<p> Granular solids such as natural rocks and concrete show nonlinear elasticity in response to dynamic deformation with a large strain amplitude. Resonance experiments can measure the nonlinear elasticity using resonance curves which show response amplitudes as a function of driving (oscillation) frequencies. To analyze the nonlinear elasticity observed in resonance experiments, I first simulate a nonlinear oscillation system (i.e., Duffing equation) that involves a cubic term in the equation of state. The simulation illustrates three critical factors, i.e., driving frequency, driving amplitude, and the initial condition of the deformation; these factors control the stable solution that is the sustained amplitude of the Duffing oscillation. </p><p> I propose a thermodynamics-based model to reproduce the nonlinear resonance features observed in laboratory experiments of rocks and concrete including (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) asymmetric resonance curves in the direction of the driving frequency, (c) the difference between resonance curves when the driving frequency is swept upward and downward, and (d) the presence of a cliff segment to the left of the resonant peak under the condition that the nonlinearity in the oscillation system is strong. This model provides a unified interpretation of nonlinear elasticity. The asymmetry of the resonance curve is caused by softening, which is documented by a reduction of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change in the response amplitude when the driving frequency is changed. </p><p> The simulated Duffing oscillation system shows similar behavior as the resonance simulations. The bifurcation originates from the strong nonlinearity in the oscillation system and is present in both simulations. Extensions of the thermodynamics-based model could include temperature, moisture (pore pressure), and confining pressure. This thesis could contribute to geophysical applications such as monitoring of fracture healing after hydraulic fracturing in unconventional oil and gas reservoirs as well as in enhanced geothermal systems.</p><p>

Probabilistic fault displacement hazard analysis (PFDHA) is a method development for assessment of the fault rupture hazard and the amount and distribution of co-seismic fault displacement. The method has been developed for normal faulting tectonic settings and developed further for being suitable for strike-slip fault types. For the thrust fault settings, only the parts regarding the probability and the amount of displacement on the primary fault have been examined, but the analysis of the distributed faulting in reverse fault environments has been lacking in the scientific discussion. The purpose of this thesis is to create a probabilistic model for predicting the surface deformation related hazard in thrust fault environments. The analysis of this thesis is based on the analysis of empirical database gathered from 11 historical, well-studied thrust earthquakes. The database was used in the analysis of the spatial distribution of secondary surface rupturing and establishing the attenuation relationships to the amount of dislocation for the increasing distance from the principal fault. The general methodology followed the one defined by previous authors for the PFDHA, but especially for the analysis of the distributed fault rupturing several methodological decisions needed to be done during the work to obtain a statistically robust and reliable model that could be used for prediction purposes. The model utilizes as input the parameters derived from the calculation of the probability of the occurrence, and the amount of distributed faulting, as well as the surface geometry of the fault to be modelled. The model computes the probability of the secondary rupturing exceeding a certain displacement level, or the amount of the secondary slip with a given probability using a 10 x 10 m grid. Together the values computed to all the grid points separately form continuities that can be illustrated on a map. This enables the location specific analysis of the seismic hazard. In the last section of this work the developed model is applicated to the Suasselkä post-glacial fault, situated in Northern Finland. The application is done for a scenario where the fault ruptures for its total surface rupture length, and the probability of surface deformation is analysed in the surroundings of the fault. The model created here can be applied to any well-known mapped fault trace of a reverse kinematics for estimating the seismic event related risk on specific locations around an active fault. / PFDHA-menetelmä (Probabilistic fault displacement hazard analysis) on kehitetty seismisiin siirrosvyöhykkeisiin liittyvän riskin sekä seismisen siirtymän määrän ja jakauman arviointiin. Menetelmä on kehitetty normaalisiirroksille, mutta sitä on kehitetty edelleen sivuttaissiirroksiin ja työntösiirroksiin sopivaksi. Työntösiiroksille on aiemmin kehitetty vain pääsiirroksen siirtymän todennäköisyyttä ja määrää kuvaavat laskelmat, mutta sekundäärisiirrosten analyysi on puuttunut tieteellisestä keskustelusta. Tämän pro gradu -tutkielman tarkoitus on luoda todennäköisyyksiin perustuva ennustusmalli, jota voidaan käyttää mallintamaan maanpinnan muutoksiin liittyvää riskiä työntösiirrosten ympäristössä. Tämän tutkielman analyysi perustuu 11 historiallisen, hyvin tutkittuun työntösiirrosmaanjäristykseen. Näistä luotua tietokantaa käytettiin sekundäärisiirrosten avaruudellisen jakauman arvioimiseen sekä sekundäärirepeämisen vaimenemissuhteen analysoimiseen etäisyyden pääsiirrokseen kasvaessa. Käytetty menetelmä perustuu pääpiirteissään perinteiseen PFDHA-menetelmään, mutta erityisesti näiden sekundäärisiirrosten analyysin osalta menetelmää koskevia päätöksiä tuli tehdä työn edetessä, jotta lopputuloksena oli tilastollisesti pitävä ja uskottava malli, jota voidaan käyttää riskin arvioinnissa. Malli käyttää syötteenään sekundäärisiirrosten tapahtumisesta ja siirrosten suuruudesta johdettujen todennäköisyysfunktioiden muuttujia, sekä mallinnettavan siirroksen pintageometriaa. Malli laskee sekundäärirepeämän todennäköisyyden ylittää annettu siirtymä tai määritetyllä todennäköisyydellä tapahtuvan siirtymän suuruuden 10 x 10 m ruudukolla pääsiirroksen ympäristössä kullekin ruudulle erikseen. Yhdessä näille ruuduille lasketuista arvoista muodostuu jatkumoja, joita voidaan kuvata kartalla. Tämä antaa mahdollisuuden maanjäristykseen liittyvän seismisen riskin tarkkaan paikkakohtaiseen analyysiin. Työn viimeisessä osassa kehitettyä mallia sovelletaan Pohjois-Suomessa sijaitsevaan Suasselän jääkauden jälkeiseen työntösiirrokseen ja sen ympäristöön. Mallia sovelletaan skenaariolle, jossa siirros liikkuu koko pituudeltaan, ja maanpinnan liikuntojen todennäköisyyttä mallinnetaan siirroksen ympäristössä. Tässä työssä kehitettyä mallia voidaan soveltaa mille tahansa hyvin tunnetulle, aktiiviseksi määritellylle työntösiirrokselle siirroksen seismisen riskin arvioimiseen tietyissä kohteissa siirroksen ympäristössä.

<p> Glacier and ice sheet geometry depend on climatic and ice dynamic processes that are coupled and often highly complex. Thus, partitioning and understanding the drivers of change to glacier and ice sheet geometry requires creative approaches. </p><p> Radiostratigraphy data document emergent layers in the ablation zone of western Greenland that emulate theoretical englacial flow paths. Yet true alignment between radar layers and the englacial flow field can be uncertain because these structures have travelled hundreds of km from their original point of deposition, have been shaped by ice deformation for millennia, and have been subjected to complex and three-dimensional ice motion across steep and rugged bedrock terrain. In Chapter 2 I address this problem. Using ice dynamics information from a thermomechanically coupled, higher order ice sheet model, in conjunction with an observationally based test built on principles of mass conservation, I demonstrate that real world effects do not disrupt alignment between targeted ablation zone emergent radar layers and the local, present-day ice flow field. </p><p> Topographically driven processes such as wind-drifting, avalanching, and shading, can sustain mountain glaciers situated in settings that are otherwise unsuitable for maintaining glacier ice. Local topography can thus disrupt the way regional climate controls glacier retreat, which limits insight into the climate representativeness of some mountain glaciers. In Chapters 3 and 4 I address this issue. Analyzing glaciological, geodetic, and meteorological data, I quantitatively demonstrate that the glacier-climate relationship at a retreating cirque glacier evolved as mass balance processes associated with local topography became more influential from 1950 to 2014. I then assess regional glacier area changes in the Northern Rockies from the Little Ice Age glacial maxima to the modern. I characterize terrain parameters at each glacier and estimate glacier thickness. Using these data and extremely simple models of ice mass loss I assess climatic, topographic, and glaciological drivers. Predictable factors like initial glacier size, aspect, and elevation only partly explain the observed pattern of glacier disappearance. This implies that less predictable and poorly resolved processes like avalanching and wind-drifting drive spatially complex patterns of glacier mass change across this mountain landscape.</p><p>

Tämä tutkielma käsittelee sähkömagneettiseksi pulssimenetelmäksi tai TEM-menetelmäksi kutsuttua geofysikaalista tutkimusmenetelmää, jonka avulla maa- ja kallioperän sähkönjohtavuusrakenteesta voidaan saada tietoa. Asioita tarkastellaan malminetsinnän näkökulmasta, mutta painottaen teoriaa käytännön esimerkkien asemesta. Tämän lisäksi tarkastelu koskee lähinnä maanpintamittauksia. Teoreettisen tarkastelun avulla pyritään havainnollistamaan primaarikentän aaltomuodon vaikutusta johteesta saatavaan vasteeseen. Jos maankamaran porrasvaste tunnetaan, sähkömagneettisia ilmiöitä kuvaavien yhtälöiden lineaarisuudesta johtuen mielivaltaisen primaaripulssin aiheuttama vaste voidaan laskea konvoluution avulla, mitä on havainnollistettu yksityiskohtaisesti tarkastelemalla johtavaa palloa eristävässä kokoavaruudessa. Lähetinsilmukassa tapahtuvan porrasmaisen virranmuutoksen seurauksena induktiokelalla mitattava db/dt-vaste on impulssivaste, joka on kääntäen verrannollinen johteen aikavakioon, jolloin suuren aikavakion omaavasta eli hyvästä johteesta saatava vaste on heikko. Tätä ilmiötä voidaan ehkäistä mittaamalla b-vaste fluxgate- tai SQUID-magnetometrillä, jolloin mitattava vaste on porrasvaste. Induktiokelalla porrasvaste voidaan mitata lähetinsilmukassa tapahtuvan lineaarisen virranmuutoksen aikana. Toisaalta, kun johteen aikavakio on pieni, johteesta saadaan voimakkaampi vaste mittaamalla impulssivaste. Riippuen kohinatasoista pienen ja suuren aikavakion välinen raja voi olla esimerkiksi 10 millisekuntia. Primaarikentän jaksollisuudesta johtuen off-time-vaste heikkenee, jos jaksonpituus on liian lyhyt verrattuna johteen aikavakioon. Mittaamalla on-time-vaste erityisen hyvästäkin johteesta saadaan aina indikaatio. Primaarikentän perustaajuuden on oltava riittävän matala, jotta useasta eri laatuisesta johteesta saatavat vasteet on mahdollista erottaa toisistaan. Tämän vuoksi sähkömagneettisen pulssimenetelmän käytössä on viimeisten kahdenkymmenen vuoden aikana siirrytty kohti yhä matalampia perustaajuuksia (< 1 Hz).

<p> Understanding the elastic properties of unconsolidated granular media is crucial for interpreting seismic and sonic log data in soils and unconsolidated petroleum reservoirs. Rock and soil deformations are often estimated indirectly using rock physics models that relate changes in elastic properties to pore compliance. The complex microstructure of geological materials in represented by simple geometries in most rock physics models. One such model, the Hertz-Mindlin model, uses a pack of identical spheres to calculate elastic properties of unconsolidated sediments. The input parameters required for this model, porosity, grain radius, coordination number (number of contact points per grain) and grain to grain contact radius, are often unknown parameters and adjusted to fit the data. Direct observations of deformation can show the limitations in applicability of rock physics models. This requires 3D images obtained under in-situ pressure and temperature conditions. </p><p> I imaged changes in dry, unconsolidated quartz sand with micro X-ray computed tomography (microCT) together with ultrasonic P-wave velocities at pressure from atmospheric pressure (0.08 MPa) to 27.6 MPa. In addition to an overall compaction of the sediment leading to a 30% reduction in porosity; the microCT images show a 60% reduction in grain size due to grain crushing, a 26% increase in coordination number, and 50% to 100% increase in contact radius. </p><p> I used the image-derived porosity, grain radius, coordination number and contact radius as input data for the Hertz-Mindlin contact-radius model to compute P-wave velocities as functions of pressure. The microCT images show that numerous assumptions of the Hertz-Mindlin model are violated in sands and consequently, the model drastically overpredicts velocities. Although the velocity mismatch can be eliminated for undamaged sediments by assigning a reduced shear modulus to the contact zones, this adjusted model still overpredicts velocities of the sediment once grain crushing occurs. Thus, the Hertzian contact model should be applied with caution to angular, unconsolidated sediments. </p><p> Understanding gas hydrate morphology and the relationship between hydrate saturation and elastic properties is crucial to characterize natural occurring hydrate resources and assess their potential for production. Gas hydrates in unconsolidated sediment are often represented by effective medium models of the sediment frame and hydrate inclusions in the pore space with different morphologies which allow us to estimate gas hydrate saturation from sonic log or seismic velocities. Most effective medium models assume microstructural parameters to predict acoustic velocities. Without the constraints of direct observation, for example, pressure- and temperature-dependent variations of the sediment frame or packing rearrangements during hydrate formation, such predictions lead to discrepancies in hydrate saturation calculated from velocities. </p><p> My results verify hydrate pore-scale distributions by direct, visual observations which were previously implied by indirect, elastic property measurements. I used laboratory measurements on THF-hydrate bearing glass beads as proxy for naturally occurring gas hydrate in unconsolidated, coarse-grained sediment. Both, microCT images and ultrasonic velocity measurements, indicate that THF hydrate forms in the pore space with a part of the hydrate bridging the grains and becoming load-bearing at higher hydrate saturations. These hydrate-bearing sediments appear to follow a pore-filling model with a portion of the hydrate becoming a load-bearing part of the sediment frame at higher hydrate saturations. </p><p>

<p> The DC resistivity method has been an important tool for mineral exploration for the direct detection of conductive bodies with economic value. It has also been used for the structural mapping of lithology and alteration where boundaries are zones of economic interest and the detection of edges is the primary goal of surveying. Edge preserving inversion has been explored extensively within the context of potential field methods but has seen relatively little attention for the DC resistivity method. The focus of this thesis is to develop and implement methods which employ specific advantages of the DC method to aid the recovery of edges in the earth&rsquo;s resistivity distribution.</p><p> I begin by utilizing sparse a priori geologic knowledge to create a geologic concept of pervasive blocky resistivity. <i>l</i>₁ and <i> l</i>₀ approximating measures of model values and model gradients are used as a vehicle to inject the a priori knowledge into a regularized inversion. An iterative method is used to solve for the model that minimizes a total objective function using these general measures.</p><p> A series of synthetic modelling and inversion scenarios demonstrate the effectiveness of <i>l</i>₁ and minimum gradient support regularization to recover boundaries when compared to traditional sum-of-squares regularization. These blocky inversion schemes also exhibit an improved recovery of the resistivity value of distinct bodies. Additionally, I recognize that the various regularization types have different strengths and weaknesses. I exploit this property to create a new composite regularization that combines smooth model and blocky model regularization. This composite regularization exhibits the strengths of both regularization styles and less of the weaknesses.</p><p> A case study on field data from the Sabajo gold deposit was performed utilizing this methodology. Sharp lithologic contacts from drillholes informed the creation of a sharp resistivity concept. A blocky inversion was performed to recover a blocky model that was consistent with this concept and compared to the results of a smooth model inversion. Important differences were noted with their economic implications. I observed that the blocky regularized inversion may have recovered better estimates of the conductivity of features and this can greatly aid prioritization of targets for drilling. Finally, the differences between the inversions utilizing diverse regularization styles provided a proxy for model uncertainty.</p><p>

<p> Gas hydrates, specifically methane hydrates, are sparsely sampled on a global scale, and their accumulation is difficult to predict geospatially. Several attempts have been made at estimating global inventories, and to some extent geospatial distribution, using geospatial extrapolations guided with geophysical and geochemical methods. The objective is to quantitatively predict seafloor total organic carbon and subsequently the geospatial likelihood of encountering methane hydrates. Predictions of TOC are produced using a sparsely observed dataset (Seiter et al., 2004) through a k-nearest neighbor (KNN) algorithm using 423 predictors and 7 nearest neighbors. KNN is unsupervised and non-parametric, as I do not provide any interpretive influence on prior probability distribution, so results are strictly data-driven. This TOC prediction, along with other global datasets (seafloor temperature, pressure, sediment thickness, and crustal heat flow) are used as parameters to train a KNN algorithm in identifying likely locations of methane and/or methane hydrate accumulation. I have selected as test sites several locations where gas hydrates have been well studied, each with significantly different geologic settings. These are: The Blake Ridge (U.S. East Coast), Hydrate Ridge (U.S. West Coast), and the Gulf of Mexico. I then use KNN to quantify similarities between these sites via the normalized distance in parameter space. Results on identification of likely methane and/or methane hydrate accumulation indicate the use of KNN as an unreliable method of identifying accumulation. However, global seafloor TOC predictions are reasonably accurate and have been incorporated to provide a potential analysis on hydrocarbon accumulation.</p><p>

In this thesis I investigate how solid Earth deformation associated with glacial isostatic adjustment and mantle convection impacted ice age climate. In particular, I discard approximations that treat the Earth's internal properties as radially symmetric and demonstrate that lateral variations in viscosity and density within the Earth's mantle play an important role in understanding and interpreting surface observations. At the beginning of this thesis, I turn my attention to the Last Glacial Maximum, ~ 21 kyr ago. Estimates of the globally averaged sea level low stand, or equivalently maximum (excess) ice volume, have been a source of contention, ranging from -120 m to -135 m. These bounding values were obtained by correcting local sea level records from Barbados and northern Australia, respectively, for deformation due to glacial isostatic adjustment using 1-D viscoelastic Earth models. I demonstrate that including laterally varying mantle structure, and particularly the presence of a high viscosity slab consistent with seismic imaging and the tectonic history of the Caribbean region, leads to a significant reinterpretation of the Barbados sea level record. The revised analysis places the sea level low stand at close to -130 m, bringing it into accord with the inferred value from northern Australia within their relative uncertainties. In the following three chapters I explore the effects of dynamic topography on sea level records during past warm periods. Dynamic topography is supported by viscous flow and buoyancy variations in the Earth's mantle and lithosphere. I begin by developing a theoretical framework for computing gravitationally self-consistent sea level changes driven by dynamic topography and then combine this framework with models of mantle convective flow to investigate two important time periods in the geologic past. First, I examine the Last Interglacial (LIG) period, approximately 125 kyrs ago, which is considered to be a recent analogue for our warming world. I show that changes in dynamic topography since the LIG are on the order of a few meters, making them a non negligible source of uncertainty in estimates of excess melting during this time period. Second, I turn to the mid-Pliocene warm period (MPWP), ca. 3 Ma ago, which is a more ancient analogue for climate of the near future since temperatures were elevated, on average by ~ 2ºC. Dynamic topography has been shown to significantly deform the elevation of shoreline markers of mid-Pliocene age, particularly along the U.S. Atlantic coastal plain. It has also profoundly altered bedrock topography within the Antarctic over the last 3 Myr. I couple my dynamic topography calculations to an Antarctic Ice Sheet model to explore this previously unrecognized connection and find that changes in topography associated with mantle flow have a significant effect on ice sheet retreat in the marine-based Wilkes basin, suggesting levels of ancient instability that are consistent with offshore geological records from the region. This finding indicates that the degree to which the mid-Pliocene can be regarded as an analogue for future climate is complicated by large-scale dynamic changes in the solid Earth. In the final section of this thesis, I move to the surface record of large igneous provinces (LIPs) - which are often cited as mantle flow induced drivers of critical events in Earth's ancient climate - and examine whether the location of LIPs carries information about the stability of large-scale structures in the deep mantle that have been imaged by seismic tomography. In particular, I investigate the spatial correlation between LIPs, which are the surface expression of deep sourced mantle plumes, and large low shear wave velocity provinces (LLSVPs) at the core mantle boundary. A correlation between LIPs and margins of LLSVPs has been used to argue that LLSVPs are thermochemical piles that have been stationary over time scales exceeding many hundreds of millions of years. My statistical analysis indicates that there is a statistically significant correlation between LIPs and the overall geographic extent of LLSVPs, and this admits the possibility that LLSVPs may be more transient, thermally dominated structures. I conclude that given the limited record of LIPs, one cannot distinguish between the two hypotheses that they are correlated with the edges or the areal extent of the LLSVPs. / Earth and Planetary Sciences

Compositional patterns are extremely common in natural minerals. While, in many cases, variations in the solid mineral composition reflect the external changes in the environment at the time of the mineral formation, the role of self-organization is increasingly acknowledged. For example, in reaction-transport systems, the patterns may form spontaneously from an unpatterned state at the time of crystal growth and then become preserved by being "frozen" in the solid mineral. In this work, the pattern formation by self-organization is investigated by means of model construction and computer simulations in several minerals from different geologic environments. The impact of environmental noise is investigated on a model of oscillatory zoning in plagioclase feldspar. It is shown that environmental noise can lead to pattern formation such as oscillatory zoning, even when no deterministic periodic solutions exist. Coherence resonance close to the Hopf bifurcation is observed. Oscillatory zoning in barite-celestite system is simulated to quantitatively describe the results of the previously reported nucleation and growth experiments. The zoning is thought to be formed by autocatalytic growth from an aqueous solution. In addition to the description of the reaction-diffusion system in terns of partial and ordinary differential equations, a cellular automata model is proposed for the first time for this oscillatory crystallization type of problems. A quantitative model of banding in Mississippi Valley-type sphalerite is presented. Banded ring-like patterns are shown to arise due to a self-propagating sequence of growth and dissolution (coarsening wave). A two-dimensional model is presented for the first time and the conditions for the pattern generation and preservation are discussed. A number of time series analysis techniques are applied to characterize the compositional patterns observed in natural minerals as well as in the colored rythmites found in the marine clay sediments of the Ottawa Valley. Several caveats in interpreting the results of such analyses are outlined.

Lake Wanapitei is located in central Ontario, 40 km northeast of Sudbury. The geophysical and morphological evidence suggest that the crater originally measured 8500 m in diameter. The original ground surface has been lowered by some 300 m; material scoured from the crater floor has been deposited as glacial float on and south of the southern shoreline. The shock metamorphosed rock fragments in these deposits consist of glassy melt rocks and suevitic breccias with lithic clasts of mainly quartzite, arkose, wacke, siltstone, and diabase. This work concentrates on establishing a compositional relationship between the Wanapitei crater lithologies and the unshocked country rocks at the area. Due to the relatively young age of the structure, the impact melt glasses are well preserved, with a low content of quench plagioclase and other alterations resulting from devitrification. Presented here are the results of bulk rock XRF and microprobe analyses of the Wanapitei crater rocks together with analyses of country rocks, that may have been exposed to the impact at the time of event. The suspected target rocks are represented by Proterozoic quartzitic sediments of Mississagi, Bruce, and Gowganda Formations, and diabase dikes of Nipissing Intrusions. A least-squares mixing model has been applied to determine which of the country rocks, were mixed to produce the observed impact glass lithologies. The results indicate 56% of Mississagi and 44% of Gowganda Formations; however, secondary evidence suggests a limited contribution of the Nipissing rocks. Based on these results, the meteoritic content of the impact melts has been established, and by comparison of siderophile geochemical data with the Wanapitei samples, a chondrite has been confirmed as the most probable projectile. The grade of shock metamorphism recorded in the Wanapitei shocked rocks suggests at least 65-70 GPa for maximum pressures and up to 2500$\sp\circ$C for maximum temperatures.