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An attempt is made to model the thermal history of a self-gravitating Moon. Since the Rayleigh number at the end of the accretionary stage is supercritical, thermal convection in the Moon is likely to have occurred as early as 4.6 billion years ago. A combination of the Stokes equation of viscous flow and the heat transfer equation is solved, using the finite element method. The numerical code used is a modification of Gartling's NACHOS, a general purpose code for transient, two-dimensional incompressible fluid flow problems. The effects of melting, viscous dissipation and adiabatic gradient are included. A uniform distribution of radioactive nucleides is assumed, and their decay with time is taken into account. The code also allows for the simulated growth of a core of 300 km radius, and the energy that such a process releases into the convecting mantle. Viscosity is assumed to be Newtonian, appropriate for a mantle of dry olivine composition. An accretionary initial temperature profile is chosen that remains everywhere below the basalt solidus. Thus unlike in previous lunar models, no initial "basalt sea" is assumed. The algorithms developed in this study have been made general enough to model the thermal histories of any of the terrestrial planets, so that these results may then be compared with those of "convection-simulated" and parametrized convection models. The results show that the convection pattern is dominated by a L-2 mode, and that viscosity is the predominant factor in controlling the nature of the thermal evolution. Partial melting is observed very early in the Moon's history, which could be related to the formation of the lunar basalt maria. The present day lithospheric thickness of the model is about 600 km and core-mantle temperatures are close to 1600(DEGREES)K. Surface heat flux is 15.3 mW/m('2), higher than the "steady state" value by about 12%.

The use of seismic attribute studies in the petroleum industry is fast spreading. Seismic attribute studies entail the integration of derived attributes from 3-D seismic data with well log, core and/or outcrop data (through multivariate linear regression, neural networks, etc.) to estimate and project physical properties in areas of sparse data control. Because of the accuracy of this technique in predicting the subsurface distribution of physical properties in 3-D space, and delineating depositionally and non-depositionally controlled trends not readily apparent from other methods commonly used in sedimentary geology (e.g., facies modeling, geostatistics, and sequence stratigraphy), it becomes an important tool for sedimentary geologists. / We illustrate the techniques and advantages of the approach to predict 3-D distribution of porosity in stratigraphically complex carbonate buildups of the Upper Jurassic Smackover Formation at Appleton Field, southwest Alabama. We predict that porosity is thicker on the forereef flanks than on the crest of paleostructure.

In this thesis, Mars Global Surveyor mapping-phase magnetic data are used to derive a combined spherical harmonic model of both Martian crustal and time-dependent external magnetic fields. / A 60-degree spherical harmonic model of the crustal magnetic anomalies is first isolated, by averaging of in-shadow data over 0.5° x 0.5° latitude and longitude bins, and covariance analysis between multiple independent models. This model is then subtracted, separately, from day-side and night-side measurements. External residual data are expended in terms of now time-dependent 30-degree spherical harmonics, using 1 year and 1/2 year periods, and with separate internal and external radial dependencies. Independent Fourier series expansions allow to validate the temporal variations of the preceding model. / As a result, I obtain, along with the crustal anomaly maps, the spatial distribution of the external fields, their steady-state features, and the amplitude maps of their yearly and half a year variations, separately for day and night sides of Mars. Although the maxima of the temporal amplitudes show good correlations with the strong crustal anomalies, there are significant differences between them. / Keywords. covariance analysis, crustal anomalies, magnetic anomalies, magnetic field, magnetosphere, Mars, Mars Global Surveyor, spherical harmonics, temporal amplitudes

Multi-channel, multi-dimensional geophysical data models are explored in this thesis. The basic data model we develop, the one-pass, multi-channel, multi-dimensional autoregressive (OPMCTDAR) data model, describes data as the linear superposition of a causal, multi-channel, two-dimensional, deterministic AR filter with a stochastic innovation which is assumed to have minimum-variance, and to be uncorrelated and Gaussian. Two-pass and four-pass extension of this basic model (TP or FPMCTDAR) are also developed in this work as a generalization of the AR data models described by Gregotski (1989), Gregotski et al. (1991) and Jensen et al. (1990, 1993). Direct inversion for the parameters of the one-pass data model is employed in the inversion processes of two-pass and four-pass data models. Least-squares estimates of the causal AR filter coefficients are used to deconvolve original data sets to recover the assumed minimum-variance innovation process. Two-channel, two-dimensional synthetic data modelling examples are presented to prove the validity of this inversion scheme for these data models. I show that two-pass and four-pass inversion schemes extended from those of the corresponding single-channel case work for the only special cases of TP or FPMCTDAR data models. I employ two-dimensional z-transform for the mathematical derivation of the data models and the discussion on the stability of the multi-channel system functions.

In this thesis I use two-dimensional thermo-chemical mantle convection models to investigate the deformation of the continental lithosphere that follows the oceanic lithosphere into the subduction zone. The models account for the compositional buoyancy of the crustal layers by considering lithospheric plates that consist of a low-density crustal layer and a high-density mantle part. They also allow the basalt-eclogite phase change in the subducted oceanic crust. Two sets of kinematic and dynamic plate models are studied. In the kinematic models, the flow is driven by an imposed surface velocity, and rigid lithospheric plates are generated by adopting temperature-dependent viscosity. In the dynamic models, the buoyancy forces due to internal density variations provide the driving force of convection, and temperature, depth, and stress-dependent viscosity is used to achieve uniform plate motion. / The results of the kinematic models show that the subduction of the continental crust is strongly controlled by the imposed surface velocity and the lithospheric viscosity. For most models with realistic rheologies, the continental lithosphere subducts to lower mantle depths as a coherent layer. Crustal detachment occurs only when crust-mantle coupling is weak. In such a case the mantle lithosphere continues its descent, while the crust detaches at depths <150 km and accumulates at the top. / In contrast, the dynamic models show that continental convergence results in crust-mantle detachment in the subducting plate and crustal thickening in both subducting and overriding plates. The depth of detachment ranges from 100 to 170 km. As the thickness of the crust increases, the convergence velocity in the collision zone decreases and the location of subduction gradually shifts toward the interior of the subducting plate. In models with greater viscosity, the subducting mantle lithosphere maintains its integrity and does not break up. In models with weaker rheology, the positive buoyancy of the thickened crust can overcome the strength of the subducting lithosphere, and subsequently a state of tensional stress develops in the upper part of the slab that ultimately causes the oceanic slab to break off and sink into the mantle. The breakoff occurs over a time interval of 10 to 20 m.y. (depending on plate velocity), which is roughly the time needed for the crust to reach its maximum thickness. The models indicate no rapid asthenospheric upflow and related heating of the base of the crust as a consequence of slab breakoff. Crustal detachment takes place over a wide range of lithospheric strength values, suggesting that in the dynamic models crustal buoyancy has an important role in the dynamics of continental subduction.

Airborne magnetic field data exhibit downward continued power spectra of the form $1/f sp beta$ (where f is the spatial frequency and $ beta$ is a non-negative real number). This form of spectrum is observed for magnetic data recorded over a range of sampling scales from various areas of the Canadian Shield. Two scaling regimes have been discovered. The first has a $ beta$ value near 3 for wavelengths $ sbsp{ sim}{$25 km. These results suggest a "variable fractal" description of the distribution of near-surface magnetic sources. / From a data modelling viewpoint, the magnetic measurements are derived from a linear superposition of a deterministic system function and a stochastic excitation process. A symmetric operator corresponds to the system function, and the near-surface magnetic source distribution represents the excitation process. The deconvolution procedure assumes an autoregressive (AR) system function and proceeds iteratively using bi-directional AR (BDAR) filtering in one dimension, which is extended to four-pass AR filtering in two dimensions. The traditional assumption of a spectrally white innovation is used in the deconvolution procedure. The data are modified prior to deconvolution by a Fourier domain prewhitening technique, to account for the long wavelength content of the fractal innovation. Deconvolution of the modified data produces the system function, which is removed from the original data to produce the near-surface magnetic source distribution. This distribution serves as a susceptibility map which can be used for enhancing magnetic field anomalies and geological mapping. Thus, the statistical descriptions of near-surface magnetic sources are useful for modelling airborne magnetic data in "shield-type" geologic environments.

The aim of this thesis is to investigate various procedures for the processing of high rate and high resolution superconducting gravimeter (SG) data. First, two SG gravity data sets from Cantley, Canada and Strasbourg, France are processed by following exactly the same steps. After we manually pre-process the recorded gravity, we perform a least squares procedure (HYCON package) to fit tides, atmospheric pressure and long term drifts. We obtain the gravity residuals and the corresponding power spectral density (PSD) using a Fast Fourier Transform. Subsequently a slew rate method is applied to automatically detect and correct the spikes and offsets in the Cantley data. A least squares procedure is again performed. The PSD of the gravity residuals show that there are no significant geophysical signals except harmonics of the daily atmospheric pressure in the sub-tidal frequency bands. In particular, we do not find evidence of the reported Slichter triplet. / In order to fully exploit the various components of the gravity data and determine what factors affect the determination of the pressure admittances, tidal parameters ($ delta, kappa$) and signal levels, we have simulated the SG data by adding together of a synthetic tide, a brown noise, an actual atmospheric pressure record, a polynomial instrumental drift, artificial spikes and offsets, and a theoretical model for the Slichter triplet. The slew rate method and a more precise least squares procedure (ETERNA package) were applied to process the combined synthetic data. Using the PSD of the residual gravity signals in the sub-tidal bands, the theoretical Slichter triplet constructed in the data could be well recovered. Therefore we are confident the reported Slichter triplet should have been seen in our observed data.

Physical analogs to the statistical properties of a theoretical flicker noise model are extracted from published accounts of the character of the record. Analogies are drawn between the temporal scales of variability of sedimentary processes, and the spatial scales of acoustic impedance variability. A linear model is proposed as a first approximation. It is consistent with both impedance characteristics and the dual, cyclic spatial and episodic temporal, nature of the sedimentary record. This model consists of the superposition of independent random processes having logarithmically distributed correlation times. Processes occurring over some discrete frequency range define distinct scales of 'stability' in the evolution of sedimentary environments. The contribution which a range of frequencies makes towards the character of the impedance spectra is a reflection of the continuity of conditions favouring the deposition of a particular lithology. The magnitude of change at a particular scale is a reflection of the recurrence interval of effective processes.