Steven Constable

Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data

The inversion of electromagnetic sounding data does not yield a unique solution, but inevitably a single model to interpret the observations is sought. We recommend that this model be as simple, or smooth, as possible, in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models.To obtain smooth models, the nonlinear forward problem is linearized about a starting model in the usual way, but it is then solved explicitly for the desired model rather than for a model correction. By parameterizing the model in terms of its first or second derivative with depth, the minimum norm solution yields the smoothest possible model.Rather than fitting the experimental data as well as possible (which maximizes the roughness of the model), the smoothest model which fits the data to within an expected tolerance is sought. A practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models, resulting in a stable and rapidly convergent algorithm. The inversion of both magnetotelluric and Schlumberger sounding field data, and a joint magnetotelluric-resistivity inversion, demonstrate the method and show it to have practical application.

Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data

Magnetotelluric (MT) data are inverted for smooth 2-D models using an extension of the existing 1-D algorithm, Occam’s inversion. Since an MT data set consists of a finite number of imprecise data, an infinity of solutions to the inverse problem exists. Fitting field or synthetic electromagnetic data as closely as possible results in theoretical models with a maximum amount of roughness, or structure. However, by relaxing the misfit criterion only a small amount, models which are maximally smooth may be generated. Smooth models are less likely to result in overinterpretation of the data and reflect the true resolving power of the MT method. The models are composed of a large number of rectangular prisms, each having a constant conductivity. Apriori information, in the form of boundary locations only or both boundary locations and conductivity, may be included, providing a powerful tool for improving the resolving power of the data. Joint inversion of TE and TM synthetic data generated from known models al...

Remote sensing of hydrocarbon layers by seabed logging (SBL): Results from a cruise offshore Angola

Detecting and assessing hydrocarbon reservoirs without the need to drill test wells is of major importance to the petroleum industry. Seismic methods have traditionally been used in this context, but the results can be ambiguous. Another approach is to use electromagnetic sounding methods that exploit the resistivity differences between a reservoir containing highly resistive hydrocarbons and one saturated with conductive saline fluids. Modeling presented by Eidesmo et al. (2002) demonstrates that by using seabed logging (SBL), a special application of frequency domain controlled source electromagnetic (CSEM) sounding, the existence or otherwise of hydrocarbon bearing layers can be determined and their lateral extent and boundaries can be quantified. Such information provides valuable complementary constraints on reservoir geometry and characteristics obtained by seismic surveying.

Ten years of marine CSEM for hydrocarbon exploration

Marine controlled-source electromagnetic CSEM surveying has been in commercial use for predrill reservoir appraisalandhydrocarbonexplorationfor10 years.Althougha recent decrease has occurred in the number of surveys and publications associated with this technique, the method has become firmly established as an important geophysical tool intheoffshoreenvironment.Thisisaconsequenceoftwoimportant aspects associated with the physics of the method: First, it is sensitive to high electrical resistivity, which, although not an unambiguous indicator of hydrocarbons, is an important property of economically viable reservoirs. Second, although the method lacks the resolution of seismic wave propagation, it has a much better intrinsic resolution than potential-field methods such as gravity and magnetic surveying, which until now have been the primary nonseismicdatasetsusedinoffshoreexploration.Althoughbymany measures marine CSEM is still in its infancy, the reliability and noise floors of the instrument systems have improved significantly over the last decade, and interpretation methodology has progressed from simple anomaly detection to 3D anisotropic inversion of multicomponent data using some of theworld’sfastestsupercomputers.Researchdirectionspresently include tackling the airwave problem in shallow water by applying time-domain methodology, continuous profiling tools, and the use of CSEM for reservoir monitoring during production.

An introduction to marine controlled-source electromagnetic methods for hydrocarbon exploration

Early development of marine electromagnetic methods, dating back about 80 years, was driven largely by defense/military applications, and use for these purposes continues to this day. Deepwater, frequency-domain, electric dipole-dipole, controlled-sourceelectromagneticCSEMmethodsarosefromacademic studies of the oceanic lithosphere in the 1980s, and although the hydrocarbon exploration industry was aware of this work, the shallow-water environments being explored at that time were not ideally suited for its use. Low oil prices and increasingly successful results from 3D seismic methods further discouraged investment in costly alternative geophysical data streams. These circumstances changed in the late 1990s, when both Statoil and ExxonMobil began modeling studies and field trialsofCSEMsurveyingindeepwateraround1000 mordeeper, specifically for characterizing the resistivity of previously identified drilling targets. Trials offshore Angola in 2000‐2002 byboththesecompaniesshowedthatCSEMdatacansuccessfully be used to evaluate reservoir resistivity for targets as deep as several thousand meters. Both companies leveraged instrumentationandexpertisefromtheacademiccommunitytomakeswift progress. The resulting rapid growth in the use of marine EM methodsforexplorationhascreatedademandfortrainedpersonnelthatisdifficulttomeet;nevertheless,atthistime,CSEMdata represent a commercial commodity within the exploration business, and acquisition services are offered by three companies. The ability to determine the resistivity of deep drilling targets from the seafloor may well make marine CSEM the most important geophysical technique to emerge since 3D reflection seismology.

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.

The electrical conductivity of an isotropic olivine mantle

In order to extend the useful temperature range of interpretation of olivine electrical conductivity σ we have used the nonlinear iterative Marquardt technique to fit experimental data over the range 720°–1500°C to the parametric form σ = σ1e−A1/kT + σ2e−A2/kT, where k is Boltzmanns constant and T is absolute temperature. The model describes conduction by migration of two different thermally activated defect populations with activation energies A1 and A2, and preexponential terms σ1 and σ2 that depend on number of charge carriers and their mobility and that may be different for each crystallographic direction. A combined interpretation of recent high (San Carlos olivine) and low (Jackson County dunite) temperature measurements has been made that demonstrates that a single activation energy A1 for all three crystallographic directions adequately fits the data. The parametric fits show that the high-temperature conduction mechanism has far greater anisotropy than the low-temperature mechanism, consistent with previous assignments to ionic and electronic conduction, respectively. The geometric mean of the conductivity in the three directions is approximately –¯=102.402e-1.60eV/kT+109.17e-4.25eV/kT S/m and is presented as a model for isotropic olivine, SO2, appropriate from 720°C to above 1500°C, at oxygen fugacities near the center of the olivine stability field. It is observed that the magnitudes of σ1 for the three crystal directions are similar to the ratios of the inter-ionic distances between the M1 magnesium sites in olivine, to within 5%, consistent with Fe3+ preferring the M1 site below 1200°C.

Marine controlled‐source electromagnetic sounding: 2. The PEGASUS experiment

The marine controlled-source electromagnetic sounding method developed over the past 15 years at Scripps Institution of Oceanography employs a towed seafloor electric dipole transmitter of moment 4 × 104 Am and multiple free-vehicle seafloor electric field recorders. A survey of 40 Ma normal oceanic lithosphere in the northeast Pacific using frequencies of 0.25 to 24 Hz and synchronous stacking of 0.25- to 12-hour-duration detected signals at transmitter-receiver ranges between 5 and 95 km. One-dimensional electrical conductivity structure is recovered from the data using the Occam process of nonlinear regularized inversion. Repeated inversion of a model terminated with an essentially infinite conductor or resistor demonstrates that the maximum depth of inference for this experiment is about 30 km, well into the upper mantle, with bounds placed on conductivity to depths of 60 km. Structure shallower than about 1 km is comparable to that obtained by a similar experiment on the East Pacific Rise and by borehole logging, with a sharp increase in resistivity at depths of 600–800 m, although strictly our experiment is sensitive only to integrated square root of conductivity, or total attenuation, in the surface layers. The lower crust and upper mantle has a resistivity between 2 and 7 × 104 Ω m and a transverse resistance of at least 109 Ω m2, suggesting at most 0.3% volume fraction of free water in the lower crust and some form of conductivity enhancement over mineral conductivity in the uppermost mantle. Although resolution is weak, below 30 km our data are compatible with a dry olivine model of mantle conductivity-temperature.

Marine magnetotellurics for petroleum exploration. Part I: A sea-floor equipment system

Induction in electrically conductive seawater attenuates the magnetotelluric (MT) fields and, coupled with a minimum around 1 Hz in the natural magnetic field spectrum, leads to a dramatic loss of electric and magnetic field power on the sea floor at periods shorter than 1000 s. For this reason the marine MT method traditionally has been used only at periods of 103 to 105 s to probe deep mantle structure; rarely does a sea‐floor MT response extend to a 100-s period. To be useful for mapping continental shelf structure at depths relevant to petroleum exploration, however, MT measurements need to be made at periods between 1 and 1000 s. This can be accomplished using ac-coupled sensors, induction coils for the magnetic field, and an electric field amplifier developed for marine controlled‐source applications. The electrically quiet sea floor allows the attenuated electric field to be amplified greatly before recording; in deep (1-km) water, motional noise in magnetic field sensors appears not to be a proble...

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...