Modeling and inversion of self-potential data

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 235-251).This dissertation presents data processing techniques relevant to the acquisition, modeling, and inversion of self-potential data. The primary goal is to facilitate the interpretation of self-potentials in terms of the underlying mechanisms that generate the measured signal. The central component of this work describes a methodology for inverting self-potential data to recover the three-dimensional distribution of causative sources in the earth. This approach is general in that it is not specific to a particular forcing mechanism, and is therefore applicable to a wide variety of problems. Self-potential source inversion is formulated as a linear problem by seeking the distribution of source amplitudes within a discretized model that satisfies the measured data. One complicating factor is that the potentials are a function of the earth resistivity structure and the unknown sources. The influence of imperfect resistivity information in the inverse problem is derived, and illustrated through several synthetic examples. Source inversion is an ill-posed and non-unique problem, which is addressed by incorporating model regularization into the inverse problem. A non-traditional regularization method, termed "minimum support," is utilized to recover a spatially compact source model rather than one that satisfies more commonly used smoothness constraints. Spatial compactness is often an appropriate form of prior information for the inverse source problem. Minimum support regularization makes the inverse problem non-linear, and therefore requires an iterative solution technique similar to iteratively re-weighted least squares (IRLS) methods.(cont.) Synthetic and field data examples are studied to illustrate the efficacy of this method and the influence of noise, with applications to hydrogeologic and electrochemical self-potential source mechanisms. Finally, a novel technique for pre-processing self-potential data collected with arbitrarily complicated survey geometries is presented. This approach overcomes the inability of traditional processing methods to produce a unique map of the potential field when multiple lines of data form interconnected loops. The data are processed simultaneously to minimize mis-ties on a survey-wide basis using either an 12 or 11 measure of misfit, and simplifies to traditional methods in the absence of survey complexity. The 11 measure requires IRLS solution methods, but is more reliable in the presence of data outliers.by Burke J. Minsley.Ph.D

Fractured Reservoir Characterization using Azimuthal AVO

Ordinary least squares is used to investigate the ability to detect changes in physical properties using Amplitude Versus Offset (AVO) information collected from seismic data. In order to characterize vertically aligned fractures within a reservoir, this method is extended to Azimuthal AVO (AVOA) analysis. Azimuthal AVO has the potential not only to detect fractured zones, but to spatially describe the fracture strike orientation and changes in fracture or fluid properties. Depending on the data acquisition geometry, signal-to-noise ratio, and extent of fracturing, AVOA analysis can be marginally successful. A study of the robustness and limitations of AVOA analysis is therefore first classified with synthetic data. These methods are then applied to seismic data collected during an Ocean Bottom Cable (OBC) survey over a known fractured reservoir.Massachusetts Institute of Technology. Earth Resources LaboratoryUnited States. Dept. of Energy (Grant DE-FC26-02NT15346)Eni S.p.A. (Firm

Hydrogeophysical Investigations at Hidden Dam, Raymond, California

Self-potential and direct current resistivity surveys are carried out at the Hidden Dam site in Raymond, California to assess present-day seepage patterns and better understand the hydrogeologic mechanisms that likely influence seepage. Numerical modeling is utilized in conjunction with the geophysical measurements to predict variably-saturated flow through typical two-dimensional dam cross-sections as a function of reservoir elevation. Several different flow scenarios are investigated based on the known hydrogeology, as well as information about typical subsurface structures gained from the resistivity survey. The flow models are also used to simulate the bulk electrical resistivity in the subsurface under varying saturation conditions, as well as the self-potential response using petrophysical relationships and electrokinetic coupling equations. The self-potential survey consists of 512 measurements on the downstream area of the dam, and corroborates known seepage areas on the northwest side of the dam. Two direct current resistivity profiles, each approximately 2,500 ft (762 m) long, indicate a broad sediment channel under the northwest side of the dam, which may be a significant seepage pathway through the foundation. A focusing of seepage in low-topography areas downstream of the dam is confirmed from the numerical flow simulations, which is also consistent with past observations. Little evidence of seepage is identified from the self-potential data on the southeast side of the dam, also consistent with historical records, though one possible area of focused seepage is identified near the outlet works. Integration of the geophysical surveys, numerical modeling, and observation well data provides a framework for better understanding seepage at the site through a combined hydrogeophysical approach

Applying Compactness Constraints to Differential Traveltime Tomography

Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizing functionals may not always be appropriate, particularly in cases where the anomaly being imaged is generated by a non-smooth spatial process. Timelapse imaging of flow-induced velocity anomalies is one such case; flow features are often characterized by spatial compactness or connectivity. By performing inversions on differenced arrival time data, the properties of the timelapse feature can be directly constrained. We develop a differential traveltime tomography algorithm which selects for compact solutions i.e. models with a minimum area of support, through application of model-space iteratively reweighted least squares. Our technique is an adaptation of minimum support regularization methods previously explored within the potential theory community. We compare our inversion algorithm to the results obtained by traditional Tikhonov regularization for two simple synthetic models; one including several sharp localized anomalies and a second with smoother features. We use a more complicated synthetic test case based on multiphase flow results to illustrate the efficacy of compactness constraints for contaminant infiltration imaging. We conclude by applying the algorithm to a CO[subscript 2] sequestration monitoring dataset acquired at the Frio pilot site. We observe that in cases where the assumption of a localized anomaly is correct, the addition of compactness constraints improves image quality by reducing tomographic artifacts and spatial smearing of target features.Massachusetts Institute of Technology. Earth Resources Laborator

Applying Compactness Constraints to Seismic Traveltime Tomography

Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizing functionals may not always be appropriate, particularly in cases where the anomaly being imaged is generated by a non-smooth spatial process. Timelapse imaging of flow-induced seismic velocity anomalies is one such case; flow features are often characterized by spatial compactness or connectivity. We develop a traveltime tomography algorithm which selects for compact solutions through application of model-space iteratively reweighted least squares. Our technique is an adaptation of minimum support regularization methods previously developed within the potential theory community. We emphasize the application of compactness constraints to timelapse datasets differenced in the data domain, a process which allows recovery of compact perturbations in model properties. We test our inversion algorithm on a simple synthetic dataset generated using a velocity model with several localized velocity anomalies. We then demonstrate the efficacy of the algorithm on a CO2 sequestration monitoring dataset acquired at the Frio pilot site. In both cases, the addition of compactness constraints improves image quality by reducing spatial smearing due to limited angular aperture in the acquisition geometry.Toksoz, M. NafiMassachusetts Institute of Technology. Earth Resources Laborator