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Cumulative oil predictions are made from stochastically inverted earth attributes. The inverted attributes are from the SEAM Life of Field model and an offshore field in West Africa. To perform the prediction, we use a naïve Bayesian classifier for its transparency in methodology, computational efficiency and flexibility. The inverted properties we use for classification consist of porosity, P‐S wave velocity ratio (Vp/Vs), acoustic impedance and density which are extracted from within a set radius around the well‐path. The production from the wells in both SEAM and the West African field serve as the labels for the naïve Bayesian classifier, which are ultimately placed into two classes: the 'high' and 'low' producers. For calculating the accuracy of the classifier, we perform full cross‐validation with a set number of training wells. The cross‐validation accuracy is 78.0% and 83.3% for the SEAM model and the West African Field respectively. The classifier's sensitivity to the chosen radius around the wells and its inherent independence assumption are investigated and shown to change the bulk accuracy by less than 3.0%. We implement full reservoir classifications on SEAM to highlight potential drilling locations and show the capability of the classifier. Overall, we demonstrate how the naïve Bayesian classifier can efficiently and transparently synthesize the entire distribution of stochastic inversions of seismic data to predict oil production. [ABSTRACT FROM AUTHOR]

In the past decade, rapid advances in distributed optical fibre sensing technologies have made it possible to record various geophysical data (e.g. strain, temperature and pressure) continuously in both time and space along the fibre, providing an unprecedented quantity and spatial density of data compared to traditional geophysical measurements as well as reducing data acquisition cost. To date, no distributed fibre‐based electromagnetic field sensing system has been implemented although electromagnetic sensing could have a broad range of applications to geophysical imaging and monitoring in borehole environments. The goal of this paper is to provide a theoretical feasibility study regarding the design and use of an electromagnetic sensing optical fibre for geophysical applications. First, we present the sensitivity analysis of a 'hypothetical' optical fibre coated with polyvinylidene fluoride, a polymer that provides relatively high piezoelectric properties, yet unlike ceramics, is flexible. Using a two‐dimensional electromagnetic modelling algorithm, we simulate the earth electric‐field‐to‐fibre‐strain transfer function and estimate the theoretical sensitivity of the optical fibre to electric fields. Given the state‐of‐the‐art distributed acoustic sensing strain sensitivities in the picometres strain range, our numerical modelling analysis suggests that a perfectly coupled polyvinylidene fluoride–coated optical fibre can measure electric field values in the mV/m to V/m amplitude range. We then apply a cylindrically symmetric modelling algorithm to simulate numerical models demonstrating the applicability of such a fibre in an oilfield environment. Scenarios investigated employ an electric field source and suggest that the measurements can be used to distinguish the oil versus water ratio with a fibre mounted inside a producing steel cased oil well as well as distinguishing between brine and hydrocarbon filled reservoir zones with a fibre located outside of the casing. [ABSTRACT FROM AUTHOR]

A coupled approach, combining the theory of rate‐ and state‐dependent friction and methods from poroelasticity, forms the basis for a quantitative relationship between displacements and fluid leak‐off from a growing fracture and changes in the rate of seismic events in the region surrounding the fracture. Poroelastic Green's functions link fracture aperture changes and fluid flow from the fracture to changes in the stress field and pore pressure in the adjacent formation. The theory of rate‐ and state‐dependent friction provides a connection between Coulomb stress changes and variations in the rate of seismic events. Numerical modeling indicates that the Coulomb stress changes can vary significantly between formations with differing properties. The relationship between the seismicity rate changes and the changes in the formation stresses and fluid pressure is nonlinear, but a transformation produces a quantity that is linearly related to the aperture changes and fluid leak‐off from the fracture. The methodology provides a means for mapping changes in seismicity into fracture aperture changes and to image an evolving fracture. An application to observed microseismicity associated with a hydrofracture reveals asymmetric fracture propagation within two main zones, with extended propagation in the upper zone. The time‐varying volume of the fracture agrees with the injected volume, given by the integration of rate changes at the injection well, providing validation of the estimated aperture changes. Key Points: Microseismicity can be used to infer aperture changes associated with fracture openingRate‐ and state‐dependent friction is used to relate seismicity to stress changes in the region around the fractureThe approach is used to image the growth of a hydrofracture in west Texas [ABSTRACT FROM AUTHOR]

ABSTRACT As motivation for considering new electromagnetic techniques for hydraulic fracture monitoring, we develop a simple financial model for the net present value offered by geophysical characterization to reduce the error in stimulated reservoir volume calculations. This model shows that even a 5% improvement in stimulated reservoir volume for a 1 billion barrel (bbl.) field results in over 1 billion U.S. dollars (US$) in net present value over 24 years for US$100/bbl. oil and US$0.5 billion for US$50/bbl. oil. The application of conductivity upscaling, often used in electromagnetic modeling to reduce mesh size and thus simulation runtimes, is shown to be inaccurate for the high electrical contrasts needed to represent steel-cased wells in the earth. Fine-scale finite-difference modeling with 12.22-mm cells to capture the steel casing and fractures shows that the steel casing provides a direct current pathway to a created fracture that significantly enhances the response compared with neglecting the steel casing. We consider conductively enhanced proppant, such as coke-breeze-coated sand, and a highly saline brine solution to produce electrically conductive fractures. For a relatively small frac job at a depth of 3 km, involving 5,000 bbl. of slurry and a source midpoint to receiver separation of 50 m, the models show that the conductively enhanced proppant produces a 15% increase in the electric field strength (in-line with the transmitter) in a 10-Ωm background. In a 100-Ωm background, the response due to the proppant increases to 213%. Replacing the conductive proppant by brine with a concentration of 100,000-ppm NaCl, the field strength is increased by 23% in the 100-Ωm background and by 2.3% in the 10-Ωm background. All but the 100,000-ppm NaCl brine in a 10-Ωm background produce calculated fracture-induced electric field increases that are significantly above 2%, a value that has been demonstrated to be observable in field measurements. [ABSTRACT FROM AUTHOR]

ABSTRACT The recent use of marine electromagnetic technology for exploration geophysics has primarily focused on applying the controlled source electromagnetic method for hydrocarbon mapping. However, this technology also has potential for structural mapping applications, particularly when the relative higher frequency controlled source electromagnetic data are combined with the lower frequencies of naturally occurring magnetotelluric data. This paper reports on an extensive test using data from 84 marine controlled source electromagnetic and magnetotelluric stations for imaging volcanic sections and underlying sediments on a 128-km-long profile. The profile extends across the trough between the Faroe and Shetland Islands in the North Sea. Here, we focus on how 2.5D inversion can best recover the volcanic and sedimentary sections. A synthetic test carried out with 3D anisotropic model responses shows that vertically transverse isotropy 2.5D inversion using controlled source electromagnetic and magnetotelluric data provides the most accurate prediction of the resistivity in both volcanic and sedimentary sections. We find the 2.5D inversion works well despite moderate 3D structure in the synthetic model. Triaxial inversion using the combination of controlled source electromagnetic and magnetotelluric data provided a constant resistivity contour that most closely matched the true base of the volcanic flows. For the field survey data, triaxial inversion of controlled source electromagnetic and magnetotelluric data provides the best overall tie to well logs with vertically transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data a close second. Vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data provided the best interpreted base of the volcanic horizon when compared with our best seismic interpretation. The structural boundaries estimated by the 20-Ω·m contour of the vertical resistivity obtained by vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data gives a maximum geometric location error of 11% with a mean error of 1.2% compared with the interpreted base of the volcanic horizon. Both the model study and field data interpretation indicate that marine electromagnetic technology has the potential to discriminate between low-resistivity prospective siliciclastic sediments and higher resistivity non-prospective volcaniclastic sediments beneath the volcanic section. [ABSTRACT FROM AUTHOR]

Including highly conductive steel infrastructure into electromagnetic (EM) earth modeling is motivated by the fact that long metal-cased boreholes have the potential to be used as boosting antennas that enable larger source dipole moments and greater signal penetration depths. Unfortunately, geophysical algorithms designed to simulate EM responses over rather regional scales are complicated by material property contrasts and structure geometries that are more typical for EM engineering applications. Hence, the great majority of earth-modeling algorithms that consider EM responses from steel-cased boreholes use integral-equation methods. To be able to model complex casing scenarios, we revisited the finite-difference time-domain (FDTD) method to advance the modeling of transient-EM field responses from steel-cased boreholes. A time-dependent function that allows for larger FDTD time steps in the DuFort-Frankel method was developed, alleviating the generally large computational overhead. We compared our method against three different kinds of benchmark solutions to demonstrate the reliability of the FDTD field solutions. These test cases were canned out to check the feasibility of a final hydraulic fracturing study. Images of the electric current distribution in a sheetlike rock fracture were calculated for the cases with and without the presence of a connecting borehole casing, demonstrating the casing's potential of illuminating deep target zones. [ABSTRACT FROM AUTHOR]

We have developed a spatial, value of information (VOI) methodology that is designed specifically to include the inaccuracies of multidimensional geophysical inversions. VOI assesses the worth of information in terms of how it can improve the decision maker's likelihood of a higher valued outcome. VOI can be applied to spatial data using an exploration example for hidden geothermal resources. This methodology is applicable for spatial decisions for other exploration decisions (e.g., oil, mining, etc.). This example evaluates how well the magnetotelluric (MT) technique is able to delineate the lateral position of electrically conductive materials that are indicative of a hidden geothermal resource. The conductive structure (referred to as the clay cap) represented where the geothermal alteration occurred. The prior uncertainty of the position of the clay cap (drilling target) is represented with multiple earth models. These prior models are used to numerically simulate the data collection, noise, inversion, and interpretation of the MT technique. MT's ability to delineate the correct lateral location can be quantified by comparing the true location in each prior model to the location that is interpreted from each respective inverted model. Additional complexity in the earth models is included by adding more electrical conductors (not associated with the clay cap) and deeper targets. Both degrade the ability of the MT technique (the signal and inversion) to locate the clay cap thereby decreasing the VOI. The results indicate the ability of the prior uncertainty to increase and decrease the final VOI assessment. The results also demonstrate how VOI depends on whether or not a resource still exists below the clay cap because the clay cap is only a potential indicator of economic temperatures. [ABSTRACT FROM AUTHOR]

Bayesian methods can quantify the model uncertainty that is inherent in inversion of highly nonlinear geophysical problems. In this approach, a model likelihood function based on knowledge of the data noise statistics is used to sample the posterior model distribution, which conveys information on the resolvability of the model parameters. Because these distributions are multidimensional and nonlinear, we used Markov chain Monte Carlo methods for highly efficient sampling. Because a single Markov chain can become stuck in a local probability mode, we run various randomized Markov chains independently. To some extent, this problem can be mitigated by running independent Markov chains, but unless a very large number of chains are run, biased results may be obtained. We got around these limitations by running parallel, interacting Markov chains with "annealed" or "tempered" likelihoods, which enable the whole system of chains to effectively escape local probability maxima. We tested this approach using a transdimensional algorithm, where the number of model parameters as well as the parameters themselves were treated as unknowns during the inversion. This gave us a measure of uncertainty that was independent of any particular parameterization. We then subset the ensemble of inversion models to either reduce uncertainty based on a priori constraints or to examine the probability of various geologic scenarios. We demonstrated our algorithms' fast convergence to the posterior model distribution with a synthetic 1D marine controlled-source electromagnetic data example. The speed up gained from this new approach will facilitate the practical implementation of future 2D and 3D Bayesian inversions, where the cost of each forward evaluation is significantly more expensive than for the 1D case. [ABSTRACT FROM AUTHOR]

ABSTRACT Effective-medium theories for either highly conductive or more resistive electrical inclusions in a moderately conducting background medium are presented for modelling macroscopic (i.e., large-scale) fluid-filled fractures or cracks in a potential reservoir rock or granular medium. Conductive fluids are most often brine and the resistive fluids of interest are oil, gas, air and/or CO2. Novel features of the presentation for conductive fluids include results for both non-interacting inclusions (using a Maxwell approximation) and for interacting inclusions (via a self-consistent effective-medium scheme). The anisotropic analysis is specifically designed to handle reservoirs with multiple orientations (usually three orthogonal sets) of oblate spheroidal cracks/fractures, while also having arbitrary aspect ratios. But these aspect ratios are strictly <1, thus excluding spherical pores and simple granular media - both already widely studied by others. Results show that the self-consistent approximation depends on fracture aspect ratio α and that this approximation becomes important when fracture porosity is about φ= 1% for aspect ratio α≃ 0.05, or φ= 3% for aspect ratio α≃ 0.10. It is shown that the self-consistent analysis is most important when the fractures have a very small aspect ratio - the inferred reason being that the fracture (or crack) number density (ρ c≡φ/α) then becomes very high and the fracture relative spacing correspondingly very small for any fixed value of porosity (but with decreasing values of the aspect ratio). Hybrid methods (combining self-consistent and non-self consistent formulas) are also developed to deal with high volume fractions and multiple sets of fractures having different aspect ratios. Whenever possible and appropriate, the results are also compared to rigorous bounds, including the Wiener bounds and the Hashin-Shtrikman bounds, in order to provide one type of partial validation of the methods being developed. [ABSTRACT FROM AUTHOR]

We developed a Bayesian model to invert magnetotelluric (MT) data using a 2D sharp boundary parameterization. We divided the 2D cross section into layers and considered the locations of interfaces and resistivity of the regions formed by the interfaces as random variables. We assumed that those variables are independent in the vertical direction and dependent along the lateral direction, whose spatial dependence is described by either pairwise difference or multivariate Gaussian priors. We used a parallel, adaptive finite-element algorithm to rapidly forward simulate frequency-domain MT responses of the 2D resistivity structure and used Markov chain Monte Carlo methods to draw many samples from the joint posterior probability distribution. We applied the Bayesian model to a synthetic case that mimics a geothermal exploration scenario. Our results demonstrated that the developed method is effective in estimating the resistivity and depths to interfaces and in quantifying uncertainty on the estimates. We also applied the developed method to the field MT data collected from the Darajat geothermal site in Indonesia. We compared our inversion results with those obtained from a deterministic inversion of 3D MT data; they are consistent even if the two inversion methods are very different and the amount of information used for inversion is different. [ABSTRACT FROM AUTHOR]

Joint inversion of seismic AVA and CSEM data requires rock-physics relationships to link seismic attributes to electric properties. Ideally, we can connect them through reservoir parameters (e.g., porosity and water saturation) by developing physical-based models, such as Gassmann's equations and Archie's law, using nearby borehole logs. This could be difficult in the exploration stage because information available is typically insufficient for choosing suitable rock-physics models and for subsequently obtaining reliable estimates of the associated parameters. The use of improper rock-physics models and the inaccuracy of the estimates of model parameters may cause misleading inversion results. Conversely, it is easy to derive statistical relationships among seismic and electric attributes and reservoir parameters from distant borehole logs. In this study, we developed a Bayesian model to jointly invert seismic AVA and CSEM data for reservoir parameters using statistical rock-physics models; the spatial dependence of geophysical and reservoir parameters were carried out by lithotypes through Markov random fields. We applied the developed model to a synthetic case that simulates a CO, monitoring application. We derived statistical rock-physics relations from borehole logs at one location and estimated seismic P- and S-wave velocity ratio, acoustic impedance, density, electric resistivity, lithotypes, porosity, and water saturation at three different locations by conditioning to seismic AVA and CSEM data. Comparison of the inversion results with their corresponding true values showed that the correlation-based statistical rock-physics models provide significant information for improving the joint inversion results. [ABSTRACT FROM AUTHOR]

Traditional deterministic geophysical inversion algorithms are not designed to provide a robust evaluation of uncertainty that reflects the limitations of the geophysical technique. Stochastic inversions, which do provide a sampling-based measure of uncertainty, are computationally expensive and not straightforward to implement for nonexperts (nonstatisticians). Our results include stochastic inversion for magnetotelluric and controlled source electromagnetic data. Two Markov Chain sampling algorithms (Metropolis-Hastings and Slice Sampler) can significantly decrease the computational expense compared to using either sampler alone. The statistics of the stochastic inversion allow for (1) variances that better reveal the measurement sensitivities of the two different electromagnetic techniques than traditional techniques and (2) models defined by the median and modes of parameter probability density functions, which produce amplitude and phase data that are consistent with the observed data. In general, parameter error estimates from the covariance matrix significantly underestimate the true parameter error, whereas the parameter variance derived from Markov chains accurately encompass the error. [ABSTRACT FROM AUTHOR]

We present a split-step complex Padé-Fourier migration method based on the one-way wave equation. The downward-continuation operator is split into two downward-continuation operators: one operator is a phase-shift operator and the other operator is a finite-difference operator. A complex treatment of the propagation operator is applied to mitigate inaccuracies and instabilities due to evanescent waves. It produces high-quality images of complex structures with fewer numerical artefacts than those obtained using a real approximation of a square-root operator in the one-way wave equation. Tests on zero-offset data from the SEG/EAGE salt data show that the method improves the image quality at the cost of an additional 10 per cent computational time compared to the conventional Fourier finite-difference method. [ABSTRACT FROM AUTHOR]

We develop a Bayesian model to jointly invert marine seismic amplitude versus angle (AVA) and controlled-source electromagnetic (CSEM) data tbr a layered reservoir model. We consider the porosity and fluid saturation of each layer in the reservoir, the bulk and shear moduli and density of each layer not in the reservoir, and the electrical conductivity of the overburden and bedrock as random variables. We also consider prestack seismic AVA data in a selected time window as well as real and quadrature components of the recorded electrical field as data. Using Markov chain Monte Carlo (MCMC) sampling methods, we draw a large number of samples from the joint posterior distribution function. With these samples, we obtain not only the estimates of each unknown variable, but also various types of uncertainty information associated with the estimation. This method is applied to both synthetic and field data to investigate the combined use of seismic AVA and CSEM data for gas saturation estimation. Results show that the method is effective for joint inversion; the incorporation of CSEM data reduces uncertainty in fluid saturation estimation compared to inversion of seismic AVA data alone. The improvement in gas saturation estimation obtained from joint inversion for field data is less significant than for synthetic data because of the large number of unknown noise sources inherent in the field data. [ABSTRACT FROM AUTHOR]

Based on an acoustic assumption (that the shear-wave velocity is zero) and a dispersion relationship, we derive an acoustic wave equation for P-waves in tilted transversely isotropic (TTI) media (transversely isotropic media with a tilted symmetry axis). This equation has fewer parameters than an elastic wave equation in TTI media and yields an accurate description of P-wave traveltimes and spreading-related attenuation. Our TTI acoustic wave equation is a fourth-order equation in time and space. We demonstrate that the acoustic approximation allows the presence of shear waves in the solution. The substantial differences in traveltime and amplitude between data created using vertical transversely isotropic (VTI) and TTI assumptions is illustrated in examples. [ABSTRACT FROM AUTHOR]

A finite-difference method for computing the first-arrival traveltimes by solving the eikonal equation in the celerity domain has been developed. This algorithm incorporates the head and diffraction wave. We also adapt a fast sweeping method, which is extremely simple to implement in any number of dimensions, to obtain accurate first-arrival times in complex velocity models. The method, which is stable and computationally efficient, can handle instabilities due to caustics and provide head wave traveltimes. Numerical examples demonstrate that the celerity domain eikonal solver provides accurate first-arrival traveltimes. This new method is three times accurate more than the second-order fast marching method in a linear velocity model with the same spacing. [ABSTRACT FROM AUTHOR]