Abstract New and existing methods for the analysis of finite strains in shear zones involving volume changes are reviewed. By assuming that the wall rocks are undeformed, the position gradients tensor can be determined from data derived from deformed passive markers with or without knowledge of the orientation of cleavage within the shear zone. The new methods are both algebraic and graphical and include those based on off-axis Mohr circles. Application of these methods to deformed sandstones at Marloes Sands reveals important volume changes that would invalidate an approach that assumes simple shear.

Abstract Crossplots are an excellent medium for the pattern-recognition and problem-solving tasks that are at the core of most log analysis. As we have seen in the last chapter, even the limitation of the computer screen to the display of two dimensions can be overcome to some degree. Projections, glyphs, and the use of color are alternative strategies for accommodating the extra dimensions of information from multiple log traces. Ultimately, all these graphical methods have their limits, prescribed both by the capacity of the technique to represent complex data and the ability of the human mind to understand the results. The most common problem of traditional log analysis is to establish the composition of the logged rocks in terms of the volumes of fluids and gases contained within the pore space and, secondarily, to determine their mineral content. The use of crossplots allows the identification of the mineral phases and crude volumetric estimations of mineral and fluid proportions. For rocks with simple compositions, the estimates of porosity are often sufficiently accurate for routine reservoir analysis. For more complex rock types, compositional analysis by traditional crossplot methods is more challenging because of the increased number of components that must be incorporated. The compositional methods described in this chapter are algebraic solutions of data patterns that can be seen on log crossplots. Operations of matrix algebra cause the coordinates of data that are located in “log space” to be remapped as coordinates in “composition space.” This duality of geometry and algebra is an

This book presents the theory of machine learning (ML) algorithms and their applications to geoscience problems. Geoscience problems include traveltime picking of seismograms by a fuzzy cluster method, migration and inversion of seismic data by neural network (NN) methods, geochemical analysis and dating of rock samples by Gaussian discriminant analysis, convolutional neural network (CNN) picking of faults, cracks, and bird types in images, Bayesian inversion of seismic data, clustering of earthquake data and semblance plots, principal component analysis of seismic data and geochemical records, filtering of seismic sections, seismic interpolation by an NN, transformer analysis of seismic data, and Recurrent NN deconvolution of a seismic trace. More than half of the described algorithms fall under the class of neural network methods. Their description is at a level that can be understood by anyone with a modest background in linear algebra, calculus, and probability. An elementary working knowledge of MATLAB is useful and almost every chapter is accompanied by lab exercises to reinforce the ML principles: lab exercises are at http://utam.gg.utah.edu/Classes/ML/LAB1/index.labs.html . Contributions of geoscience ML labs from readers will be welcome, and vetted labs will be posted to make this an evolving document of fast-growing ML methods. YouTube lectures associated with some chapters will be posted as well, e.g. https://www.youtube.com/watch?v=PEjUYeIKAjo . For readers unfamiliar with MATLAB or Python, many of the labs use the CoLaboratory (CoLab) notebook, which is an easy-to-use product from Google that allows for the execution of Keras-based ML computer codes. It also provides for the free use of a cloud-based GPU processor that can be accessed as soon as you log into the site. There is no need for the troublesome installation of notebook software.