Chapter 1 sets the stage for a quantitative introduction to structural geology. We begin by identifying forces that cause deformation in Earth’s lithosphere and asthenosphere. Then, we describe three different styles of deformation, and five broad classes of geologic structures that result from this deformation. To lay out the methodology for studying geologic structures, we introduce what we mean by a complete mechanics and by canonical models of structural geology. Then we examine the roles of physics and mathematics in studying the origins of geologic structures. Finally, we describe applications of structural geology to problems facing our society and the careers that utilize structural geology to solve those problems.

Now that you have seen the logic of some designs that are more feasible than randomized clinical trials (RCTs), this chapter will examine how to choose the most appropriate design and how to improve the plausibility of any tentative causal inferences that can be drawn from them. You’ll see how calculating a user-friendly statistic – the within-group effect size – can help improve the value of a basic one-group pretest–posttest design. The chapter then will move on to designs that offer more control for alternative explanations and thus more support for inferring causality. The chapter will conclude by discussing how to select the most appropriate design.

As we move from the simple model, y = a + bx + error to the more general y = β0 + β1x1 + β2 x2 + . . . + error, complexities arise, involving choices of what predictors x to include in the model, interpretations of the coefficients and how they interact, and construction of new predictors from existing variables to capture discreteness and nonlinearity. We need to learn how to build and understand models as new predictors are added. We discuss these challenges through a series of examples illustrated with R code and graphs of data and fitted models.

Linear regression is an additive model, which does not work for binary outcomes–that is, data y that take on the values 0 or 1. To model binary data, we need to add two features to the base model y = a + bx: a nonlinear transformation that bounds the output between 0 and 1 (unlike a + bx, which is unbounded), and a model that treats the resulting numbers as probabilities and maps them into random binary outcomes. This chapter and the next describe one such model–logistic regression–and then in Chapter 15 we discuss generalized linear models, a larger class that includes linear and logistic regression as special cases. In the present chapter, we introduce the mathematics of logistic regression and also its latent-data formulation, in which the binary outcome y is a discretized version of an unobserved or latent continuous measurement z. As with the linear model, we show how to fit logistic regression, interpret its coefficients, and plot data and fitted curves. The nonlinearity of the model increases the challenges of interpretation and model-building, as we discuss in the contextof several examples.

Chapter 11 begins by defining intrusions, then describes the different characteristic forms of intrusions, and ends by deriving the solution for the rise of a spherical body of viscous liquid in a more dense viscous liquid. This classic solution from fluid dynamics is the canonical model for the intrusion of salt in sedimentary basins. In general, an intrusion is a body of rock that, in a former more mobile state, was injected into and deformed the surrounding host rock. Intrusions take the form of dikes, sills, laccoliths, stocks, plutons, and diapirs. The intruded material could be magma, rising due to buoyancy from deep in Earth’s asthenosphere (Section 1.1.2), or magma injected laterally from a shallow pressurized chamber in Earth’s lithosphere (Section 6.8.2). The intruded material could be salt, moving upward in a diapir due to buoyancy (Section 5.8), or a mobilized slurry of sand injected into the surrounding sedimentary rock (Section 11.1). The intruded material also could be molten rock, formed due to frictional heating on a fault during an earthquake (Section 8.6.3). The diversity of intrusions makes them an interesting and challenging topic for structural geologists.