DIFFERENT DATA, DIFFERENT RATES?Materials:
Procedure:
The exercises below will take you through a series of problems involving conflicting (hypothetical) studies of fault slip. Though the studies in each exercise may appear to contradict each other, all of them are literally correct -- key pieces of information may be missing, but any information given will not be in error (i.e. there are no "trick questions"). It is up to you to find a solution that resolves the apparent conflict of the different studies in each exercise.
You will need to make several calculations, and though diagrams will be given for some of the examples, you may want to sketch out some scenarios to help you consider a solution. Thus, you may want a calculator and some scratch paper handy. With that said, you are ready to begin the first exercise below.
Exercise 1
Ancient
Lava vs. Recent Peat
The two studies below focus upon displacements discovered along the hypothetical Brighton fault, a moderately long strike-slip fault in a remote area of southern California, which is known to have been active for over 5 million years, but has not ruptured in historic times. Read through the results of each study, and then answer the questions below.
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Study #1 A group of geologists has discovered and mapped a pair of lava flows which extend across the Brighton fault (roughly at the midpoint of its length), and have been offset by a significant amount of right-lateral slip. They have taken accurate measurements of the ages of these lava flows, and are confident that they are 1.3 million years and 2.4 million years old. The younger flow has been offset by 2.8 kilometers, and the older flow shows 6.0 kilometers of offset (both purely right-lateral). |
Study #2 Another team of geologists has dug a trench across the Brighton fault, near the area where the lava flows were mapped. By dating the sediments deposited and offset along the surface trace of the fault, they have determined the timing of the four most recent events, and the amount of slip in each event. The four most recent events occurred 2000, 4900, 7600, and 9900 years before the present, and the average slip per event is estimated at 3.2 meters. |
Find the slip rate of the Brighton fault using the
data determined by Study #2. That is, first calculate an average
recurrance interval, then use the average slip per rupture to
find the slip rate.
Is the value for the slip rate of the Brighton fault which
you obtained using Study #2 similar to any of the values you obtained
from Study #1? How does it compare to those values?
Assuming both studies are accurate and correct, what
would you say is happening to the slip rate of the Brighton fault?
Which slip rate value, from which study, would you use in estimating
the current slip rate of the Brighton fault? If you were modelling
the behavior of faults in southern California between 2 and 4 million
years ago, which slip rate value would you use for it then?
Exercise 2Three
Studies in Conflict
The Windy Valley fault is a young and active fault -- geologists agree it is only about 500,000 years old, and yet it has already created a very obvious scarp along the northern edge of the Mineral Mountains. The fault dips steeply, at 80° to the southwest, and thus its strike is roughly the same as its trend: 80° west of north (N80W; almost east-west). Though these details are known, its slip history has generally been ignored until recently. Now three different studies have come out with new information that may help determine its slip rate. Below are their findings. Read through each study report, then answer the questions below.
A team of geologists has mapped the area on both sides of the
Windy Valley fault scarp, and has found a layer of sediment
within the mountains that is exactly the same in composition
and age as a layer of sediment found on the low (north) side of
the fault (see figure at right). The sediment dates back to 750,000
years, so it was probably there before the fault began to break and slip.
The difference in elevation between the two halves of the layer
is 1.1 kilometers.
A researcher studying old mining claims and mining company documents (for, indeed, the Mineral Mountains have been heavily mined) found a set of records dating back from 100 years ago which tell of a particularly rich mineral vein that was found on both sides of the Windy Valley fault. The mineral composition of the vein was very unusual, it seems, so the miners figured that each half, having the same unusual combination of minerals, must be part of the same original vein, cut in two by the fault. Unfortunately, the records are sparse, and they do not mention the direction of the displacement of the two sides, only the total distance between them: 1 mile (which is equivalent to 1.6 kilometers).
Through research into previous geochemical studies, this lone researcher also determined that this mineral vein is probably similar in origin to others in the area which date back to at least 20 million years before the present.
A research group studying data from GPS stations in the area has
determined the following, using a setup like that shown at right:
Station 1, relative to station 2, is moving due
west at about 2.3 mm/yr. (This data only applies to the stations'
relative horizontal positions (i.e. no vertical separation rates
were calculated).)
The relative motion found by Study #3 is along a strictly
east-west line (N90W or N90E), but the strike of the Windy Valley fault
is N80W. This seems to suggest another component in the fault's sense
of slip. What is this apparent other component? Does this agree
with or contradict Study #1? What, then, would you consider the true
sense of slip of this fault to be?
Assuming the cumulative offset found by each of the first
two studies is for a 500,000 year period, what is the implied slip rate
of the Windy Valley fault in each of these two studies?
You now have three different slip rate measurements to describe
the motion of the Windy Valley fault. Assume the slip rate calculated
from Study #1 represents the vertical component of the fault's slip rate,
and the rate given by the GPS data of Study #3 represents the horizontal
component of the slip rate. Calculate the resultant slip rate using
the two right-angle components, and then compare this total oblique
slip rate to the rate calculated using the displacement found by Study
#2. Are they roughly the same? If so, you should feel confident
that you have correctly determined both the slip rate and sense of slip
of the Windy Valley fault.
Exercise 3Something's Missing...
The figure to the right shows a hypothetical area (north
is at top) with two GPS stations, marked A and B.
In between them lies a large thrust fault called the Alder Thrust.
Geological and seismological studies
have previously determined that the slip rate of the Alder Thrust
is 5.4 mm/yr. The sense of slip is pure thrust, and the dip of this
thrust fault is 39°, due east.
A few years after the GPS stations were put in place, studies of their
relative motion discovered that station B is moving (horizontally)
toward station A at a rate of 5.5 mm/yr. Since both studies have
a high degree of precision and accuracy, these findings present a slight
problem for researchers. Work through the questions below to see why,
and to look for a solution.
You should have discovered a horizontal component of 4.2 mm/yr,
meaning that there is a horizontal slip "deficit" of 1.3 mm/yr between
stations A and B. What could account for this disparity?
Is there evidence in the diagram to suggest a solution?
Indeed, because of the difference in horizontal slip rates, scientists suggest that there may be an active blind thrust fault at work below the hills to the east of GPS station A. This extra fault might add enough horizontal slip between the stations to explain the GPS measurements. A preliminary study finds that the hills are being uplifted at a rate of about 0.75 mm/yr. Assuming that figure is the vertical component of a pure thrust fault, and that the fault dips at roughly 30° (a reasonable estimate), could this supposed blind thrust fault account for the extra 1.3 mm/yr of horizontal slip?
Exercise 4Torn
Between Two Slip Rates
Now, on with the exercise:
The figure at right shows two views of an area crossed by
two thrust faults, connected by a tear fault. All the thrust fault
segments shown have exactly the same strike (due north-south), and
the tear fault is at a perfect right angle to them. The larger
thrust fault is known as the Montane Thrust, and it
forms the western boundary of a range of mountains known as the
Sylvan Range. Reaching the surface west of the Montane Thrust
is a smaller thrust fault, known as the Palos Thrust.
The tear fault connecting them is a right-reverse fault with a
near-vertical dip, known (appropriately) as the Torn Valley fault.
South of its intersection with the Torn Valley fault, the slip rate
of the Montane Thrust declines. For this reason, geologists consider
the Montane Thrust divided into northern and southern segments at
this point.
GPS measurements have shown that this entire area (the whole block shown) is shortening (horizontally) along an east-west at a rate of 4.5 mm/yr. Geologic studies seem to agree with this. The slip rate along the northern segment of the Montane Thrust is 5.4 mm/yr, and its dip is roughly 34° due east, which yields a horizontal slip rate of 4.5 mm/yr. Studies of the Palos Thrust place its dip at about 26° due east, and its total slip rate at about 2.2 mm/yr, meaning that its horizontal slip rate must be about 2.0 mm/yr. The Torn Valley fault provides support for this -- the right-lateral component of its slip rate is 2.0 mm/yr. Keep in mind that the Palos Thrust is underneath the southern segment of the Montane Thrust all the way to the base of the crust.
The real puzzle in this area is that the uplift rate along the entire
western front of the Sylvan Range is constant, north and south of
the intersection with the Torn Valley fault.
Work through the questions below to solve the mystery of this area. In solving this problem, model all the thrust faults as parallel in strike (i.e. ignore differences in strike).
Given all of the above information, can you calculate
the horizontal and vertical components of the slip rate of the southern
Montane Thrust? (Hint: you will have to calculate the uplift rate
of the Palos Thrust.)
What is the slip rate of the southern section of the
Montane Thrust? Other than slip rate, what basic fault property of the
Montane Thrust must change, south of the Torn Valley fault?
The exercises above also touched upon a subject we will treat later in more detail: that the total slip across any line in the crust (horizontal, as in exercise 3, or vertical, as in exercise 4) is the sum of the slip rates of the faults that cross that length. Activity #13: Partitioning Slip will expand upon this idea.
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