# 5.3.4: Paleoseismology, the Slip Rates and Earthquake Recurrence Intervals

- Page ID
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)## Overview

Major earthquakes are generally followed by aftershocks, some large enough to cause damage and loss of life on their own. The aftershocks are part of the earthquake that just struck, like echoes, but last for months and even years. But if you have just suffered through an earthquake, the aftershocks may cause you to ask: when will the next earthquake strike? I now restate this question: when will the next large earthquake (as opposed to an aftershock) strike **the same section of fault**?

The San Fernando Valley in southern California had an earthquake in 1994, twenty-three years after it last experienced one in 1971. But these earthquakes were on different faults: the 1971 earthquake had a surface rupture, the 1994 earthquakes did not. That is not the question I ask here. To answer my question, the geologist tries to determine the** slip rate**, the rate at which one side of a fault moves past the other side over many thousands of years and many earthquakes. This is done by identifying and then determining the age of a feature like a river channel that was once continuous across the fault but is now offset by it, like the examples in Figure 3-5a.

It is also necessary for us to identify and determine the ages of earthquakes that struck prior to our recorded history, a science called **paleoseismology**. For example, in central California, Wallace Creek is offset 420 feet (130 meters) across the San Andreas Fault. Sediments deposited in the channel of Wallace Creek prior to its offset are 3,700 years old, based on radiocarbon dating of charcoal in the deposits. The slip rate is the amount of the offset, 420 feet, divided by the age of the channel that is offset, 3,700 years, a little less than 1.4 inches (35 millimeters) per year.

Wallace Creek crosses that part of the San Andreas Fault where strike-slip offset during the great Fort Tejon Earthquake of 1857 was 30-40 feet. How long would it take for the fault to build up as much strain as it released in 1857? To find out, divide the 1857 slip, 30-40 feet, by the slip rate, 1.4 inches per year, to get 260 to 340 years, which is an estimate of the **average earthquake recurrence interval** for this part of the fault. (I round off the numbers because the age of the offset Wallace Creek, based on radiocarbon dating, and the amount of its offset are not precisely known.) Paleoseismologic investigation of backhoe trench excavations shows that the last earthquake to strike this part of the fault prior to 1857 was around the year 1480, an interval of 370 to 380 years, which agrees with our calculations within our uncertainty of measurement. This is reassuring because the lowest estimate of the recurrence interval, 260 years, won’t end until after the year 2100.

Crustal faults in the Pacific Northwest have much slower slip rates, and so the earthquake recurrence times are much longer. Say that we learned that a reverse fault has a slip rate of 1/25 inch (1 millimeter) per year, and we conclude from a backhoe trench excavation across the fault that an earthquake on the fault will cause it to move 10 feet (120 inches). The return time would be three thousand years. Could we use that information to forecast when the next earthquake would occur on that fault?

Unfortunately, this question is not easy to answer because the faults and the earthquakes they produce are not very orderly. For example, the 1812 and 1857 earthquakes on the same section of the San Andreas Fault ruptured different lengths of the fault, and their offsets were different. Displacements on the same fault during the same earthquake differ from one end of the rupture to the other. The recurrence intervals differ as well. We were reassured by the recurrence interval of 370 to 380 years between the 1857 earthquake and a prehistoric event around A.D. 1480, but the earthquake prior to A.D. 1480 struck around A.D. 1350, a recurrence interval of only 130 years. For a fault with an average recurrence interval of three thousand years, the irregularity in return times could be more than a thousand years, so that the average recurrence interval would have little value in forecasting the time of the next earthquake in that section of the fault.

We can give a statistical likelihood of an earthquake striking a given part of the San Andreas Fault in a certain time interval after the last earthquake (see Chapter 7), but we can’t nail this down any closer because of the poorly understood variability in strength of fault zones, variability in time as well as position on the fault. Another difficulty is in our use of radiocarbon dating to establish the timing of earlier earthquakes. Charcoal may be rare in the faulted sediments we are studying. And radiocarbon doesn’t actually date an earthquake. It dates the youngest sediments cut by a fault and the oldest unfaulted sediments overlying the fault, assuming that these sediments have charcoal suitable for dating.