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

Non-Linear Constraints with Application to Self-Potential Source Inversion

We investigate the use of non-linear constraints for geophysical inverse problems, with specific examples applied to source inversion of self-potential data. Typical regularization methods often produce smooth solutions by introducing a quadratic term in the objective function that minimizes the L2 norm of a low-order differential operator applied to the model. In some cases, however, the properties of interest may not vary smoothly. Two alternative constraints are examined that provide inversion stability while allowing for solutions with non-smooth properties. One method, often referred to as ‘compactness’ or ‘minimum support’, seeks to minimize the area (in 2D) or volume (in 3D) occupied by non-zero model parameters. The second method, ‘total variation’, minimizes an approximation of the L1 norm of the gradient of the model. Both approaches involve a non-linear regularization functional, and must therefore be solved iteratively. We discuss the practical aspects of implementing these regularization methods and compare several examples using self-potential source inversion on a synthetic model. We also apply the compactness constraint for self-potential source inversion using a field data example.Kuwait-MIT Center for Natural Resources and the EnvironmentMassachusetts Institute of Technology. Earth Resources Laborator

An Experimental Study of Turbidite Channel Deposits: Implications for Channel Evolution and Sandstone Deposits

Gaining a detailed understanding of turbidite bed sequences is important for the characterization of sandstone reservoir properties, correlation of well cores, and geological interpretation. Many factors influence the internal structure of sandstone reservoirs: source material, source location in time, transport processes, basin geometry, fan channel development and evolution to name a few. Sandstone deposits associated with channel complexes are easy to find but difficult to develop. Here, we conduct tank experiments of scaled sediment-laden turbidity currents traversing a submerged channel to: (1) establish a state-of-the-art data collection and data processing system that has the potential to gain a unique understanding of the processes and deposits that build submarine fan environments; and (2) to use the facility to demonstrate how the interaction of a depositive turbidity current with a sinuous channel may influence the geometry, spatial relationships and grain size sorting of sandstone deposits. Our data shows the construction of prominent levees, asymmetric levee growth, continuous channel overspill, enhanced channel overspill downstream of bend corners, and lobate-shaped lobe deposits. Our preliminary results are qualitative, but indicate that channel wavelength, bend curvature, and bend peak-to-peak amplitude may have strong controls on down-channel and cross-channel depositional patterns, deposit thickness and grain size sorting.ChevronTexaco (Firm

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

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

Characterization of Scattered Waves from Fractures by Estimating the Transfer Function Between Reflected Events Above and Below Each Interval

It is important to be able to detect and characterize naturally occurring fractures in reservoirs using surface seismic reflection data. 3D finite difference elastic modeling is used to create simulated surface seismic data over a three layer model and a five layer model. The elastic properties in the reservoir layer of each model are varied to simulate different amounts of vertical parallel fracturing. The presence of the fractures induces ringing wave trains primarily at times later than the bottom reservoir reflection. These ringy or scattered wave trains appear coherent on the seismograms recorded parallel to the fracture direction. While there are many scattered events on the seismograms recorded perpendicular to the direction of the fractures, these events appear to generally stack out during conventional processing. A method of characterizing and detecting scattering in intervals is developed by deconvolution to give an interval transfer function. The method is simple for the case of two isolated reflections, one from the top of the reservoir and the other from the bottom of the reservoir. The transfer function is computed using the top reflection as the input and the bottom reflection as the output. The transfer function then characterizes the effect of the scattering layer. A simple pulse shape indicates no scattering. A long ringy transfer function captures the scattering within the reservoir interval. When analyzing field data, it is rarely possible to isolate reflections. Therefore, an adaptation of the method is developed using autocorrelations of the wave trains above (as input) and below (as output) the interval of interest for the deconvolution process. The presence of fractures should be detectable from observed ringy transfer functions computed for each time interval. The fracture direction should be identifiable from azimuthal variations – there should be more ringiness in the direction parallel to fracturing. The method applied to ocean bottom cable field data at 4 locations show strong temporal and azimuthal variations of the transfer function which may be correlated to the known geology.Massachusetts Institute of Technology. Earth Resources LaboratoryUnited States. Dept. of Energy (Grant DE-FC26-02NT15346)Eni S.p.A. (Firm

Fracture Detection using Amplitude versus Offset and Azimuth Analysis of a 3D P-wave Seismic Dataset and Synthetic Examples

Amplitude versus offset (AVO) analysis of seismic reflection data has been a successful tool in describing changes in rock properties along a reflector. This method is extended to azimuthal AVO (AVOA) in order to characterize vertically aligned fractures within a reservoir, which can be important fluid migration pathways. AVOA analysis is performed on synthetic data using a least squares inversion method to investigate the effects of varying acquisition geometry, amount of noise, and fracture properties. These tests show that it is possible to detect the fractured layer and determine the fracture strike orientation under typical acquisition conditions. This method is also applied to field data collected during an Ocean Bottom Cable (OBC) survey. These data include a broad offset-azimuth range, which is important for the AVOA analysis. The fracture location and strike orientation recovered from the field data analysis are well correlated with borehole information from this area. Based on an understanding of AVOA behavior under synthetic conditions, this technique provides an effective methodology for describing the spatial variability of a fractured reservoir using 3D seismic data.Eni S.p.A. (Firm)United States. Dept. of Energy (Grant number DE-FC26-02NT15346)Massachusetts Institute of Technology. Earth Resources Laborator