This work is supported by the National Science Foundation’s Transforming Undergraduate Education in STEM program within the Directorate for Education and Human Resources (DUE ). B ACKGROUND I NFORMATION ON F IRST M OTION M ODELS FOR E ARTHQUAKES Bruce Douglas (Indiana University—Bloomington) Gareth Funning (University of California—Riverside) Version: Dec 7, 2015

We use a specific set of symbols to identify faulting geometry on maps. The symbols are called earthquake focal mechanisms or sometimes seismic “beach balls.” A focal mechanism is a graphical summary of the strike, dip, and slip directions. An earthquake focal mechanism is a projection of the intersection of the fault surface and an imaginary lower hemisphere surrounding the center of the rupture. E ARTHQUAKE F OCAL M ECHANISMS

First motions On a seismogram, the first motion is the direction of ground motion as the P wave arrives at the seismometer. Upward ground motion indicates an expansion in the source region; downward motion indicates a contraction. E ARTHQUAKE F OCAL M ECHANISMS

Seismic wave generation Rupture starts at focus and spreads erratically and non-uniformly Irregularities on fault plane (asperities) may act as barriers and temporarily slow propagation in certain direction Rupture stops when rocks not sufficiently strained to allow it to continue After rupturing ceases, adjacent sides of fault rebound Seismic waves radiate from numerous places on fault plane Rupture velocity variable sometimes ~ walking speed (1960 Chile quake took an hour for full rupture) Typically 2–3 km/sec Fault plane Radiating rupture surface F S EISMIC WAVE GENERATION

F IRST M OTIONS In the early 20th Century, Japanese seismologists began investigating the sense of motion that accompanied the very first seismic wave arrival at a seismometer. They found that these first motions are either upward or away from the source, or arrive downward or toward the source. Though initially thought to be the result of different types of earthquakes, it was soon discovered that a single earthquake could produce both types of motion. This knowledge, combined with the developing theories of fault rupture, led to the suggestion that these first wave motions were indicators of slipping motion from the actual fault rupture producing the seismic waves.

F IRST M OTIONS Imagine an east-west oriented, right-lateral strike-slip fault. Now imagine standing on the south side of that fault, facing east, when an earthquake begins to rupture the stretch of fault in front (east) of you. What would you feel?

F IRST M OTIONS The first motion you would experience would be a “push,” pushing you away from the source of the earthquake, as your side of the fault experiences compressional force from the motion of the fault rupture. The areas of the block diagram that turn red experience compression when the fault moves. Those areas that fade to white experience the opposite kind of motion, dilatation, as they are initially pulled toward the source with “pull” motion.

F IRST M OTIONS Analysis of records made from the seismic instruments surrounding the source of an earthquake allow seismologists to determine the sense of slip of that earthquake, even if the rupture does not reach the surface. This is done by creating a model of the initial rupture motion, called a focal mechanism.

First Motion Radiation Pattern for a Strike Slip Earthquake

F OCAL M ECHANISMS — S EISMOLOGICAL “B EACH B ALLS ” A focal mechanism is a model of the exact orientation and sense of slip of the fault rupture that generates an earthquake. The model can be described with a sphere, cut by two perpendicular nodal planes that intersect in the center, dividing the sphere into four equal quadrants.

F OCAL M ECHANISMS — S EISMOLOGICAL “B EACH B ALLS ” Each quadrant has either push or pull Since focal mechanisms are constructed using first motions, the direction of the first deflection recorded by a seismometer as that instrument experiences the initial arrival of seismic waves. It takes a large number of seismometers in the area surrounding the hypocenter to produce a reliable focal mechanism. Gaps in coverage will increase the uncertainty in the model.

C REATING F OCAL M ECHANISMS Now we need to plot the first motions recorded from our earthquake. To do this, we check the waveforms recorded by various seismic stations in the area and mark the first arrivals as “up” (compressional) or “down” (dilatational). Each station’s location relative to the hypocenter is then projected onto our circular diagram with a symbol representing the type of motion—up or down—first recorded there. Stations that fall within the “missing” upper hemisphere (above the horizontal) are translated appropriately onto our lower- hemisphere projection.

C REATING F OCAL M ECHANISMS Once the first motions are correctly plotted, it is time to solve for the two nodal planes. The sphere is divided into quadrants using two perpendicular planes that best fit the set of first motions. Again, since the two-dimensional plot shows only the projection of the inner surface of the lower hemisphere, those planes will look like two intersecting lines within a circle. Though the two nodal planes must intersect at the hypocenter, the center of the sphere, the intersection of these lines—since it occurs on the sphere’s surface—need not be in the center of our circular projection.

C REATING F OCAL M ECHANISMS After the nodal planes have been identified, the symbol is complete, but of somewhat limited use, because either of the two nodal planes could be the fault plane. Other types of data can be useful in determining which plane is the fault plane, and consequently, what type of slip occurred in the earthquake.

First Motion Solution

First Motion Radiation Patterns for Normal and Reverse Fault Earthquake

First Motions for a Reverse Fault: The Dilation, Nodal Plane and Compression responses are shown along with the deflection recorded by a seismometer responding to the initial arrival of seismic waves

R EADING F AULT P LANE S OLUTIONS Interpreting fault plane solutions can be a little tricky. There are several things to keep in mind when converting a symbol (like the one at lower left) to a sense of slip and fault plane orientation. First, the fault plane solution is generally given as a two-dimensional projection of the lower hemisphere of a focal mechanism sphere, not just an overhead view of the outside of that sphere. Also keep in mind that the lines crossing the circle represent the intersection of two perpendicular planes with a sphere.

+ + - Normal dip-slip fault R EADING F AULT P LANE S OLUTIONS If you can determine which nodal plane on a fault plane solution corresponds to the orientation of the geologic fault plane, you know that the other plane must be the auxiliary plane. Because this plane is oriented perpendicular to the direction of slip, its point of intersection with the fault plane (and the lower surface of the sphere) provides information about the relative proportions of dip slip and strike slip involved in the fault rupture. If the line of the auxiliary plane bisects the fault plane’s line, this represents pure strike slip.

F OCAL M ECHANISMS — S EISMOLOGICAL “B EACH B ALLS ” Focal mechanisms really only describe the motion involved at the start of a rupture—the hypocenter (also called the focus, hence their name)—because they are calculated using the very first wave arrivals from an earthquake. In an earthquake large enough to involve several kilometers of fault rupture, slip will sometimes “evolve,” changing in sense and/or orientation as the rupture propagates. This can happen in response to changes in fault geometry or rupture boundary conditions. In such a case, the entire fault rupture may not exactly match the model supplied by the focal mechanism. The focal mechanism will still provide insight into the initial rupture behavior at the hypocenter.

R EADING F AULT P LANE S OLUTIONS Knowing the geology of the area will help you identify the most likely fault geometry. Aftershocks can be of great assistance; aftershock sequences can provide valuable hints about fault plane orientation at depth. Though not always feasible, the use of these insights can lead to a final determination of the fault plane solution.

Fault plane solutions from first motions Type of fault can be determined remotely from first motions on a seismogram P-wave: detected as either a push or a pull P-wave first motions will depend where seismograph is located relative to fault Those located at points where fault at the focus is moving away record pulls (dilatations) Seismographs located such that as fault is moving toward them will record pushes or compressions Normal dip-slip fault Reverse dip-slip fault