In this Chapter

Numerical solutions to a variety of problems in geodynamics are given in this chapter utilizing MATLAB. In some cases, a specific boundary value problem given in a previous chapter is generalized to arbitrary boundary conditions. One example is the bending of the lithosphere under a load. The solution for a point load given in Chapter 3 is generalized to arbitrary load distributions. Solutions for lithospheric bending under axisymmetric loads are presented. The gravity anomaly over rectangular prisms is calculated, and a new formalism based on Fourier transforms is presented to solve for the gravity over arbitrary topography. Axisymmetric solutions for postglacial rebound and crater relaxation are developed. Finite amplitude thermal convection requires the solution of nonlinear partial differential equations. These solutions must be obtained using numerical methods. A MATLAB code for a two-dimensional steady solution is given. Finally, the discussion of faulting in Chapter 8 is extended to more complex geometries and faulting scenarios.

Bending of the Lithosphere under a Triangular Load

In Section 3.16 we solved for the bending of the elastic lithosphere under the load of a volcanic island chain by representing the island chain as a line load on the plate. With a numerical solution it is possible to represent the load on the plate more realistically, e. g., by a triangular load. We first develop the numerical approach by going back to the line load problem whose analytic solution provides a benchmark against which to evaluate the numerical solution.

According to the books of Chronicles, King David instituted worship for the new temple to be built by his son Solomon. Worship in the temple included various types of sacrifices on an altar outside the temple, while the ark of the covenant was inside. At that time, it is said, King David appointed certain priests of the tribe of Levi to serve in the temple with harps, lyres, cymbals, and trumpets, in regular praise and thanksgiving to Yahweh (1 Chronicles 16:1–6). And, also at the same time, it is claimed that David ordered the place of music in Israel’s worship.

In this Chapter

The plate tectonic model provides a framework for understanding many geodynamic processes. Earthquakes, volcanism, and mountain building are examples. The plate velocities, 10–100 mm yr−1, imply a fluid-like behavior of the solid Earth. Hot mantle rock can flow (behave as a fluid) on geological time scales due to solid-state creep and thermal convection. The hot mantle rock is cooled by heat loss to the Earth’s surface resulting in a cold thermal “boundary layer.” This boundary layer is rigid and is referred to as the lithosphere. The surface lithosphere is broken into a series of plates that are in relative motion with respect to each other. This motion results in “plate tectonics.”

Plates are created at mid-ocean ridges, where hot mantle rock ascends. Partial melting in the ascending rock produces the magmas that form the basaltic ocean crust. The surface plates reenter the mantle at ocean trenches (subduction). The cold rock in the plate (lithosphere) is denser than the adjacent hot mantle rock. This results in a downward gravitational body force that drives the motion of the surface plate. Complex volcanic processes at subduction zones generate the continental crust. This crust is thick and light and does not participate in the platetectonic cycle. Thus the continental crust is about a factor of 10 older, on average, than the oceanic crust (1 Ga versus 100 Ma).

Interactions between plates at plate boundaries are responsible for a large fraction of the earthquakes that occur. Earthquakes are caused by episodic ruptures and displacements on preexisting faults. These displacements provide the relative motions between surface plates. Plate boundary processes are also responsible for a large fraction of the surface volcanism.

In this Chapter

One of the important aspects of geodynamics is the fluid behavior of the solid mantle. This behavior should not be a surprise since crystalline solid ice in glaciers flows freely. The similarity to ice in a glacier is that the ice is close to its melting point and rock in the mantle is close to its melting point. In both cases strongly temperature-dependent movement of crystal vacancies and/or dislocations leads to solid-state creep in a stress field. This strong temperature dependence controls the cooling of the Earth. As the amount of radioactive heat production decreases with time, the vigor of the mantle convection required to extract the heat decreases. This allows the mantle temperature to decrease and the Earth to cool, contributing significantly to the observed surface heat flow.

In this chapter we consider other rock rheologies. Viscoelasticity combines the elastic and viscous behavior of solid rock. Viscoelasticity explains why rock can transmit shear waves (requiring elastic behavior) at short time scales and behave viscously (mantle convection) at long times. Viscoelasticity will also quantify the thickness of the elastic lithosphere as a fraction of the thickness of the thermal lithosphere. When large stresses are applied to the elastic lithosphere irreversible plastic deformation occurs. The result is the development of plastic hinges in the lithosphere at some subduction zones.

Introduction

At atmospheric pressure and room temperature most rocks are brittle; that is, they behave nearly elastically until they fail by fracture. Cracks or fractures in rock along which there has been little or no relative displacement are known as joints. They occur on all scales in both sedimentary and igneous rocks. Joints are commonly found in sets defining parallel or intersecting patterns of failure related to local stress orientations. The breakdown of surface rocks by erosion and weathering is often controlled by systems of joints along which the rocks are particularly weak and susceptible to disintegration and removal. These processes in turn enhance the visibility of the jointing. Igneous rocks often develop joints as a result of the thermal stresses associated with cooling and contraction. Columnar jointing in basaltic lava flows (Figure 7.1) and parallel jointing in granitic rocks (Figure 7.2) are examples.

Not everyone sees the OT’s legacy of monotheism as a good thing. The belief in only one God is necessarily exclusive, defining itself over and against belief in many gods. This exclusivity may lead to intolerance of other views and eventually to violence against others. Some therefore connect monotheism to violence. Others blame monotheism for centuries of mistreatment of women, arguing that the feminine aspects of the divine were suppressed in the process of reducing all divine aspects to only one God.

What you think about God – if you think about God at all – affects nearly everything else you believe to be true. Wars have been fought and nations divided based on what people think about God. On a more individual level, important personal and ethical decisions are often made based on what we think about God.

Millions of believers around the globe consider the Old Testament the “word of God.” Of these, many study and read it looking for divine direction or comfort. Other believers don’t read it at all even though they consider it God’s word in some manner; they value it but don’t read it. For all these, the OT is in some way religiously authoritative. It somehow stands as inspired, or inspiring, as a word of truth or a word that has its origins in God – the word of God. As such, the OT is a living tradition that shapes communities and provides inspiration for believers within those communities.

Now we come to that portion of the OT that binds Jews, Christians, and Muslims together more than any other – and sadly also divides them. Judaism, Christianity, and Islam are known as Abrahamic religions. They share Abraham as a common ancestor, but they also disagree about his significance. In this chapter, we will talk about why this is the case. We will explore how Abraham became the father of faith for millions of believers around the world.

In this Chapter

In this chapter we consider heat flow and temperature distributions. We give a summary of surface heat flow measurements that constrain the loss of heat from the interior of the Earth. An important source of this heat is radiogenic isotopes in the Earth’s interior. Fourier’s law of heat conduction gives the linear dependence of heat flow on the spatial gradients of temperature. The heat equation is one of the most important equations in geophysics. It gives the balance between heat storage, heat generation, and heat conduction. Examples of solutions to the heat equation are given. The solution for the annual variability of the temperature at the surface of the Earth is obtained. The solution for the instantaneous cooling of a half-space is given. This solution is used to determine the cooling and thickening of the oceanic lithosphere as a function of the distance from the oceanic ridge where it was created. This solution predicts the measured values of surface heat flow and, using isostasy, explains the elevation distribution of oceanic lithosphere. A solution is given for the surface solidification of a liquid. The result predicts the rate of crustal thickening on a lava lake. Solutions of the heat equation are also applied to surface erosion.

Additional material relevant to this chapter can be found in Chapters 11 and 12 (Sections 12.3, 12.4, and 12.5). These appendices use MATLAB to numerically solve a number of the heat flow problems considered in this chapter, including temperature, surface heat flux, and depth for the plate model of the cooling oceanic lithosphere, and the post-solidification cooling of a dike.

The OT comes from a specific time and place, a definite world very different from our own. Don’t think of the OT as a holy book dropped from the sky without historical context. Quite the contrary! The OT reflects the world of antiquity rich in literature, in art, and in something we might even call “the sciences,” and with elaborate philosophies about the nature of the world. And the world in which the ancient Israelites lived and worked had a history already spanning thousands of years. The first cities of human civilization and first fledgling empires were as distant in time to ancient Israel as the Roman Empire is to you and me.

The concept of “land” has been a recurring theme in the Pentateuch. At times, the theme has come to the surface as central to our narrative, such as the account of Israel’s first ancestors, Abraham, Isaac, and Jacob, who were promised land as part of their covenant relationship with Yahweh. At other times, the theme of the “promised land” has been just below the surface, such as during the Israelites’ long sojourn in the desert, when they were not permitted to enter it. As we move from the Pentateuch now into the OT’s historical books, this theme of Israel’s relationship to the promised land returns as a central component of Israel’s story. As readers, it’s as though our movement from the Pentateuch to the historical books reflects the Israelites’ movement from the desert to the land promised to their ancestors.

Types of euthanasia and the criminal law – ‘killing’ versus ‘letting die’ and double effect

There comes a point in the treatment of some patients when it is clear that they are not going to recover: their injuries are too severe, they are in an irreversible coma, or they are simply too old and nothing can be done. In such scenarios, palliative care becomes appropriate. Palliative care is medical treatment that is designed not to ‘cure’ the patient of any disease, but instead to try to help her to be as comfortable as possible as she dies. This may include a range of actions and omissions, such as the provision of pain relief (which may shorten life), the withholding of artificial nutrition and hydration or even determinations not to resuscitate the patient should she stop breathing. These are obviously difficult and controversial decisions, and there is considerable disagreement, as we shall see, regarding whether they amount to euthanasia. Before considering the legality or otherwise of euthanasia, it is first necessary to distinguish between the two types of the practice – ‘active’ and ‘passive’ euthanasia. The distinction between these two is certainly not as intuitive as it initially sounds. ‘Active’ euthanasia is the process imagined by most people when they consider the practice, and it involves actively ending someone’s life, most usually through the injection of a drug that will painlessly kill the patient. It is called ‘active’ euthanasia because the doctor will take active steps to shorten and end the life of the patient, and the cause of death will be the act of the doctor rather than the progression of the disease from which the patient suffers. ‘Passive’ euthanasia occurs when the doctor fails to act to save the life of the patient. This involves withholding treatment from the patient, such as antibiotics or, more controversially, artificial ventilation or nutrition and hydration. The distinction is that in this scenario the patient’s disease will kill him, rather than any drug administered by the doctor. Essentially, the difference is seen to be one between killing and letting die, although, as we discuss below in relation to the ethical aspects, this is not without its problems, as recognised by the House of Lords.

The Warnock Committee Report

As we shall see, assisted reproduction is regulated in England by the Human Fertilisation and Embryology Act (HFEA) 1990 (as amended), which contains the rules and imposes the regulatory structure that must be followed by clinics providing a service. The Act, however, was born as a result of the report of a committee chaired by Baroness Warnock assigned to look into these issues. The remit of the committee was wide, as it was charged with considering:

The scope of the report thus covered artificial insemination, surrogacy and new processes of artificial reproduction. Abortion and contraception were, however, outside the ambit of the brief. It is worthy of note that the committee was asked to look not just at existing technology, but also at potential developments. Given this, the report would have to construct a framework that would respond to change. The remit of the committee was therefore far wider than that of this chapter, which considers only the issue of assisted reproduction. However, the importance of the wide remit lies in the influence it had over the regulatory framework that it suggested and that was implemented by the 1990 Act. Essentially, the committee faced two particular problems. First, it had to establish a clear and coherent ethical position surrounding not just the moral status of embryos and gametes, but also the type of families that they were content to facilitate. In this respect, the committee also had to ensure that there was some sort of enforcement mechanism that would ensure that this ethical position was adopted and maintained by clinics offering services. Secondly, the committee had to create a structure that was flexible and able to respond to change, so that any future technological developments could be brought within the ambit of the Act if necessary.