Academic literature on the topic 'Computational geochemistry'

Least-squares reverse time migration (LSRTM) has become increasingly popular for complex wavefield imaging due to its ability to equalize image amplitudes, attenuate migration artifacts, handle incomplete and noisy data, and improve spatial resolution. The major drawback of LSRTM is the considerable computational cost incurred by performing migration/demigration at each iteration of the optimization. To ameliorate the computational cost, we introduced a fast method to solve the LSRTM problem in the image domain. Our method is based on a new factorization that approximates the Hessian using a superposition of Kronecker products. The Kronecker factors are small matrices relative to the size of the Hessian. Crucially, the factorization is able to honor the characteristic block-band structure of the Hessian. We have developed a computationally efficient algorithm to estimate the Kronecker factors via low-rank matrix completion. The completion algorithm uses only a small percentage of preferentially sampled elements of the Hessian matrix. Element sampling requires computation of the source and receiver Green’s functions but avoids explicitly constructing the entire Hessian. Our Kronecker-based factorization leads to an imaging technique that we name Kronecker-LSRTM (KLSRTM). The iterative solution of the image-domain KLSRTM is fast because we replace computationally expensive migration/demigration operations with fast matrix multiplications involving small matrices. We first validate the efficacy of our method by explicitly computing the Hessian for a small problem. Subsequent 2D numerical tests compare LSRTM with KLSRTM for several benchmark models. We observe that KLSRTM achieves near-identical images to LSRTM at a significantly reduced computational cost (approximately 5–15× faster); however, KLSRTM has an increased, yet manageable, memory cost.

The acoustic wave equation has been widely used for the modeling and reverse time migration of seismic data. Numerical implementation of this equation via finite-difference techniques has established itself as a valuable approach and has long been a favored choice in the industry. To ensure quality results, accurate approximations are required for spatial and time derivatives. Traditionally, they are achieved numerically by using either relatively very fine computation grids or very long finite-difference operators. Otherwise, the numerical error, known as numerical dispersion, is present in the data and contaminates the signals. However, either approach will result in a considerable increase in the computational cost. A simple and computationally low-cost modification to the standard acoustic wave equation is presented to suppress numerical dispersion. This dispersion attenuator is one analogy of the antialiasing operator widely applied in Kirchhoff migration. When the new wave equation is solved numerically using finite-difference schemes, numerical dispersion in the original wave equation is attenuated significantly, leading to a much more accurate finite-difference scheme with little additional computational cost. Numerical tests on both synthetic and field data sets in both two and three dimensions demonstrate that the optimized wave equation dramatically improves the image quality by successfully attenuating dispersive noise. The adaptive application of this new wave equation only increases the computational cost slightly.

To exploit Hessian information in full-waveform inversion (FWI), the matrix-free truncated Newton method can be used. In such a method, Hessian-vector product computation is one of the major concerns due to the huge memory requirements and demanding computational cost. Using the adjoint-state method, the Hessian-vector product can be estimated by zero-lag crosscorrelation of the first-/second-order incident wavefields and the second-/first-order adjoint wavefields. Different from the implementation in frequency-domain FWI, Hessian-vector product construction in the time domain becomes much more challenging because it is not affordable to store all of the time-dependent wavefields. The widely used wavefield recomputation strategy leads to computationally intensive tasks. We have developed an efficient alternative approach to computing the Hessian-vector product for time-domain FWI. In our method, discrete Fourier transform is applied to extract frequency-domain components of involved wavefields, which are used to compute wavefield crosscorrelation in the frequency domain. This makes it possible to avoid reconstructing the first- and second-order incident wavefields. In addition, a full-scattered-field approximation is proposed to efficiently simplify the second-order incident and adjoint wavefield computation, which enables us to refrain from repeatedly solving the first-order incident and adjoint equations for the second-order incident and adjoint wavefields (re)computation. With our method, the computational time can be reduced by 70% and 80% in viscous media for Gauss-Newton and full-Newton Hessian-vector product construction, respectively. The effectiveness of our method is also verified in the frame of a 2D multiparameter inversion, in which our method almost reaches the same iterative convergence of the conventional time-domain implementation.

It would be interesting to compare the two computational algorithms proposed by Raiche with Boerner and West's approach, to see which of the three is computationally fastest under similar conditions. I also note that although the semi-analytic algorithm proposed by Raiche is more elegant and may require less storage, the paper does not make it entirely clear whether we get a real reduction in computing time; reduced computational time was the motivation for the procedure in the first place.

Over many years, induction logging systems have been used to create well formation logs. The major drawback for the utilization of these tools is the long simulation time for a single forward computation. We proposed an efficient computational method based on a contrast-type of integral-equation formulation, in which we applied an approximation for the 3D electromagnetic field. We assumed that the dominant contribution in the integral equation is obtained by the contribution around the singularity of Green’s kernel. It is expected that the approximation yields reliable results when the (homogeneous) background conductivity around the logging tool is close to the actual conductivity at the location of the tool. We have developed a data-driven method to determine this background conductivity from the dominant part of the measured coaxial magnetic fields, which are mainly influenced by the conductivity at the tool sensors. For a synthetic model, the results were compared to the ones of a rigorous solution of the integral equation and show a good simulation response to small-scale variations in the medium. Further, the method was used to simulate the response of a realistic reservoir model. Such a model is created by a geological modeling program. We concluded that our approximate method was able to improve the approximation results in highly heterogeneous structures compared to the Born approximation and provide an effective medium-gradient around the tool. Our method, based on the wavefield approximation, also estimates the error, and hence yields a warning when the method becomes unreliable.

Computational physics has become an essential research and interpretation tool in many fields. Particularly in reservoir geophysics, ultrasonic and seismic modeling in porous media is used to study the properties of rocks and to characterize the seismic response of geologic formations. We provide a review of the most common numerical methods used to solve the partial differential equations describing wave propagation in fluid-saturated rocks, i.e., finite-difference, pseudospectral, and finite-element methods, including the spectral-element technique. The modeling is based on Biot-type theories of dynamic poroelasticity, which constitute a general framework to describe the physics of wave propagation. We explain the various techniques and discuss numerical implementation aspects for application to seismic modeling and rock physics, as, for instance, the role of the Biot diffusion wave as a loss mechanism and interface waves in porous media.

With the current developments in imaging/computational techniques and resources, computational rock physics has been emerging as a new field of study. Properties of rocks are examined by carrying out extensive numerical simulations on rocks that have been digitized using high-resolution X-ray CT scans. The ultimate goal of computational rock physics is to supplement the traditional laboratory measurements, which are time consuming, with faster numerical simulations that allow the parameter space to be explored more thoroughly. We applied the finite-element method to compute the static effective elastic properties from 3D microtomographic images of Berea sandstone saturated with different fluids. From the computations, we found discrepancies between the numerical results and the laboratory measurements. The reason for such a problem is the loss of small features, such as fine cracks and micropores, in the digitized matrix during the imaging and aggregation process. We used a hybrid approach, combining the numerical computation and the effective media theories — the differential effective medium model and the Kuster-Toksöz model — to deduce the lost cracks by a very fast simulated annealing method. We analyzed the sensitivity of the inverted results — the distributions of crack aspect ratios and concentrations — to the clay content. We found that the inverted crack distribution is not so sensitive to clay content. Compared with the effect of cracks on the computed effective elastic properties, clay has only a secondary effect. Our approach can recover the lost cracks and is capable of predicting the effective elastic properties of the rocks from the microtomographic images for different fluid saturations. Compared with the traditional inversion schemes, based only on the effective media theories, this hybrid scheme has the advantage of utilizing the complex microstructures that are resolved in the imaging process, and it helps define the inversion space for crack distribution.

Machine learning algorithms are designed to identify efficiently and to predict accurately patterns within multivariate data. They provide analysts computational tools to aid predictive modelling and the interpretation of interactions between data and the phenomena under investigation. The analysis of large volumes of disparate multivariate geospatial data using machine learning algorithms therefore offers great promise to industry and research in the geosciences. Geoscience data are frequently characterised by a restriction in the number and distribution of direct observations, irreducible noise in these data and a high degree of intraclass variability and interclass similarity. The choice of machine learning algorithm, or algorithms and the details of how algorithms are applied must therefore be appropriate to the context of geoscience data. With this knowledge, I aim to employ machine learning as a means of understanding the spatial distribution of complex geological phenomena. I conduct a rigorous and comprehensive comparison of machine learning algorithms, representing the five general machine learning strategies, for supervised lithology classification applications. I also develop and test a novel method for obtaining robust estimates of the uncertainty associated with machine learning algorithm categorical predictions. The insights gained from these experiments leads to the further development and comparison of new methods for the incorporation of spatial-contextual information into machine learning supervised classifiers. In using machine learning algorithms for geoscience applications, I have developed bestpractice methodologies that address the challenges facing geoscientists for geospatial supervised classification. Guidelines are established that detail the preparation and integration of disparate spatial data, the optimisation of trained classifiers for a given application and the robust statistical and spatial evaluation of outputs. I demonstrate, through a case study in a region that is prospective for economic mineralisation, the combination of supervised and unsupervised machine learning algorithms for the critical appraisal of pre-existing geological maps and formulation of meaningful interpretations of geological phenomena. The experiments conducted as part of my research confirm the efficacy of machine learning algorithms to generate accurate geological maps representing a variety of terranes. I identify and explore key aspects of the spatial and statistical istributions of geoscience data that affect machine learning algorithm performance. My research clearly identifies Random Forests™ as a good first-choice algorithm for the prediction of classes representing lithologies using commonly available multivariate geological and geophysical data. Furthermore, Random Forests prediction uncertainty is shown to be closely related to ambiguous and/or erroneous classifications and, thus provides a practical means of indicating variable levels of confidence. Spatial-contextual information is best incorporated into machine learning supervised classifiers via the pre-processing of input variables and/or the post-regularisation of classifications. My findings indicate that a trade-off between optimal predictive models and interpretable explanatory models exists, whereby, intuitively interpretable models are not necessarily the most accurate. The practical application of machine learning algorithms requires the implementation of three key stages: (1) data pre-processing; (2) algorithm training; and (3) prediction evaluation. This methodology provides the foundation for generating accurate and geologically meaningful predictions with minimal user intervention and assists in the formulation of robust interpretations of complex geological phenomena. For example, classifications obtained by Random Forests are useful for critically appraising interpreted geological maps. Clusters produced by Self-Organising Maps indicate the presence of discrete, spatially contiguous and geologically significant sub-classes within individual lithological units, which represent regions of contrasting primary composition and alteration styles. My results may be widely applied to a broad range of practical geoscience challenges such as ore deposit targeting, geo-hazard risk assessment, engineering and construction projects, hydrological and environmental modelling and ecological studies. The applications of machine learning algorithms detailed in this thesis align well with state-of-the-art Big Data online infrastructure and virtual laboratories currently emerging in Australia.

Stable and clumped isotopic compositions of molecules and minerals carry the signatures of temperatures and other physical and chemical conditions of the time of their formation. Isotopic compositions of such precipitate are preserved in carbonate that provides information about the climate through geological time. The carbonates formed in the aquatic environment serve as an archive for past climate and temperature reconstruction. In nature, sedimentary carbonate rocks are primarily composed of minerals calcite (CaCO3) and dolomite (CaMg(CO3)2). They comprise ~20% of the surface sedimentary rocks on Earth and are also found in other planets, with the oldest being ~3.5 Ga, almost as primitive as the Earth itself. The majority of them form in the aquatic environments that ranged from the warm, sunlit shallow seafloor to the cold, perpetually dark, deep ocean. Carbonate rocks are also traced in the terrestrial and extraterrestrial environment, which includes terrestrial spring waters, rivers and lakes, caves, soils, and meteorites from outer space. Ab initio quantum chemical simulations are used to calculate the extent of equilibrium and kinetic isotope fractionations, which provided additional theoretical references in clumped isotope paleothermometry. Ab initio quantum chemical simulations provide the inputs in terms of vibration frequencies and thermal energies of the optimized stable molecules and the transition state structures for the partition function calculations of equilibrium and kinetic fractionations. Ab initio calculations using density functional theory (DFT) are performed using 'Gaussian09' computational chemistry packages. Equilibrium constant and partition function calculations are performed using scripts in Matlab and Python. Though the clumped isotope proxy is based on the temperature dependence of 13C-18O bonding preference in the mineral lattice, which is captured in the product CO2, there is limited information on the phosphoric acid reaction mechanism and the magnitude of clumped isotopic fractionation (mass 63 in CO32- to mass 47 in CO2) during the acid digestion. We explored the reaction mechanism for phosphoric acid digestion of calcite using first-principles density functional theory. We identified the transition state structures for each protonation reaction involving different isotopologues and used the corresponding vibrational frequencies in reduced partition function theory to estimate Δ47 acid fractionation. We showed that the acid digestion reaction, which results in the formation of CO2 enriched with 13C-18O bonds, commences with the protonation of calcium carbonate in the presence of water. Our simulations yielded a relationship between Δ47 acid fractionation for calcite and reaction temperature as Δ47 acid fractionation in calcite = -0.30175 + 0.57700*105/ T2 - 0.10791* (105/ T2)2, with T varying between 298.15 K and 383.15 K. This relationship shows a higher slope (Δ47 acid fractionation vs. 1/T2 curve) than previous studies based on the H2CO3 model. The theoretical estimates from the present and earlier studies encapsulate experimental observations from both 'sealed vessel' and 'common acid bath' acid digestion methods from literature. Previous theoretical models for determining clumped isotopic fractionation in product CO2 during acid digestion of carbonates are independent of the cations present in the carbonate lattice. Hence further study is required to understand the cationic effect. We studied the acid reaction mechanism and calculated the acid fractionation factor for dolomite using partition functions and vibrational frequencies obtained for the transition state structure, and determined the effect of cations on the acid fractionation factor. Theoretically obtained acid fractionation factor for dolomite can be expressed as Δ47 acid fractionation in dolomite = -0.28563 + 0.49508*(105/ T2) - 0.08231* (105/ T2)2 for a temperature range between 278.15 K and 383.15 K. The theoretical slope of the dolomite-acid digestion curve is lower than that of the calcite-acid digestion curve obtained using the identical reaction mechanism. Our theoretical slope is consistent with the result from the common acid bath experiments but higher than the slope obtained in the experimental study using the sealed vessel and modified sealed vessel method and previous theoretical study using the H2CO3 model. Transition state structure, obtained in our study, includes the cations present in the carbonate minerals and provides distinct acid fractionation factors for calcite and dolomite. The observed gentler slope of theoretically calculated dolomite-acid digestion curve compared to calcite is expected considering the stronger Mg-O bond. In the present theoretical study, we provided the acid digestion reaction mechanism based on the protonation and determined a quantitative acid digestion correction factor for a range of reaction temperature for the experimental protocols where the product CO2 is immediately removed from the system, and there is not enough chance of post-digestion isotope exchanges. We suggest using appropriate acid digestion correction factors depending on the experimental techniques used for acid digestion of carbonates.
CSIR-UGC NET JRF & SRF Fellowship

In this chapter, the most important quantum-mechanical methods that can be applied to geological materials are described briefly. The approach used follows that of modern quantum-chemistry textbooks rather than being a historical account of the development of quantum theory and the derivation of the Schrödinger equation from the classical wave equation. The latter approach may serve as a better introduction to the field for those readers with a more limited theoretical background and has recently been well presented in a chapter by McMillan and Hess (1988), which such readers are advised to study initially. Computational aspects of quantum chemistry are also well treated by Hinchliffe (1988). In the section that follows this introduction, the fundamentals of the quantum mechanics of molecules are presented first; that is, the “localized” side of Fig. 1.1 is examined, basing the discussion on that of Levine (1983), a standard quantum-chemistry text. Details of the calculation of molecular wave functions using the standard Hartree-Fock methods are then discussed, drawing upon Schaefer (1972), Szabo and Ostlund (1989), and Hehre et al. (1986), particularly in the discussion of the agreement between calculated versus experimental properties as a function of the size of the expansion basis set. Improvements on the Hartree-Fock wave function using configuration-interaction (CI) or many-body perturbation theory (MBPT), evaluation of properties from Hartree-Fock wave functions, and approximate Hartree-Fock methods are then discussed. The focus then shifts to the “delocalized” side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field Xα method (MS-SCF-Xα) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is followed by discussion of empirical simulation, and we conclude by mentioning a recent approach incorporating density-functional theory and molecular dynamics (Car and Parrinello, 1985).

As geochemists, we frequently need to describe the chemical states of natural waters, including how dissolved mass is distributed among aqueous species, and to understand how such waters will react with minerals, gases, and fluids of the Earth's crust and hydrosphere. We can readily undertake such tasks when they involve simple chemical systems, in which the relatively few reactions likely to occur can be anticipated through experience and evaluated by hand calculation. As we encounter more complex problems, we must rely increasingly on quantitative models of solution chemistry and irreversible reaction to find solutions. The field of geochemical modeling has grown rapidly since the early 1960s, when the first attempt was made to predict by hand calculation the concentrations of dissolved species in seawater. Today's challenges might be addressed by using computer programs to trace many thousands of reactions in order, for example, to predict the solubility and mobility of forty or more elements in buried radioactive waste. Geochemists now use quantitative models to understand sediment diagenesis and hydrothermal alteration, explore for ore deposits, determine which contaminants will migrate from mine tailings and toxic waste sites, predict scaling in geothermal wells and the outcome of steam-flooding oil reservoirs, solve kinetic rate equations, manage injection wells, evaluate laboratory experiments, and study acid rain, among many examples. Teachers let their students use these models to learn about geochemistry by experiment and experience. Many hundreds of scholarly articles have been written on the modeling of geochemical systems, giving mathematical, geochemical, mineralogical, and practical perspectives on modeling techniques. Dozens of computer programs, each with its own special abilities and prejudices, have been developed (and laboriously debugged) to analyze various classes of geochemical problems. In this book, I attempt to treat geochemical modeling as an integrated subject, progressing from the theoretical foundations and computational concerns to the ways in which models can be applied in practice. In doing so, I hope to convey, by principle and by example, the nature of modeling and the results and uncertainties that can be expected. Hollywood may never make a movie about geochemical modeling, but the field has its roots in top-secret efforts to formulate rocket fuels in the 1940s and 1950s.

A complex reservoir usually requires tools and workflow which are beyond conventional formation evaluation techniques. In the case of source rock plays, the complex petrophysics are solved with the addition of advanced logging tools such as NMR for porosity and permeability determination, dielectric for fluid saturation, elemental spectroscopy for identification and quantification of minerals, and core data, ideally pressure core for petrophysical calibration. Formation evaluation for source rocks must be integrated with geochemical analysis to evaluate TOC and/or kerogen, geomechanics analysis to evaluate rock fracability and quantification of faults and natural fractures if present. TOC analysis can be done with standard logging tools with the DeltalogR or Schmoker methods, and the geomechanical analysis can be done with dipole or multipole sonic tools through anisotropy evaluation and elastic properties computations to help quantify areas where fracture conductivity is easier to achieve. Geochemistry and geomechanics log results require high quality core data to calibrate TOC and organic material maturity using pyrolysis or LECO combustion technique and to calibrate elastic properties using triaxial pressure test., Leak Off Test (LOT/XLOT), or microfrac/DFIT. This paper presents a proven workflow and lessons learnt from recent source rock reservoir evaluations using advanced logging tools. The goal of this presentation is to improve understanding on how source rock reservoirs must be evaluated to be completed and commercially produced, such as in emerging Indonesian Source Rock plays.