Download Seismicity Analysis: Predicting Earthquake Occurrence in Northern California and more Lab Reports Environmental Science in PDF only on Docsity! Name ____________________________ EPS 20: Earthquakes Laboratory Exercise 4 Seismicity of Northern California Purpose: Learn how we make predictions about seismicity from the relationship between the number of earthquakes which occur and their magnitudes. Background: The Number of Earthquakes We know that there are more small earthquakes than large ones. If we can identify a pattern, and if we can express the pattern quantitatively, we can use the pattern to tell us what we might expect in terms of the sizes and numbers of earthquakes to come. Let us consider one particular region of the world and one particular time interval. We can use the magnitude M as a measure of the size of an earthquake and count them. For some particular magnitude M, we will find there are n earthquakes. For a different magnitude, we will find a different value of n. n will be bigger for small earthquakes than for large ones. We say: n is a function of M and write: n(M) = number of earthquakes with magnitude M As you would expect, the exact value of n for any particular magnitude depends on the length of time for which the count is made. To avoid this, we usually normalize n by the number of years for which we have counted (like a batting average). This gives us a new definition of n n(M) = number of earthquakes with magnitude M per year This measure of the number of earthquakes still has some problems. For example, it depends upon how accurately the magnitudes are measured and how precisely they are tabulated. For instance, the n(M) values will be different if earthquake magnitudes are given to the closest 0.5 units of magnitude or the closest 0.1 units of magnitude. A better way to express the number of earthquakes is to use the cumulative number of earthquakes, NC(M) = number of earthquakes per year with magnitude greater than or equal to M. This measure of the number of earthquakes is much less sensitive to the way the data are saved. Note that the number NC(M) is also normalized by the length of time used and is given as the number of earthquakes per year. For several areas in the world, scientists have graphed NC(M) and have discovered that there is usually a very simple relationship between NC(M) and M. Specifically, when log10[NC(M)] is plotted versus M, the data fall nearly on a straight line. The graph for a straight line is y = A + bx, where x and y are variables (the axes), b is the slope of the line and A is the intercept of the line with the y-axis. So if we plot log10[NC(M)] versus M and get a straight line, it suggests that we can write log10[NC(M)] = A - b . M where A and b are constants (-b means the line slopes downward to the right). Here A is the intercept of the earthquake occurrence curve at magnitude zero (remember, this does not mean “no earthquake”, magnitude zero means a relative amplitude of “1” in the measurement that is the basis for the magnitude scale). The value b is the negative slope of the line. It describes how many more small earthquakes there are for a given number of large earthquakes. Using this formula it is very easy to characterize the seismicity of a region. We (1) define a region, (2) pick a time interval, (3) count the earthquakes for each magnitude M in the catalog for the region, (4) calculate NC(M), (5) plot NC(M) versus M, and then (6) estimate the parameters A and b. By this process we can summarize the seismicity of a region using just two numbers. The number A gives an estimate of the general level of seismicity for the region: how many earthquakes of any size (greater than 0) can we expect in the region during the course of the year. The number b tells us about what magnitudes we can expect. How many of those earthquakes will be big, or how often will big (or really big) earthquakes occur? For most regions, we have found that the number b is very close to 1.0. That means 2
