Section 1: What is an Earthquake?

Activity #14: PARTITIONING SLIP

Materials:

• scratch paper and/or a calculator for making simple calculations
  
• a scientific calculator (or trig tables) for solving trigonometric equations
  

Procedure:

This activity will present you with four exercises that deal with the partitioning of slip within scenarios involving two or more faults. You will need to make several calculations in each exercise, so it is recommended that you have a calculator and/or some scratch paper handy, but no other additional materials will be required. Each exercise is self-explanatory, so without further instruction, you may proceed to work through the exercises below.

Exercise 1Parallel Faults

At right is a diagram of an area cut by three parallel, right-lateral strike-slip faults, labelled A, B, and C. Two GPS stations, here labelled 1 and 2, have been installed on opposite sides of this area, so that all three faults run between them, perpendicular to a line connecting the two stations. According to the measurements made by the GPS stations, station 1 is moving, relative to station 2, as if there were a single right-lateral strike-slip fault with a slip rate of 13 mm/yr running between them, perpendicular to a line connecting them (and thus parallel to the actual faults in the area).

Using these initial conditions, determine the slip rates for Faults A, B, and C in the following scenarios:

1. The slip rate of Fault A has been measured as 10 mm/yr. Stream offsets across Fault C are about 20% the size of those across Fault B, implying a similar ratio of slip rates. What slip rates, then, would you expect for Faults B and C? How would the stream offsets across Fault C likely compare to those across Fault A (in terms of percentage)?
   

2. None of the three faults has a known slip rate. However, a large wash cuts across all three faults in a perpendicular fashion, and is offset by each one. The wash is offset 140 meters by Fault A, 40 meters by Fault B, and 20 meters by Fault C. Assuming these offsets are directly proportional to the slip rates of these faults, then what, given an overall rate of 13 mm/yr from the GPS measurements, are the individual slip rates for these three faults?
   

3. Two groups of researchers, performing studies along all three faults of sediments disturbed by previous ruptures, have revealed the average slip for a typical major rupture along each of the faults. These studies have also yielded ages for these ruptures that have led to the calculation of recurrence intervals for all three faults. Fortunately, the two groups that carried out this research agree upon the sizes of the typical major ruptures (listed below). Unfortunately, the two groups arrived at different values for these recurrence intervals, probably due to a problem with one or both of the dating methods used. Oddly enough, one thing both groups do agree upon is that all three faults have exactly the same recurrence interval!

   Now that you have the GPS measurements, you can take advantage of this unusual situation. The average slip for major ruptures along the three faults are: 4.4 meters along Fault A, 1.3 meters along Fault B, and 80 centimeters along Fault C. Using this, along with the original GPS information, work through the following:

   1. What are the slip rates of these three faults?
      

   2. Of the two original research teams, one claimed the recurrence interval was 750 years, while the other claimed 400 years. Was either correct, and if not, what is the correct recurrence interval?
      

Exercise 2An Intersection of Faults

Two pure strike-slip faults with vertical dips intersect in an area located between two GPS stations, labelled A and B, as shown in the map view at right. Stations A and B lie on a perfect north-south line, and have been operational for some time, though no data from the stations has been released for analysis yet. Your job is to figure out what the GPS data should look like, in advance of actually receiving it, by calculating the total slip rate and direction across the A-B line. This way, any abnormalities will be easy to spot once the data is properly analyzed.

To help you do this, you have access to the latest and most accurate measurements of the strike, dip, sense of slip, and slip rate of each of the two faults in question. They are noted in the map view diagram, at right, and in the table below:

Your job now, if not simple, is straightforward:

1. Determine the total slip (rate and direction) between stations A and B. Express this motion as the rate and direction station A is moving relative to station B, if station B is considered to be fixed (motionless). (Drawing out diagrams, and breaking down the slip vectors into north-south and east-west components will help.)
   

2. If there were only one fault between the two stations causing the exact same total slip as above, what would its strike, sense of slip, and slip rate be?
   

Exercise 3Keeping in Step with Fault Slip

At right is a pair of diagrams showing a convergent fault step (a right step on a left-lateral fault). The top diagram is a map view showing the trace of the fault, the highlands that have resulted inside the fault step due to local compression, and a point marked X, in the middle of the fault step.

The lower diagram is a schematic showing how you will model this fault step for the purposes of this exercise. The main fault is a pure left-lateral strike-slip fault with a slip rate of 6.0 mm/yr. Where each segment of the main fault ends, assume there is a thrust fault connecting the two segments of the fault, both dipping at 45° toward the center of the block (marked, again, by a point labelled X). Assume the slip rates of the two thrust faults are identical. In addition, assume the slip along the main left-lateral fault is divided evenly between the two segments at the fault step. (The points marked 1 and 2 will be used only for the last question below.)

Work through the rates of the various faults, and investigate how their properties affect this scenario, by answering the questions below.

1. What is the slip rate on each of the two left-lateral segments which bound the inside "block" of this fault step? (Remember that the total slip rate within this block diagram, measured anywhere across the main fault zone, is 6.0 mm/yr.)
   

2. The answer to the question above is the horizontal component of the slip rate along each of the thrust faults. What, then, is the rate of uplift (vertical component of slip rate) of point X?
   

3. If the angle of dip of each thrust fault were decreased, would the rate of uplift of point X increase or decrease?
   

4. Look at the positions of points 1 and 2 on the diagram. Are they moving toward or away from each other, and at what rate? Would this rate increase, decrease, or stay the same if the dip of the thrust faults were decreased?
   

Exercise 4A Slip Model of the Plate Boundary in Southern California

For this exercise, you will be using a much simplified (and thus altered and somewhat inaccurate) map of the slip rates of major southern California faults, shown at right. This map is similar to the map of slip rates you looked at in Activity #13, though with a much lower resolution. The slip rate color scale used here is exactly the same as that of the map in Activity #13. The number of faults, and their orientations, have been greatly simplified, as promised. The apparent total slip between the two plates will be slightly less than the real-world value. This map has also been divided into five sections, shown in more detail below. The section boundaries run roughly perpendicular to the direction of plate motion at this tectonic plate boundary between the North American and Pacific Plates. The San Andreas fault, in red, is typically (though not always) parallel to that direction of motion.

Your job is to see to it that all the slip rates given "add up" to the correct total rate of slip across the plate boundary. Although the San Andreas fault is often designated as the "plate boundary", the fact of the matter is that the boundary is more a broad zone of shearing, and not all the slip between the plates is handled by the San Andreas fault. For the purposes of this exercise, consider the following to be true:

1. The edges of the "slices" below are completely "fixed" on their respective tectonic plates, labelled P (Pacific) and NA (North American).
   

2. The total slip across each slice should be 39 mm/yr, in a right-lateral sense.
   

3. With one exception, ignore the effects of the angle of each modelled fault segment when finding a total slip rate sum. (i.e. Assume the angle has been factored in already (with one noted exception), and that all slip rates given are parallel to the plate motion.)
   

4. All faults are right-lateral in slip unless otherwise noted. Two reverse faults will be shown, but you will note that they effectively work as right-lateral faults.
   

In addition to the color scale, the slip rates have been written next to the faults as rough estimates, in mm/yr. A few omissions exist, for you to fill in yourself. Brief explanations of each section will be given below. Answer the questions posed for each section, then move on to the next.

Section 1

This is the simplest section. In reality, this area is much more complex, but either way, the slip rate of the San Andreas fault dominates all else. The three fault zones on the eastern end of this modelled "slice" of California are characterized by only minor slip.

1. Assume the two unlabelled faults have exactly the same right-lateral slip rate. For the total slip to add up correctly, what must this slip rate be?
   

Section 2

Here is the northern edge of the Big Bend of the San Andreas fault. The long orange-yellow line across the top of the diagram is the Garlock fault. Its slip rate is inconsequential in this model, because it runs parallel to the section boundary (in some ways, it is the section boundary), and thus, does not affect the total right-lateral slip across this section. The curve of roughly the same color represents all the reverse faults in the western Transverse Ranges and the Los Angeles basin, rolled into one. It acts like a large right-lateral fault because of its orientation. The four lines on the North American side of the San Andreas fault are a simplified version of the faults in the Mojave. The slip rates of these faults are quite low.

1. Simply put, what's wrong with this picture?
   

2. The problem is with the San Andreas fault. The segment shown here -- the Mojave segment -- is part of the "Big Bend" of the fault. Though all other slip rates have been adjusted to represent only the parallel component of the slip rate of each modeled fault zone, this one has not. A rate of 30 mm/yr is the actual total slip rate on this segment. But since the segment is not parallel to the plate motion, that slip rate is greater than the component we are interested in. Assuming the rest of the diagram is correct, what is the rate of the component we're looking for?
   

3. Given this parallel component and the actual total slip rate for the Mojave segment of the San Andreas fault, at what angle is the fault bent from its "proper" trend in this section of the Big Bend?
   

Section 3

Here in section 3, the Big Bend begins to get more complex. This time, slip rates have been adjusted to account for the angle of deflection of the San Andreas fault, as well as the angles of other faults (i.e. everything is at face value). A new large fault zone is visible, splitting off from the San Andreas fault zone at the top of the section. This is the San Jacinto fault zone. The faults of the Mojave, with one exception, continue in this section. Several new but fairly minor fault zones appear to the west of the San Jacinto fault. All are right-lateral faults. The "oddball" fault in this diagram is the North Frontal fault zone of the San Bernardino Mountains. This is a thrust fault which, because of its orientation, acts as a right-lateral fault, though with only a very small slip rate.

1. Assume the through-going faults of the Mojave maintain their slip rates (you may need to refer back to the previous section to recall those rates). What is the slip rate, then, of the San Jacinto fault zone in this section?
   

2. The five right-lateral fault zones west of the San Andreas will appear in the rest of the sections (in other words, they run continuously, southward from here, as far south as this exercise will cover). Keep this in mind and note how they change in slip between sections. Currently, what general trend in their slip rates can you see as you move away from the San Andreas fault (westward)? Do you expect this trend to change?
   

Section 4

Here the San Andreas fault is split, in such a way that neither section is obviously dominant (in this map view at right, it looks like an orange "V"). The real workings of the fault in this area are terribly complex and not well understood, but for the purposes of this model, we have simplified it immensely. The same five fault zones are at work to the west of the branched San Andreas fault zone -- note that the San Jacinto fault zone accomodates essentially as much slip as each half of the San Andreas fault zone. To the east, the Mojave faults have basically died out, cut off by the left-lateral Pinto Mountain fault zone. While the Pinto Mountain fault zone is, in actuality, more like the Garlock fault zone, and probably should not be considered parallel to plate motion, we have included it here to show how an opposing sense of slip affects your calculations of total slip rate across an area.

1. What is the slip rate of the "faster" branch of the San Andreas fault, as shown in this model? (Remember that the Pinto Mountain fault is left-lateral, and that the total right-lateral slip rate across this area is 39 mm/yr.)
   

2. Note again the five faults west of the San Andreas fault zone. Has the general east-west trend in their relative slip rates changed?
   

3. Have the slip rates of those faults changed along strike (that is, north to south, along each fault)? What is the general trend here?
   

Section 5

In this final section, we are down to six faults -- all right-lateral, all parallel. The red fault represents, of course, the San Andreas fault zone. The five faults to its west are the same as in the previous two sections. The San Jacinto fault zone is not labelled with a slip rate this time.

1. What is the slip rate of the San Jacinto fault zone, here?
   

2. Is the slip rate of the recombined San Andreas fault zone equivalent to the sum of the two branches in the previous section? (Refer to the previous section if necessary.)
   

3. Is the east-west trend in slip rates still the same as before? What about the north-south trend? (Refer to the previous sections if necessary.)
   

4. Look back at the very first section. Do you notice a similarity to this last section? The Big Bend is not present in either section, but there is more similarity even than that. Note the side of the San Andreas fault on which all the other faults lie. In each diagram, is this side the "inside corner" or "outside corner" of the Big Bend? (In other words, if you followed the trend of these faults, would you intersect the bend or would the bend turn away from you?)
   

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