the resulting N×N linear system of equations. However, the finite-volume approach has an advantage in that it naturally admits quadrature integration methods for accurate representation of highly compact or exponentially varying source terms constituting the right side of the resulting linear system of equations. This linear system is solved using a coupled two-term recurrence, quasi-minimal residual algorithm that doesnot require explicit storage of the coefficient matrix, thus reducing storage costs from 22N to 10N complex, double-precision words with no decrease in computational performance. The disk model serve...

Electromagnetic induction in a fully 3‐D anisotropic earth

The bulk electrical anisotropy of sedimentary formations is a macroscopic phenomenon which can result from the presence of porosity variations, laminated shaly sands, and water saturation. Accounting for its effect on induction log responses is an ongoing research problem for the well-logging community since these types of sedimentary structures have long been correlated with productive hydrocarbon reservoirs such as the Jurassic Norphlet Sandstone and Permian Rotliegendes Sandstone. Presented here is a staggered-grid finite-difference method for simulating electromagnetic (EM) induction in a fully 3-D anisotropic medium. The electrical conductivity of the formation is represented as a full 3£ 3 tensor whose elements can vary arbitrarily with position throughout the formation. To demonstrate the validity of this approach, finite-difference results are compared against analytic and quasi-analytic solutions for tractable 1-D and 3-D model geometries. As a final example, we simulate 2C‐40 induction tool responses in a crossbedded aeolian sandstone to illustrate the magnitude of the challenge faced by interpreters when electrical anisotropy is neglected.

Adaptive finite-element modeling using unstructured grids: The 2D magnetotelluric example

Existing numerical modeling techniques commonly used for electromagnetic EM exploration are bound by the limitations of approximating complex structures using a rectangular grid.A more flexible tool is the adaptive finite-element FE method using unstructured grids. Composed of irregular triangles, an unstructured grid can readily conform to complicated structural boundaries. To ensure numerical accuracy, adaptive refinement usinganaposteriorierrorestimatorisperformediterativelytorefinethegridwheresolutionaccuracyisinsufficient.Tworecently developed asymptotically exact a posteriori error estimators are based on a superconvergent gradient recovery operator.The first reliessolelyonthenormeddifferencebetweentherecoveredgradients and the piecewise constant FE gradients and is effective for lowering the global error in the FE solution. For many problems, an accurate solution is required only in a few discrete regionsandamoreefficienterrorestimatorispossiblebyconsidering the local influence of errors from coarse elements elsewhere in the grid. The second error estimator accomplishes this by using weights determined from the solution to an appropriate dual problem to modify the first error estimator. Application of thesemethodsfor2DmagnetotelluricMTmodelingreveals,as expected, that the dual weighted error estimator is far more efficientinachievingaccurateMTresponses.Refiningabout15%of elements per iteration gives the fastest convergence rate. For a given refined grid, the solution error at higher frequencies varies in proportion to the skin depth, requiring refinement about every

The fallacy of the “shallow-water problem” in marine CSEM exploration

The recent explosion of activity in offshore controlled-source electromagnetic (CSEM) exploration has shown, both theoretically and in practice for the time-harmonic case, that shallow-water environments (depths less than, say, 300 m ) can pose a significant challenge for detection and characterization of thin resistive targets in the subsurface because the weakly attenuated atmospheric response overprints the weaker target response. As an alternative, the transient CSEM experiment is considered to explore the nature of the “airwave” signature when viewed from the perspective of CSEM time series. The signature of a thin, isolated, resistive horizon is computed by using the quasi-analytic solution for a 1D earth in response to excitation by a horizontal electric dipole antenna. That signature, clearly seen in the transient data, generally lies in the time interval between the arrivalof the airwave and the late-time seawater response.The fact that either decreasing the water depth or increasing the source-r...

Mapping 3D salt using the 2D marine magnetotelluric method: Case study from Gemini Prospect, Gulf of Mexico

The dominant salt body at Gemini Prospect, Gulf of Mexico, has been analyzed by seismic methods, revealing a complex 3D salt volume at depths 1 to 5 km beneath the mud line. Because of the high contrast in electrical conductivity between the salt and surrounding sediments, Gemini is an attractive target for electromagnetic interrogation. Using a broadband magnetotelluric (MT) sensor package developed at the Scripps Institution of Oceanography, data in the period band of 1 to 3000 s were collected at 42 sites in a series of profiles over Gemini, one of which was directly over a linear ridgelike salt feature striking roughly northwest–southeast and another orthogonal to it. These two profiles reveal that the strongest MT response arises when the electric field is oriented northeast– southwest. We test the suitability of 2D inversion of these data for recovering the true salt structure by examining inversions of both actual data and synthetic 3D MT responses derived from the seismically inferred salt volume. Occam inversions of the northeast–southwest component result in resistivity images that generally agree with the seismic data, whereas inversions of the complementary component yield significantly poorer fidelity. Disagreement is greatest (1– 2 km) along the salt sides and base. Depth errors for top of salt are less than 500 m. Although thin, deep salt (< 1k m thick at 5 km depth) is not well resolved, the inversions reveal a resistive basement and a shallow subseabed environment rich in electrical heterogeneity that is weakly, if at all, suggested by the seismic data. A notable exception is a correlation between a previously uninterpreted seismic reflector and the base of a shallow resistivity anomaly whose presence is consistent with gas accumulation near the hydrate stability zone.

Electromagnetic induction in a generalized 3D anisotropic earth, Part 2: The LIN preconditioner

A practical limitation in the use of generalized 3D forward modeling algorithms for inversion of electromagnetic data is the high computational cost of solving large, ill‐conditioned systems of linear equations arising from the discretization of the governing Maxwell equations. To address this problem, a new class of preconditioners has recently been proposed which is based on a Helmholtz decomposition of the electric field in the low induction number (LIN) regime. This paper further develops that idea and introduces a LIN preconditioner which can be applied to problems characterized by a fully generalized anisotropic medium. Included are sample calculations demonstrating a reduction by two orders of magnitude in the number of “quasi‐minimal residual” iterates and a speedup by a factor of approximately four in the solution time for one forward calculation. Also included are results previously unobtainable by standard Jacobi preconditioning for simulating multicomponent induction sonde response in a horizo...

3-D finite element analysis of induction logging in a dipping formation mark

Electromagnetic induction (EMI) by a magnetic dipole located above a dipping interface is of relevance to the petroleum well-logging industry. The problem is fully three-dimensional (3-D) when formulated as above, but reduces to an analytically tractable one-dimensional (1-D) problem when cast as a small tilted coil above a horizontal interface. The two problems are related lay a simple coordinate rotation. An examination of the induced eddy currents and the electric charge accumulation at the interface help to explain the inductive and polarization effects commonly observed in induction logs from dipping geological formations. The equivalence between the 1-D and 3-D formulations of the problem enables the validation of a previously published finite element solver for 3-D controlled-source EMI.

Anomalous diffusion of electromagnetic eddy currents in geological formations

Controlled-source electromagnetic (EM) induction in some geological formations isshown here to be compactly described by an anomalous subdiffusion process. Such aprocess, which is not universal, is governed by a fractional diffusion equation oralternatively the convolutional form of Ohm’s law. A subdiffusing eddy current vortex,or electromagnetic smoke ring, propagates in such a way that its position of medianintensity overruns its position of peak intensity. This behavior is not allowed in classicaldiffusion but is a simple consequence of diffusion within a stationary fractal medium.A similar analysis has been applied to understand heavy-tailed traveltime distributions thatappear in certain hydrological time series. The tell-tale signature of anomalouselectromagnetic diffusion is a slope b of the magnetic zero-crossing moveout curve that isconstant with transmitter-receiver (RX) offset and significantly different from unity.Neither lateral heterogeneity nor unixial anisotropy can generate such a constant-slopemoveout curve with an economy of model parameters. Controlled-source EM data fromtwo sites in Texas and one in New Mexico are used in this study to test the eddy currentsubdiffusion hypothesis.

Mapping 3D salt using 2D marine MT: Case study from Gemini Prospect, Gulf of

Gemini Prospect, Gulf of Mexico (GoM) has served as the test bed deployment site for the development of a broadband marine magnetotelluric (MT) method. Located in 1 km deep water, Gemini contains a complex three-dimensional (3D) shaped salt body at depths of 1-5 km beneath the seafloor. The high electrical resistivity of the salt contrasts greatly with the surrounding conductive sediments and provides a suitable target for electrical methods. Using a broadband MT instrument that responds to higher frequency electric and magnetic fields than traditional marine MT systems, we have collected 42 sites of MT data in the period band of 1-3000 seconds in a two-dimensional (2D) grid over the Gemini salt body. This is an excellent data set for testing marine MT’s ability to map salt structures and also for developing and testing 2D and three-dimensional (3D) modeling techniques.