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de Groot-Hedlin, C, Constable S.  2004.  Inversion of magnetotelluric data for 2D structure with sharp resistivity contrasts. Geophysics. 69:78-86.   10.1190/1.1649377   AbstractWebsite

We have developed a linearized algorithm to invert noisy 2-D magnetotelluric data for subsurface conductivity structures represented by smooth boundaries defining sharp resistivity contrasts. We solve for both a fixed number of subsurface resistivities and for the boundary locations between adjacent units. The boundary depths are forced to be discrete values defined by the mesh used in the forward modeling code. The algorithm employs a Lagrange multiplier approach in a manner similar to the widely used Occam method. The main difference is that we penalize variations in the boundary depths, rather than in resistivity contrasts between a large number of adjacent blocks. To reduce instabilities resulting from the breakdown of the linear approximation, we allow an option to penalize contrasts in the resistivities of adjacent units. We compare this boundary inversion method to the smooth Occam inversion for two synthetic models, one that includes a conductive wedge between two resistors and another that includes a resistive wedge between two conductors. The two methods give good agreement for the conductive wedge, but the solutions differ for the more poorly resolved resistive wedge, with the boundary inversion method giving a more geologically realistic result. Application of the boundary inversion method to the resistive Gemini subsalt petroleum prospect in the Gulf of Mexico indicates that the shape of this salt feature is accurately imaged by this method, and that the method remains stable when applied to real data.

Constable, S, Weiss CJ.  2006.  Mapping thin resistors and hydrocarbons with marine EM methods: Insights from 1D modeling. Geophysics. 71:G43-G51.   10.1190/1.2187748   AbstractWebsite

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.

Medin, AE, Parker RL, Constable S.  2007.  Making sound inferences from geomagnetic sounding. Physics of the Earth and Planetary Interiors. 160:51-59.   10.1016/j.pepi.2006.09.001   AbstractWebsite

We examine the nonlinear inverse problem of electromagnetic induction to recover electrical conductivity. As this is an ill-posed problem based on inaccurate data, there is a critical need to find the reliable features of the models of electrical conductivity. We present a method for obtaining bounds on Earth's average conductivity that all conductivity profiles must obey. Our method is based completely on optimization theory for an all-at-once approach to inverting frequency-domain electromagnetic data. The forward modeling equations are constraints in an optimization problem solving for the electric fields and the conductivity simultaneously. There is no regularization required to solve the problem. The computational framework easily allows additional inequality constraints to be imposed, allowing us to further narrow the bounds. We draw conclusions from a global geomagnetic depth sounding data set and compare with laboratory results, inferring temperature and water content through published Boltzmann-Arrhenius conductivity models. If the upper mantle is assumed to be volatile free we find it has an average temperature of 1409-1539 degrees C. For the top 1000 km of the lower mantle, we find an average temperature of 1849-2008 degrees C. These are in agreement with generally accepted mantle temperatures. Our conclusions about water content of the transition zone disagree with previous research. With our bounds on conductivity, we calculate a transition zone consisting entirely of Wadsleyite has < 0.27 wt.% water and as we add in a fraction of Ringwoodite, the upper bound on water content decreases proportionally. This water content is less than the 0.4 wt.% water required for melt or pooling at the 410 km seismic discontinuity. Published by Elsevier B.V.

Weitemeyer, K, Gao GZ, Constable S, Alumbaugh D.  2010.  The practical application of 2D inversion to marine controlled-source electromagnetic data. Geophysics. 75:F199-F211.   10.1190/1.3506004   AbstractWebsite

An algorithm is presented for the inversion of marine controlled-source electromagnetic (CSEM) data that uses a 2D finite difference (FD) forward driver. This code is demonstrated by inverting a CSEM data set collected at Hydrate Ridge, Oregon, consisting of 25 seafloor sites recording a 5-Hz transmission frequency. The sites are located across a bathymetric high, with variations in water depth of approximate to 300 m along the 16-km profile. To model this complex seafloor bathymetry accurately, the FD grid was designed by careful benchmarking using a different 2D finite element (FE) forward code. A comparison of the FE and FD forward model solutions verifies that no features in the inversion are due to inaccuracies of the FD grid. The inversion includes the local seawater conductivity-depth profile as recorded by the transmitter's conductivity-temperature-depth gauge, because seawater conductivity is known to have a significant effect on the CSEM responses. An apparent resistivity pseudosection of the CSEM data resembles the 2D inversion in general appearance. However, the inversion provides depth and geometric control of features that cannot be provided by the pseudosection and eliminates artifacts generated from the pseudosection projection.

Van Beusekom, AE, Parker RL, Bank RE, Gill PE, Constable S.  2011.  The 2-D magnetotelluric inverse problem solved with optimization. Geophysical Journal International. 184:639-650.   10.1111/j.1365-246X.2010.04895.x   AbstractWebsite

P>The practical 2-D magnetotelluric inverse problem seeks to determine the shallow-Earth conductivity structure using finite and uncertain data collected on the ground surface. We present an approach based on using PLTMG (Piecewise Linear Triangular MultiGrid), a special-purpose code for optimization with second-order partial differential equation (PDE) constraints. At each frequency, the electromagnetic field and conductivity are treated as unknowns in an optimization problem in which the data misfit is minimized subject to constraints that include Maxwell's equations and the boundary conditions. Within this framework it is straightforward to accommodate upper and lower bounds or other conditions on the conductivity. In addition, as the underlying inverse problem is ill-posed, constraints may be used to apply various kinds of regularization. We discuss some of the advantages and difficulties associated with using PDE-constrained optimization as the basis for solving large-scale nonlinear geophysical inverse problems. Combined transverse electric and transverse magnetic complex admittances from the COPROD2 data are inverted. First, we invert penalizing size and roughness giving solutions that are similar to those found previously. In a second example, conventional regularization is replaced by a technique that imposes upper and lower bounds on the model. In both examples the data misfit is better than that obtained previously, without any increase in model complexity.

Weitemeyer, K, Constable S.  2014.  Navigating marine electromagnetic transmitters using dipole field geometry. Geophysical Prospecting. 62:573-596.   10.1111/1365-2478.12092   AbstractWebsite

The marine controlled source electromagnetic (CSEM) technique has been adopted by the hydrocarbon industry to characterize the resistivity of targets identified from seismic data prior to drilling. Over the years, marine controlled source electromagnetic has matured to the point that four-dimensional or time lapse surveys and monitoring could be applied to hydrocarbon reservoirs in production, or to monitor the sequestration of carbon dioxide. Marine controlled source electromagnetic surveys have also been used to target shallow resistors such as gas hydrates. These novel uses of the technique require very well constrained transmitter and receiver geometry in order to make meaningful and accurate geologic interpretations of the data. Current navigation in marine controlled source electromagnetic surveys utilize a long base line, or a short base line, acoustic navigation system to locate the transmitter and seafloor receivers. If these systems fail, then rudimentary navigation is possible by assuming the transmitter follows in the ship's track. However, these navigational assumptions are insufficient to capture the detailed orientation and position of the transmitter required for both shallow targets and repeat surveys. In circumstances when acoustic navigation systems fail we propose the use of an inversion algorithm that solves for transmitter geometry. This algorithm utilizes the transmitter's electromagnetic dipole radiation pattern as recorded by stationary, close range (<1000m), receivers in order to model the geometry of the transmitter. We test the code with a synthetic model and validate it with data from a well navigated controlled source electromagnetic survey over the Scarborough gas field in Australia.

Ray, A, Key K, Bodin T, Myer D, Constable S.  2014.  Bayesian inversion of marine CSEM data from the Scarborough gas field using a transdimensional 2-D parametrization. Geophysical Journal International. 199:1847-1860.   10.1093/gji/ggu370   AbstractWebsite

We apply a reversible-jump Markov chain Monte Carlo method to sample the Bayesian posterior model probability density function of 2-D seafloor resistivity as constrained by marine controlled source electromagnetic data. This density function of earth models conveys information on which parts of the model space are illuminated by the data. Whereas conventional gradient-based inversion approaches require subjective regularization choices to stabilize this highly non-linear and non-unique inverse problem and provide only a single solution with no model uncertainty information, the method we use entirely avoids model regularization. The result of our approach is an ensemble of models that can be visualized and queried to provide meaningful information about the sensitivity of the data to the subsurface, and the level of resolution of model parameters. We represent models in 2-D using a Voronoi cell parametrization. To make the 2-D problem practical, we use a source-receiver common midpoint approximation with 1-D forward modelling. Our algorithm is transdimensional and self-parametrizing where the number of resistivity cells within a 2-D depth section is variable, as are their positions and geometries. Two synthetic studies demonstrate the algorithm's use in the appraisal of a thin, segmented, resistive reservoir which makes for a challenging exploration target. As a demonstration example, we apply our method to survey data collected over the Scarborough gas field on the Northwest Australian shelf.

Weitemeyer, K, Constable S, Shelander D, Haines S.  2017.  Mapping the resistivity structure of Walker Ridge 313 in the Gulf of Mexico using the marine CSEM method. Marine and Petroleum Geology. 88:1013-1031.   10.1016/j.marpetgeo.2017.08.039   AbstractWebsite

A marine controlled source electromagnetic (CSEM) campaign was carried out in the Gulf of Mexico to further develop marine electromagnetic techniques in order to aid the detection and mapping of gas hydrate deposits. Marine CSEM methods are used to obtain an electrical resistivity structure of the subsurface which can indicate the type of substance filling the pore space, such as gas hydrates which are more resistive. Results from the Walker Ridge 313 study (WR 313) are presented in this paper and compared with the Gulf of Mexico Gas Hydrate Joint Industry Project II (JIP2) logging while drilling (LWD) results and available seismic data. The hydrate, known to exist within sheeted sand deposits, is mapped as a resistive region in the two dimensional (2D) CSEM inversion models. This is consistent with the JIP2 LWD resistivity results. CSEM inversions that use seismic horizons provide more realistic results compared to the unconstrained inversions by providing sharp boundaries and architectural control on the location of the resistive and conductive regions in the CSEM model. The seismic horizons include: 1) the base of the gas hydrate stability zone (BGHSZ), 2) the top of salt, and 3) the top and bottom of a fine grained marine mud interval with near vertical hydrate filled fractures, to constrain the CSEM inversion model. The top of salt provides improved location for brines, water saturated salt, and resistive salt. Inversions of the CSEM data map the occurrence of a 'halo' of conductive brines above salt. The use of the BGHSZ as a constraint on the inversion helps distinguish between free gas and gas hydrate as well as gas hydrate and water saturated sediments. (C) 2017 Published by Elsevier Ltd.

Constable, S, Kowalczyk P, Bloomer S.  2018.  Measuring marine self-potential using an autonomous underwater vehicle. Geophysical Journal International. 215:49-60.   10.1093/gji/ggy263   AbstractWebsite

The marine self-potential (SP) method is used to explore for hydrothermal venting and associated seafloor mineralization. Measurements are commonly made in deep water using instruments towed close to the seafloor, which requires dedicated ship time, is limited to slow speeds, and is subject to navigation errors. Instead, we mounted a three-axis electric field receiver on an autonomous underwater vehicle (AUV), and tested the method with data collected in the Iheya area of the Okinawa Trough, off Japan. Parts of this prospect have documented hydrothermal venting and seafloor massive sulfide (SMS) deposits. An International Submarine Engineering Limited explorer-class AUV was fitted with a controlled-source electromagnetic (CSEM) amplifier and logging system, modified to collect DC SP data using silver chloride electrodes on approximately 1 m dipoles. A 1 km x 1 km area was surveyed with a flight pattern of six lines, collected three times to assess repeatability and noise levels. The entire data set was collected in a single day on station with a 10 hr AUV deployment. Flying height was 70 m, navigation errors were less than 3 m, collection speed was 1.1 m s(-1) and electric field noise levels were less than 5 mu V m(-1). Localized anomalies of 0.3 mV m(-1) were observed, from which potentials were estimated using regularized inversion, yielding negative SP anomalies of 15-25 mV. Modelling electric field data as dipoles shows that the negative poles causing the anomalies are localized near the seafloor with a diffuse return current deeper than 1000 m below seafloor. Apparent conductivities as high as 30 S m(-1) were derived from CSEM data collected during the same deployment, which strongly suggests that SMS mineralization is associated with one of the SP anomalies, although the localization near the seafloor and the lack of a dipolar signal suggest that the causative mechanism for the SP anomalies is due to hydrothermal venting. In either case, we have demonstrated that AUV-mounted instrument systems are an efficient, effective and low noise means of collecting marine SP data.