# Class Summary – 26 Jan, 2015 – Stress & Strain

We finished stress and strain and I introduced Hooke’s Law and the equations of motion. You should be able to read Chapter 3 of the text now, not all of it is simple, but you have the basic definitions. Understanding all the mathematical details should be your goal, but at least now, so we can move forward, you should understand how the key ideas of stress, strain, Hooke’s Law and Newton’s 2nd Law are combine to produce the equations of motion.

$$\sigma_{ij,j} + f_i = \rho \ddot{u}_{i,t}$$

# Stress & Strain

The text assumes that you know the basics of elasticity. Unfortunately, the softening of geoscience degree programs insures that many do not have a firm foundation in continuum mechanics. I can’t spend weeks covering the material, but I started with a review of stress and strain. The plan to insure that you understand derivation of the fundamental equations and boundary conditions of seismic wave propagation and excitation at least in outline form. That is, I want you to be a blue to follow the progression from Newton’s Law and Hooke’s Law to the fundamental equations. The better students will struggle through the details to understand deeply, but hopefully all will appreciate the path through the material.

When we move from elementary physics and the study of the effect of forces on “point” objects, we must deal with how the forces are transmitted through a material, it is convenient to consider forces normalized by the area  they operate across. This leads to the idea of stress, a force per unit area. Pressure is a simple example, but more generally, we are also interested on orientation of the surface (the area) on which the force is operating, so the concept of stress is abstracted somewhat. Strain is a deformation, and we are interested in deformations because seismic waves are deformations (disturbances) from equilibrium that transmit energy from the source (earthquake) region (where it was stored as strains) outward, in all directions surrounding the source. Seismic waves are important because they can cause substantial damage to human-made constructions, and they are valuable because the transmit information on the earthquake process and Earth’s interior. We use a rather simple (appropriate for small deformations) definition of strain that is nonetheless precise. Precision is necessary to reason quantitatively about the processes that are involved in seismic excitation and propagation.

Read your old structural geology or continuum mechanics notes. Try to connect them to what we discuss. The Schaum’s Outline by Mase is a good short review of continuum mechanics, and there are many good books on the subject (check out the library). You won’t have time to read a whole book and keep up with the class, but self study at a slower pace is a good way to understand the details. You might have to start with a review of some mathematics (vector calculus and tensors).

You should be reading Chapter 3 of Udias et al. (2014) to see where we are headed.

# Searching For Earthquake Information

In the last 10 minutes of class, to break from the theoretical work, I reviewed three common places for searching for earthquake information: the USGS, the Global CMT Catalog, and the ISC. Examples are shown at http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/AdvSeismo/. You should walk through some examples that interest you to get a feel for how to search these data bases interactively. Each also has more efficient way to search using computer programs or scripts, but I often find myself browsing or checking ideas by searching these sites.

# Class Pre-Test – 23 Jan, 2015

I gave an ungraded pre-test before class to help you recall as much as you could about the concepts that we will discuss this class and next. Studies show that you will retain material better if you first struggle with problems (or questions) before you are shown “answers”.  Learning is more deep and meaningful when there is some struggle to recall.

• What is stress?
• What is strain?
• What is a tensor?
• What is Newton’s 2nd Law?
• What is a wave?
• What is the wave equation?

Any serious earthquake-science graduate student should be able to answer these questions. If you couldn’t it only means you should probably discuss the material more often – everyone forgets. Reinforcing understanding through discussion is an important reason universities work, they are places where such discussions occur naturally. Talk to each other about your work. Practice explaining things.

# SAC

SAC is short for Seismic Analysis Code, and it is an old tool for looking at seismograms. I do not recommend SAC for modern studies of seismic data, but I use it frequently to get a quick look at some data (not always seismic data either). SAC was developed at the Lawrence Livermore National Laboratory in California, and is now painted and distributed by the IRIS community. You can find the official SAC pages here, and if you google for SAC and seismic, you will find many tutorials around the web. The book referenced on that page is available through our library. You can find it through this link.

My SAC examples can be found:

# Class Summary – 12 Jan, 2015 – Time Series Review

The data that are used by seismologists generally originate as seismograms, which are time series. I assume that you have a rudimentary understanding of time series analysis. This lecture reviews some of the many ways that time-series analysis is used in seismological research. The slides are on ANGEL.

You should have at least one good time series reference if you are a seismologist or geophysicist. The subject requires you to work through it though, not just casual reading. Fortunately, SAC, Matlab, and other tools enable you to explore the concepts relatively easily. Will look at SAC next class to help you get started.

# Welcome to the GEOSC 559

GEOSC 559 is an advanced seismology course designed for students involved in seismological or related research. The course objectives are to review a suite of advanced seismology topics related to earthquake processes and seismic-wave propagation at a level that instills a deep appreciation of seismological methods in the students. The primary goal is help students learn how to study advanced material and to relate that material back to seismological observations using a mix of observation, computation,  and theory.

# Planned Topics

We will begin with an introduction to acquiring seismic data and earthquake information, an introduction to using the Seismic Analysis Code (SAC). We will explore various ways of acquiring earthquake information and seismic data. Then we will begin with a overview of continuum mechanics appropriate for seismic analyses. Then we will explore simple, point-source earthquakes models such as the double-couple, and the moment tensor. Then we will review simple methods for computing body-wave seismograms for teleseismic source & receiver-function analyses and discuss how to use these to estimate faulting geometry and the spatial and temporal distribution of an earthquake’s seismic moment using seismic observations. Then we will discuss dynamic models of earthquake rupture and discuss how these might be constrained using seismic observations. After the break we will investigate methods used for earthquake location and seismic structural imaging (such as receiver functions and surface-wave dispersion).

# Text Book & Reference Materials

You should have access to and read an introductory (quantitative) seismology book such as those written by Shearer, Stein & Wysession, Lay & Wallace, or Kennett, or something comparable. In the first half of the course we will work through much of the text Source Mechanisms of Earthquakes by Udias, Madariaga and Buforn (2014). The second half of the course will use sections of Aki and Richards (1980) and  Kennett (1983), which is an earlier edition of his newer books, but which is also freely available in PDF format. When helpful, I will provide references to scientific articles that you should read.