Geoscience Problems Research Articles

Automatic differentiation in geophysical inverse problems

Summary Automatic differentiation (AD) is the technique whereby output variables of a computer code evaluating any complicated function (e.g. the solution to a differential equation) can be differentiated with respect to the input variables. Often AD tools take the form of source to source translators and produce computer code without the need for deriving and hand coding of explicit mathematical formulae by the user. The power of AD lies in the fact that it combines the generality of finite difference techniques and the accuracy and efficiency of analytical derivatives, while at the same time eliminating ‘human’ coding errors. It also provides the possibility of accurate, efficient derivative calculation from complex ‘forward’ codes where no analytical derivatives are possible and finite difference techniques are too cumbersome. AD is already having a major impact in areas such as optimization, meteorology and oceanography. Similarly it has considerable potential for use in non-linear inverse problems in geophysics where linearization is desirable, or for sensitivity analysis of large numerical simulation codes, for example, wave propagation and geodynamic modelling. At present, however, AD tools appear to be little used in the geosciences. Here we report on experiments using a state of the art AD tool to perform source to source code translation in a range of geoscience problems. These include calculating derivatives for Gibbs free energy minimization, seismic receiver function inversion, and seismic ray tracing. Issues of accuracy and efficiency are discussed.

Toward an automated parallel computing environment for geosciences

Software for geodynamic modeling has not kept up with the fast growing computing hardware and network resources. In the past decade supercomputing power has become available to most researchers in the form of affordable Beowulf clusters and other parallel computer platforms. However, to take full advantage of such computing power requires developing parallel algorithms and associated software, a task that is often too daunting for geoscience modelers whose main expertise is in geosciences. We introduce here an automated parallel computing environment built on open-source algorithms and libraries. Users interact with this computing environment by specifying the partial differential equations, solvers, and model-specific properties using an English-like modeling language in the input files. The system then automatically generates the finite element codes that can be run on distributed or shared memory parallel machines. This system is dynamic and flexible, allowing users to address different problems in geosciences. It is capable of providing web-based services, enabling users to generate source codes online. This unique feature will facilitate high-performance computing to be integrated with distributed data grids in the emerging cyber-infrastructures for geosciences. In this paper we discuss the principles of this automated modeling environment and provide examples to demonstrate its versatility.

The high precision gamma-ray spectrometer for lunar polar orbiter SELENE

The high precision gamma-ray spectrometer (GRS) is scheduled to be launched on the lunar polar orbiter of the SELENE mission in 2007. The GRS consists of a large Ge crystal as a main detector and massive bismuth germanate crystals as an anticoincidence detector. A Stirling cryocooler was adopted in cooling the Ge detector. The flight model of SELENE GRS has been completed and an energy resolution of 3.0 keV (FWHM) at 1.332 MeV has been achieved. The spectrometer aims to observe nuclear line gamma rays emitted from the lunar surface in a wide energy range from 100 keV to 12 MeV for one year and more to obtain chemical composition on the entire lunar surface. The gamma-ray data enable us to study lunar geoscience problems including crust and mantle composition, and volatile reservoirs at polar regions.

A model for calculating the errors of 2D bulk analysis relative to the true 3D bulk composition of an object, with application to chondrules

Certain problems in Geosciences require knowledge of the chemical bulk composition of objects, such as, for example, minerals or lithic clasts. This 3D bulk chemical composition (bcc) is often difficult to obtain, but if the object is prepared as a thin or thick polished section a 2D bcc can be easily determined using, for example, an electron microprobe. The 2D bcc contains an error relative to the true 3D bcc that is unknown. Here I present a computer program that calculates this error, which is represented as the standard deviation of the 2D bcc relative to the real 3D bcc. A requirement for such calculations is an approximate structure of the 3D object. In petrological applications, the known fabrics of rocks facilitate modeling. The size of the standard deviation depends on (1) the modal abundance of the phases, (2) the element concentration differences between phases and (3) the distribution of the phases, i.e. the homogeneity/heterogeneity of the object considered. A newly introduced parameter “ τ” is used as a measure of this homogeneity/heterogeneity. Accessory phases, which do not necessarily appear in 2D thin sections, are a second source of error, in particular if they contain high concentrations of specific elements. An abundance of only 1 vol% of an accessory phase may raise the 3D bcc of an element by up to a factor of ∼8. The code can be queried as to whether broad beam, point, line or area analysis technique is best for obtaining 2D bcc. No general conclusion can be deduced, as the error rates of these techniques depend on the specific structure of the object considered. As an example chondrules—rapidly solidified melt droplets of chondritic meteorites—are used. It is demonstrated that 2D bcc may be used to reveal trends in the chemistry of 3D objects.

Computational Geosciences with Mathematica: (William C. Haneberg)

As a young geoscientist growing up during the early expansive phase of computational geoscience, I had occasion to learn how to program in a variety of languages, from assembly language to FORTRAN, BASIC (Dartmouth BASIC, QuickBASIC, TrueBASIC, RealBASIC), Pascal, PL-1, XPL, APL, FOCUS, and so on. Today, those who write programs to support their own work tend to use programming environments like Code Warrior or higher-level languages like MATLAB, Maple and Mathematica . For example, MATLAB scripts are included in geoscience texts by Middleton (2000) and Pollard and Fletcher (2005). In recent years, the trend has been more toward using black-box applications programmed by someone else, which typically consist of either user-antagonistic freeware/shareware or quite expensive commercial packages. (The single-user license for an application that I use to make structural cross sections from surface and well data costs $35,000.) The problem is that most geoscience students and professionals have a limited time to devote to gaining a functional knowledge of a computer language. Because Mathematica is potentially such a powerful and versatile tool for geoscientists, William Haneberg's new book Computational Geosciences with Mathematica (2005) has proven to be the most useful book that I have acquired in the last year. To my knowledge, Haneberg's book is the only text available that explains the use of Mathematica in solving a wide array of geoscience problems, although Costain and Coruh (2004) authored a text on exploration seismology that utilizes Mathematica . I can give no higher compliment or recommendation than to state that information and ideas in Haneberg's book have led directly to several significant enhancements …

A new generation of cyberinfrastructure and data services for earth system science education and research

Abstract. A revolution is underway in the role played by cyberinfrastructure and modern data services in the conduct of research and education. We live in an era of an unprecedented data volume from diverse sources, multidisciplinary analysis and synthesis, and active, learner-centered education emphasis. Complex environmental problems such as global change and water cycle transcend disciplinary and geographic boundaries, and their solution requires integrated earth system science approaches. Contemporary education strategies recommend adopting an Earth system science approach for teaching the geosciences, employing pedagogical techniques such as enquiry-based learning. The resulting transformation in geoscience education and research creates new opportunities for advancement and poses many challenges. The success of the scientific enterprise depends heavily on the availability of a state-of-the-art, robust, and flexible cyberinfrastructure, and on the timely access to quality data, products, and tools to process, manage, analyze, integrate, publish, and visualize those data. Concomittantly, rapid advances in computing, communication, and information technologies have revolutionized the provision and use of data, tools and services. The profound consequences of Moore's Law and the explosive growth of the Internet are well known. On the other hand, how other technological trends have shaped the development of data services is less well understood. For example, the advent of digital libraries, web services, open standards and protocols have been important factors in shaping a new generation of cyberinfrastructure for solving key scientific and educational problems. This paper presents a broad overview of these issues, along with a survey of key information technology trends, and discuses how those trends are enabling new approaches to applying data services for solving geoscientific problems.

Mass spectrometry and natural variations of iron isotopes

Although the processes that govern iron isotope variations in nature are just beginning to be understood, multiple studies attest of the virtue of this system to solve important problems in geosciences and biology. In this article, we review recent advances in the geochemistry, cosmochemistry, and biochemistry of iron isotopes. In Section 2, we briefly address the question of the nucleosynthesis of Fe isotopes. In Section 3, we describe the different methods for purifying Fe and analyzing its isotopic composition. The methods of SIMS, RIMS, and TIMS are presented but more weight is given to measurements by MC-ICPMS. In Section 4, the isotope anomalies measured in extraterrestrial material are briefly discussed. In Section 5, we show how high temperature processes like evaporation, condensation, diffusion, reduction, and phase partitioning can affect Fe isotopic composition. In Section 6, the various low temperature processes causing Fe isotopic fractionation are presented. These involve aqueous and biologic systems.

An inverse method for radiation transport

Adjoint functions have been used with forward functions to compute gradients in implicit (iterative) solution methods for inverse problems in optical tomography, geoscience, thermal science and other fields, but only once has this approach been used for inverse solutions to the Boltzmann transport equation. In this paper, this approach is used to develop an inverse method that requires only angle-independent flux measurements, rather than angle-dependent measurements as was done previously. The method is applied to a simplified form of the transport equation that does not include scattering. The resulting procedure uses measured values of gamma-ray fluxes of discrete, characteristic energies to determine interface locations in a multilayer shield. The method was implemented with a Newton-Raphson optimisation algorithm and it worked very well in numerical 1-D spherical test cases. A more sophisticated optimisation method would better exploit the potential of the inverse method.

LIDAR Validation Using GIS: A Case Study Comparison between Two LIDAR Collection Methods

In the summer of 2000, the Annapolis Valley of Nova Scotia, Canada was selected for a high‐resolution elevation survey utilizing LIDAR (Light Detection And Ranging). Two different LIDAR systems were used to acquire data for the area. The vertical accuracy specification for the survey called for heights to be within an average of 15 cm of measured GPS heights and 95% of the data to be within 30 cm. Prior to the application of these data to geoscientific problems, extensive validation procedures were employed. High precision GPS and traditional surveys were conducted to collect height validation checkpoints. Two validation methods were developed in a GIS environment that involved comparing the checkpoints to the original LIDAR points and to an interpolated “bald earth” DEM. A systematic height error between flight lines for one of the LIDAR methods was detected that related to the calibration procedures used in the survey. This study highlights the differences between laser systems, calibration and deployment methodologies and emphasizes the necessity for independent validation data.

Synchrotron radiation and high pressure: new light on materials under extreme conditions

With the steady development of static high-pressure techniques in recent years, it is now possible to probe in increasing detail the novel behavior of materials subjected to extreme conditions of multimegabar pressures (>300 GPa) and temperatures from cryogenic states to thousands of degrees. By and large, the growth in this area has been made possible by accelerating developments in diamond-anvil cell methods coupled with new synchrotron radiation techniques. Significant advances have occurred in high-pressure powder and single-crystal diffraction, spectroscopy, inelastic scattering, radiography, and infrared spectroscopy. A brief overview of selected highlights in each of these classes of experiments is presented that illustrate both the state-of-the-art as well as current technical and scientific challenges. The experiments have been made possible by the development of a spectrum of new techniques at both third- and second-generation high-energy sources together with key advances in high-pressure technology. The results have implications for a variety of problems in physics, chemistry, materials science, geoscience, planetary science, and biology.

Tectonic evolvement of metamorphic complexes at Jilin paleocontinental margin during the transition from late Archaean to early Proterozoic

The kinematics and dynamical process of tectonic evolvement of metamorphic complexes at the interim from late Archaean to early Proterozoic is one of the key problems in geosciences. For the disputation on the genesis of metamorphic complexes at the margin of Jilin palaeocontinent, this paper takes the example of Banshigou region, Jilin Province to discuss the dynamical evolution of palaeocontinent during the transition from late Archaean to early Proterozoic (2600-2000 Ma). On the time sequence, from center to palaeocontinental margin, it shows a series of dynamical movements including underplating, horizontal movement, subduction, intraplate extension and separation. And its corresponding sequence of kinematical modes is as follows: vertical movement, horizontal movement, extension and shearing in contact zone, uplift-sliding movement in paleocontinental margin and interformational sliding, resulting in such tectonite sequence, tectonic gneiss, gneissic complex, gneissic complex-mylonite, mylonite and fracture cleavage-mylonite, which consist of the main body of metamorphic complexes. Their palaeostresses are: < 20, 20.40, 21.72, 28.80 and 30.8-69.8 MPa respectively. The deformational metamorphic temperature is between hornblende and low-grade greenschist facies. The general deformational characters of Jilin palaeocontinent reflect a complete dynamic system of crust evolution, which indicates that the formation of the metamorphic complexes and the tectonic evolution are altered from vertical movement to compression to extension. It also indicates a continuous tectonic transformation from deep to shallow, and from ductile to brittle. The transformation between different dynamic mechanisms not only forms tectonic rocks, but also benefits the linking up, exchange and enrichment with rock-forming minerals and ore-forming elements. This research is helpful to classifying regional tectonic events and making further study on the evolution of palaeocontinental dynamics.

Two‐dimensional Numerical Modeling Research on Continent Subduction Dynamics

Abstract Continent subduction is one of the hot research problems in geoscience. New models presented here have been set up and two‐dimensional numerical modeling research on the possibility of continental subduction has been made with the finite element software, ANSYS, based on documentary evidence and reasonable assumptions that the subduction of oceanic crust has occurred, the subduction of continental crust can take place and the process can be simplified to a discontinuous plane strain theory model. The modeling results show that it is completely possible for continental crust to be subducted to a depth of 120 km under certain circumstances and conditions. At the same time, the simulations of continental subduction under a single dynamical factor have also been made, including the pull force of the subducted oceanic lithosphere, the drag force connected with mantle convection and the push force of the mid‐ocean ridge. These experiments show that the drag force connected with mantle convection is critical for continent subduction.

The importance of being cratered: The new role of meteorite impact as a normal geological process

Abstract— This paper is a personal (and, in many ways, incomplete) view of the past development of impact geology and of the newly recognized importance of impact events in terrestrial geological history. It also identifies some exciting scientific challenges for future investigators: to determine the full range of impact effects preserved on the Earth, to apply the knowledge obtained from impact phenomena to more general geological problems, and to continue the merger of the once exotic field of impact geology with mainstream geosciences.Since the recognition of an impact event at the Cretaceous‐Tertiary (K‐T) boundary, much current activity in impact geology has been promoted by traditionally trained geoscientists who have unexpectedly encountered impact effects in the course of their work. Their studies have involved: 1) the recognition of additional major impact effects in the geological record (the Chesapeake Bay crater, the Alamo breccia, and multiple layers of impact spherules in Precambrian rocks); and 2) the use of impact structures as laboratories to study general geological processes (e.g., igneous petrogenesis at Sudbury, Canada and Archean crustal evolution at Vredefort, South Africa). Other research areas, in which impact studies could contribute to major geoscience problems in the future, include: 1) comparative studies between low‐level (≤7 GPa) shock deformation of quartz, and the production of quartz cleavage, in both impact and tectonic environments; and 2) the nature, origin, and significance of bulk organic carbon (“kerogen”) and other carbon species in some impact structures (Gardnos, Norway, and Sudbury, Canada).

A complex systems model approach to quantified mineral resource appraisal.

For federal and state land management agencies, mineral resource appraisal has evolved from value-based to outcome-based procedures wherein the consequences of resource development are compared with those of other management options. Complex systems modeling is proposed as a general framework in which to build models that can evaluate outcomes. Three frequently used methods of mineral resource appraisal (subjective probabilistic estimates, weights of evidence modeling, and fuzzy logic modeling) are discussed to obtain insight into methods of incorporating complexity into mineral resource appraisal models. Fuzzy logic and weights of evidence are most easily utilized in complex systems models. A fundamental product of new appraisals is the production of reusable, accessible databases and methodologies so that appraisals can easily be repeated with new or refined data. The data are representations of complex systems and must be so regarded if all of their information content is to be utilized. The proposed generalized model framework is applicable to mineral assessment and other geoscience problems. We begin with a (fuzzy) cognitive map using (+1,0,-1) values for the links and evaluate the map for various scenarios to obtain a ranking of the importance of various links. Fieldwork and modeling studies identify important links and help identify unanticipated links. Next, the links are given membership functions in accordance with the data. Finally, processes are associated with the links; ideally, the controlling physical and chemical events and equations are found for each link. After calibration and testing, this complex systems model is used for predictions under various scenarios.

Geological prior information and its applications to geoscientific problems

Abstract Geological information can be used to solve many practical and theoretical problems, both within and outside of the discipline of geology. These include analysis of ground stability, predicting subsurface water or hydrocarbon reserves, assessment of risk due to natural hazards, and many others. In many cases, geological information is provided as an a priori component of the solution (i.e. information that existed before the solution was formed and which is incorporated into the solution). Such information is termed ‘geological prior information’. The key to the successful solution of such problems is to use only reliable geological information. In turn this requires that: (1) multiple geological experts are consulted and any conflicting views reconciled, (2) all prior information includes measures of confidence or uncertainty (without which its reliability and worth is unknown), and (3) as much information as possible is quantitative, and qualitative information or assumptions are clearly defined so that uncertainty or risk in the final result can be evaluated. This paper discusses each of these components and proposes a probabilistic framework for the use and understanding of prior information. We demonstrate the methodology implicit within this framework with an example: this shows how prior information about typical stacking patterns of sedimentary sequences allows aspects of 2-D platform architecture to be derived from 1-D geological data alone, such as that obtained from an outcrop section or vertical well. This example establishes how the extraction of quantitative, multi-dimensional, geological interpretations is possible using lower dimensional data. The final probabilistic description of the multi-dimensional architecture could then be used as prior information sequentially for a subsequent problem using exactly the same method.

Density and local attribute estimation of an infectious disease using MapInfo

Recent developments in local statistics have generally concentrated on area-based data. In this paper, we describe the development and implementation of a set of point-based local statistical methods within the MapInfo GIS. These include the well-documented techniques of density estimation, and a number of extensions that we call “local attribute estimation”. The extensions use traditional summary measures to describe the distribution of continuous attributes, and draw on techniques of facies triangle mapping and the Weaver–Thomas combination index to describe categorical attributes. The methods are demonstrated using a point pattern of cases of an infectious disease in London, UK, but are equally applicable to other problems in geoscience.

The Role of a Shadow Course in Improving the Mathematics Skills of Geoscience Majors

We offer a course that our majors enroll in concurrently with their calculus course that “shadows” the topics covered by the calculus professor. In the shadow course, the students work collaboratively to build mathematical skills and apply calculus concepts to solve geoscience problems provided by the instructor (two examples are given). Students earn a grade of “pass” by demonstrating their involvement in learning. It is not feasible to assess statistically the effect of the shadow course on students' grades in the calculus courses; however, the shadow course has led to other positive outcomes. Our majors have developed more positive attitudes toward mathematics, including calculus, and get the message that geoscience faculty value and actively support their learning of calculus. We have gained insight into our students' strengths and weaknesses in mathematics that may help us to incorporate mathematics more effectively into geoscience courses. The shadow course is helping to foster active collaboration among geoscience and mathematics faculty that strengthens the teaching of scientific problem-solving using quantitative methods in both the calculus and the shadow courses.

A fractional-step finite-element method for the Navier–Stokes equations applied to magma-chamber withdrawal

We develop an algorithm to solve numerically the Navier–Stokes equations using a finite element method. The algorithm uses a fractional step approach that allows the use of equal interpolation spaces for the pressure and velocity fields and can be used to solve both compressible and incompressible flows. The standard Galerkin method is used to space-discretize the equations in which convective terms are dominant because the equations are reformulated in a characteristics co-moving frame providing thus the required artificial diffusion in a consistent way. The algorithm depends on four different parameters. Depending on their values, a fully implicit, a semi-implicit or a fully explicit solution can be obtained. The proposed algorithm may be useful in solving a wide spectrum of problems in geology, engineering and geosciences. Several flows frequently encountered in practical applications such as incompressible, slightly compressible or perfect gas are taken into account. As an example, we use it to model the withdrawal of magma from shallow chambers during explosive volcanic eruptions. Our model constitutes a first attempt to characterize the temporal evolution of the most relevant physical parameters during such a process.

On utilization ofa priori knowledge in inversion of remote sensing models

Satellite remote sensing deals with a complex system coupling atmosphere and surface. Any physical model with reasonable precision needs several to tens of parameters. Without a priori knowledge of these parameters, Proposition 3 of Verstraete et al. requires the number of independent observations to be greater than the number of unknown parameters. This requirement can hardly be satisfied even in the coming EOS era. As Tarantola pointed out, the inversion problems in geoscience are always underdetermined in some sense. In order to make good use of every kind of a priori knowledge for effectively extracting information from remote sensing observations, the right question to set is as follows:Given an imperfect model and a certain amount ofa priori information on model parameters, in which sense should one modify thea priori information, given the actual observation with noise?A priori knowledge of physical parameters can be presented in different ways such as physical limits, global statistical means and variance fora certain landcover type, or previous statistics and temporal variation of a specific target. When sucha priori knowledge can be expressed as joint probability density. Bayessian theorem can be used in the inversion to obtain posterior probability densities of parameters using newly acquired observations. There is no prerequirement on how many independent observations must be made, and the knowledge gained merely depends on the information content of the new observations. Some specific problems about knowledge accumulation and renewal are also discussed.

Survey yields data on unique metamorphic rock complex in China

Seismic data from survey work last year in Dabie Shan, China, are giving scientists their first view of the subsurface structure of a unique metamorphic rock complex. The work, in which a joint Chinese‐German research team surveyed possible sites for a super deep borehole, set the stage for more intensive petrological and seismic investigations this year and next.Data were collected by near‐vertical seismic imaging at Dabie Shan, the Earth's largest outcrop of ultra‐high pressure metamorphic (UHM) rocks, some exhumed from depths of 100 km. Processing so far has revealed unexpectedly strong mid‐and lower‐crustal reflections, predominantly dipping west to east, indicating the involved tectonic history of the region. Upcoming research will look more closely at the three‐dimensional structure of the rock and other matters. Scientific deep drilling is essential in addressing a wide range of major geoscientific problems of global importance. The International Continental Scientific Drilling Programme (ICDP) coordinates such, and one key target of ICDP is the Dabie Shan. To find the most appropriate location for a drill site and to extend the findings of the drilling beyond the drill hole, geophysical methods, especially seismic investigations, play an important role. Integrated interpretation of seismic and drill results in the Dabie Shan will lead to a better understanding of the structure and dynamic processes of the collisional history of the Yangtze and Sino‐Korean Cratons. The Dabie Shan is located in the eastern part of the Qinling orogen in Anhui province, central China. The rocks there contain microdiamonds and coesite within a 20‐km‐thick eclogite zone representing a part of the lower lithosphere of the Yangtze Craton [Okay, 1993]. Such rocks suggest that continental crust had been subducted to depths greater than 100 km and exhumed afterwards [Hackeretal, 1995].