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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]

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 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]