Browsing by Subject "Geophysics"

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

The focus of this work is to use geologic and geophysical methods to better understand the faults and fracture systems at Puna, in southeastern Hawaii, and southern Montserrat, in the Lesser Antilles. The particular interest is understanding and locating the deep fracture networks that are necessary for fluid circulation in hydrothermal systems. The dissertation first presents a study in which identification of large scale faulting places Montserrat into a tectonic context. Then follow studies of Puna and Montserrat that focus on faults and fractures of the deep hydrothermal systems.

The first chapter consists of the results of the SEA-CALIPSO experiment seismic reflection data, recorded on a 48 channel streamer with the active source as a 2600 in3 airgun. This chapter discusses volcaniclastic debris fans off the east coast of Montserrat and faults off the west coast. The work places Montserrat in a transtensional environment (influenced by oblique subduction) as well as in a complex local stress regime. One conclusion is that the stress regime is inconsistent with the larger arc due to the influence of local magmatism and stress.

The second chapter is a seismic study of the Puna hydrothermal system (PHS) along the Kilauea Lower East Rift Zone. The PHS occurs at a left step in the rift, where a fracture network has been formed between fault segments. It is a productive geothermal field, extracting steam and reinjecting cooled, condensed fluids. A network of eight borehole seismometers recorded >6000 earthquakes. Most of the earthquakes are very small (< M.2), and shallow (1-3 km depth), likely the result of hydrothermal fluid reinjection. Deeper earthquakes occur along the rift as well as along the south-dipping fault plane that originates from the rift zone.

Seismic methods applied to the PHS data set, after the initial recording, picking, and locating earthquakes, include a tomographic inversion of the P-wave first arrival data. This model indicates a high seismic velocity under the field that is thought to be an intrusion and the heat source of the hydrothermal system. A shear wave splitting study suggested the PHS fracture system is largely oriented rift-parallel with some orthogonal fractures. Shear wave splitting data also were used in a tomographic inversion for fracture density. The fracture density is high in the PHS, which indicates high permeability and potential for extensive fluid circulation. This has been confirmed by high fluid flow and energy generation. The high fracture density is consistent with the interpretation of a transfer zone between the rift segments where a fracture mesh would be expected. In Puna the transfer zone is a relay ramp.

The results from the PHS are used as an example to examine the proposed hydrothermal system at St. George's Hill, Montserrat. In southern Montserrat, hot springs and fumaroles suggest a deep hydrothermal system heated by local magmatism. A magnetotelluric study obtained resistivity data that suggest focused alteration under southeastern Montserrat that is likely to be along fault segments. Several faults intersect under SGH, making it the probable center of the hydrothermal system. At Puna, and also Krafla, Iceland, where faults interact is an area of increased permeability, acting as a model to be applied to southern Montserrat. The conclusion is that in both Puna and Montserrat large faults interact to produce local areas of stress transfer that lead to fracturing and permeable networks; these networks allow for high-temperature hydrothermal circulation.

The mapping of induced seismicity in enhanced geothermal systems presents the best tool available for understanding the resulting hydro-fractured reservoir. In this thesis, two geothermal systems are studied; one in Krafla, Iceland and the other in Basel Switzerland. The purpose of the Krafla survey was to determine the relation between water injection into the fault system and the resulting earthquakes and fluid pressure in the subsurface crack system. The epicenters obtained from analyzing the seismic data gave a set of locations that are aligned along the border of a high resistivity zone ~2500 meters below the injection well. Further magneto-telluric/seismic-data correlation was seen in the polarity of the cracks through shear wave splitting. The purpose of the Basel project was to examine the creation of a reservoir by the initial stimulation, using an injection well bored to 5000 meters. This stimulation triggered a M3.4 event, extending the normal range of event sizes commonly incurred in hydro-fractured reservoirs. To monitor the seismic activity 6 seismometer sondes were deployed at depths from 317 to 2740 meters below the ground surface. During the seven-day period over 13,000 events were recorded and approximately 3,300 located. These events were first located by single-difference techniques. Subsequently, after calculating their cross-correlation coefficients, clusters of events were relocated using a double-difference algorithm. The event locations support the existence of a narrow reservoir spreading form the injection well. Analysis of the seismic data indicates that the reservoir grew at a uniform rate punctuated by fluctuations which occurred at times of larger events, which were perhaps caused by sudden changes in pressure. The orientation and size of the main fracture plane was found by determining focal mechanisms and locating events that were similar to the M3.4 event. To address the question of whether smaller quakes are simply larger quakes scaled down, the data set was analyzed to determine whether scaling relations held for the source parameters, including seismic moment, source dimension, stress drop, radiated energy and apparent stress. It was found that there was a breakdown in scaling for smaller quakes.

The need for an improved ability to "see into the earth" has resulted in the use of geophysical techniques, especially the electrical resistivity method, in engineering and environmental investigations. The major challenge in the use of electrical resistivity measurements however is the interpretation of the electrical response. This is due to the lack of adequate understanding of the relationships between the physical factors controlling the engineering behavior of geomaterials (earth materials) and their measurable electrical parameters. This research work therefore sets out to investigate the linkages between engineering and petrophysical properties of geomaterials and their geoelectrical parameters. This goal is achieved through the development of laboratory equipments and the conduction of both laboratory and field studies. The laboratory experiments involve the measurement of the complex resistivity responses of natural and artificial soil samples under varying effective stress conditions. The field study involves the characterization of subsurface fracture parameters from field electrical measurements in complex fractured terrains at selected farming communities in Ghana.

The results from this study improve on our knowledge and understanding of the influence of fundamental engineering properties of geomaterials on their electrical responses. It results will aid in the interpretation of field electrical measurements and provide a means for engineering properties of geomaterials to be estimated from measurable electrical parameters. It will also contribute towards using non-invasive electrical measurements to locate weak zones in the subsurface, assess and monitor the stability conditions of soil units and assist in the environmental impact assessment of anthropogenic activities on groundwater resources in complex fractured terrain.

An important challenge in the physics of granular materials is understanding how the properties of single grains, such as grain shape and friction, influence the mechanical strength and dynamical response of the bulk granular material. While spherical grains are often used to study granular materials in experiments and simulations, the interactions among grains, and in many cases the flow and stability of granular packings, change when grain shape is modified. In this dissertation, we explore the influence of friction and grain shape on grain-scale dynamics, properties of mesoscale force chains, and macroscopic stick-slip dynamics of granular materials through novel experiments. In one set of experiments, an intruder is pushed by a spring through an annular cell filled with a quasi-2D monolayer of photoelastic grains that either contact a glass substrate or float on water. We characterize the effects of basal friction between the substrate and grains, intergrain friction, intruder size, and grain shape on the dynamics of the intruder, the flow of grains during slip events, and spatial distribution of stresses within the granular material in stable sticking periods. In another set of experiments, a slider is pulled by a spring across a quasi-2D monolayer of gravity-packed grains set between two glass plates. We observe the influence of grain angularity on statistical properties characterizing the stick-slip dynamics of the slider as well as grain-scale dynamics and stresses.

We first compare the dynamics of the intruder driven through packings of disks that either contact the glass base -- having basal friction -- or float on water -- having no basal friction. At high packing fractions, we find that the intruder exhibits stick-slip dynamics when basal friction acts on the grains, but the intruder instead flows freely through the granular material, with only occasional sticking periods (called intermittent flow or clogging-like dynamics, quantified by the average time between sticking periods), when basal friction is removed. We also observe when basal friction is present that the intruder's dynamics transition from stick-slip to intermittent flow with decreasing packing fraction; this transition occurs at a higher packing fraction with lower intergrain friction. Lastly, in simulations that model this experimental system, we vary static and dynamic basal friction coefficients and show that dynamic basal friction, rather than static basal friction, determines whether the intruder exhibits stick-slip or intermittent flow at high packing fractions.

We next vary the size of the intruder and, at several different packing fractions for each intruder size, compute statistics of the waiting time between sticking periods, duration of sticking periods, energy released in slip events, and force of grains acting on the intruder. We show that each statistical measure for all intruder sizes collapses to a single curve when packing fraction is rescaled by the packing fraction below which the intruder carves out a completely open channel in the granular material. With a geometrical model, we relate the packing fraction of open channel formation to a characteristic packing fraction of the material and the ratio of the intruder's diameter and the width of the annular cell, and we confirm the prediction of this model.

We thirdly compare the dynamics of the intruder and grains with packings of disks and pentagons. We observe that the packing of pentagons exerts comparable forces on the intruder as the packing of disks, though at significantly lower packing fractions. We also find from the average flow fields of grains during slip events that disks circulate around the intruder and rotate about their centers of mass significantly more than pentagons, which tend to flow forward from the intruder. Lastly, using photoelasticimetry, for the packing of disks we measure a significantly larger spatial extent of stresses around the annular cell, and a significantly larger fraction of events that feature back-bending force chains, compared with the packing of pentagons.

In the last set of experiments, we vary grain angularity of a vertical (gravity-packed) granular material sheared by a slider. We observe that the average shearing force required to initiate slip events increases with angularity. As a result, sticking periods last longer and slip events release more energy in packings with more angular grains. We also observe differences in the flow fields of disks and angular grains in slip events; disks tend to form a pile in front of the slider, while other grains do not. Moreover angular grains are able to form local column-like structures at the surface of the bed that prop up the slider during sticking periods, while disks do not. We lastly show that the depth of the shear band and the depth of stress fluctuations between sticking periods are unaffected by grain angularity.

Overall, these novel observations from each experiment demonstrate that friction and grain shape are important factors determining properties of macroscopic stick-slip dynamics of granular materials, stress transmission in stable granular materials, and grain-scale dynamics during slip events. Our observations also serve as motivation for more robust modeling and theoretical descriptions of granular stability and flow more generally by considering the influences of basal friction and changes in grain shape.

The high power, broadband very low frequency (VLF, 3--30 kHz) and extremely low frequency (ELF, 3--3000 Hz) electromagnetic waves generated by lightning discharges and propagating in the Earth-ionosphere waveguide can be used to measure the average electron density profile of the lower ionosphere (D region) across the wave propagation path due to several reflections by the upper boundary (lower ionosphere) of the waveguide. This capability makes it possible to frequently and even continuously monitor the D region electron density profile variations over geographically large regions, which are measurements that are essentially impossible by other means. These guided waves, usually called atmospherics (or sferics for short), are recorded by our sensors located near Duke University. The purpose of this work is to develop and implement algorithms to derive the variations of D region electron density profile which is modeled by two parameters (one is height and another is sharpness), by comparing the recorded sferic spectra to a series of model simulated sferic spectra from using a finite difference time domain (FDTD) code.

In order to understand the time scales, magnitudes and sources for the midlatitude nighttime D region variations, we analyzed the sferic data of July and August 2005, and extracted both the height and sharpness of the D region electron density profile. The heights show large temporal variations of several kilometers on some nights and the relatively stable behavior on others. Statistical calculations indicate that the hourly average heights during the two months range between 82.0 km and 87.2 km with a mean value of 84.9 km and a standard deviation of 1.1 km. We also observed spatial variations of height as large as 2.0 km over 5 degrees latitudes on some nights, and no spatial variation on others. In addition, the measured height variations exhibited close correlations with local lightning occurrence rate on some nights but no correlation with local lightning or displaced lightning on others. The nighttime profile sharpness during 2.5 hours in two different nights was calculated, and the results were compared to the equivalent sharpness derived from International Reference Ionosphere (IRI) models. Both the absolute values and variation trends in IRI models are different from those in broadband measurements.

Based on sferic data similar to those for nighttime, we also measured the daytime D region electron density profile variations in July and August 2005 near Duke University. As expected, the solar radiation is the dominant but not the only determinant source for the daytime D region profile height temporal variations. The observed quiet time heights showed close correlations with solar zenith angle changes but unexpected spatial variations not linked to the solar zenith angle were also observed on some days, with 15% of days exhibiting regional differences larger than 0.5 km. During the solar flare, the induced height change was approximately proportional to the logarithm of the X-ray fluxes. During the rising and decaying phases of the solar flare, the height changes correlated more consistently with the short (wavelength 0.5-4 Å), rather than the long (wavelength 1-8 Å) X-ray flux changes. The daytime profile sharpness during morning, noontime and afternoon periods in three different days and for the solar zenith angle range 20 to 75 degrees was calculated. These broadband measured results were compared to narrowband VLF measurements, IRI models and Faraday rotation base IRI models (called FIRI). The estimated sharpness from all these sources was more consistent when the solar zenith angle was small than when it was large.

By applying the nighttime and daytime measurement techniques, we also derived the D region variations during sunrise and sunset periods. The measurements showed that both the electron density profile height and sharpness decrease during the sunrise period while increase during the sunset period.

Low frequency noise in measured sensor data is amplified when integrated. In the integration of measured acceleration data to displacement, such low frequency noise can lead to significant drift errors. In non-real-time applications, time domain and frequency domain detrending methods can be employed to remove bias and drift errors. For real-time applications, recursive high-pass digital filters, such as Butterworth filters, are computationally simple to implement. This research focuses on developing a discrete time state-space model to simultaneously filter out low frequency noise, deconvolve, and integrate voltage measurements from a geophone sensor. A circuit model for the sensor was chosen. Forward and inverse dynamical systems describing the circuit were derived utilizing the theory of linear time-invariant systems. The stability and accuracy of Butterworth filter design using the bilinear transformation method can be affected by the filter order and cut-off frequency. This research reveals the root cause of the numerical instability of high-pass digital Butterworth filters having low cutoff frequencies (less than half a percent of the sampling frequency) and high filter orders (greater than 6). These instabilities arise when filter coefficients are computed from discrete time poles and can be avoided by converting a continuous-time state-space model for the filter to discrete time via a matrix exponential. The method is demonstrated using measured geophone data.