Hello. I’m Kathryn Materna, and I’m excited to talk to you today about rates
of interseismic deformation near Humboldt Bay in southern Cascadia.
This is a collaborative project with Jessica Murray at the USGS and
Lucy Sandoe and Roland Bürgmann at UC-Berkeley.
To begin, I’d like to bring us all to the study area of this project,
the Mendocino Triple Junction. The triple junction is at the intersection
of San Andreas Fault, the Mendocino Fault zone,
and the Cascadia subduction zone. It’s a very seismically active area
that hosted a magnitude 7 earthquake in 1992.
North of the triple junction, there are number of Quaternary
active structures in the USGS Faults and Folds Database that serve,
to some degree, as motivation for this project.
In the map on the right, I’m showing the overall tectonic overview of this
area plus a number of annotations. I’m adding the horizontal GPS velocity
vectors with respect to a stable North American Plate, and I also annotated
a number of the major faults in the Quaternary Faults and Folds Database.
We can see, based on the colors and the annotations, that some of these
faults we don’t know very much about. But the fault that is thought to be
most active out of this set is the Little Salmon Fault, which is
thought to have a slip rate of between 4 and 12 millimeters per year.
Trenching studies on this fault have suggested that it has
experienced at least three earthquakes in the last 1,700 years.
So the Little Salmon Fault and some of the others in this area
are thought to be quite active.
One of the exciting features about the Mendocino Triple Junction is
its vertical deformation, evident on long and short time scales.
On long time scales, vertical deformation
at the triple junction is evident in the geologic record.
Vertical deformation rates from marine terrace dating suggest that,
in certain places, the uplift rates are up to 4 millimeters per year.
In particular, these high uplift rates are located near the King Range terrane,
where I’ve annotated in red on this map.
But, throughout the area, there is evidence for uplift along the coast.
And we can see in some of the photographs of the area that there
is geomorphic evidence for uplifted terraces
and young and steep topography.
For context, 4 millimeters per year of long-term uplift is quite fast
and is among the fastest of any region in the lower 48.
It’s thought to be second only to Ventura, California,
in southern California. And the uplift rates on this order
of magnitude in Ventura were associated with significant hazard.
On shorter time scales – geodetic time scales,
there’s also interesting evidence in vertical deformation.
In this map here, I’m showing geodetic data that comes from leveling in the
circles, tide gauges in the squares, and GPS in the triangles.
These come from various – from different data centers.
The GPS comes from the USGS, and the leveling in the tide gauges
are courtesy of the Humboldt Bay Vertical Working Group.
When taken together, these vertical velocities show an interesting pattern
with systematic subsidence around the area of Humboldt Bay
in a block that seems to be fault-bounded.
So this vertical deformation field in the geodetic domain is the
motivation of our project. And we’re interested in understanding,
what are the implications of the three-component geodetic data
for fault slip and for seismic hazard in the region,
and especially for these upper crustal faults.
In order to answer this question, we are going to start by looking at
the two-dimensional data alone. And the analysis technique we’re
going to use with two-dimensional data is to investigate strain.
So why are we doing this? The strain rate is a measurement that
we can obtain from GPS velocities, and it’s convenient because it’s
independent of the reference frame, and it removes – it removes for us
the solid-body rotation component of the velocity field.
The strain rate is giving as a tensor – epsilon-ij – and it is computed from
displacement gradients. In the most general sense,
the tensor is three-dimensional and has 3-by-3 components,
but, because we’re looking at 2D horizontal velocities,
and we’re only looking at 2D strain, we only use the 2-by-2 in the
top corner – the X and Y components. The diagonal components are
normal strains, and the off-diagonal components are shear strains.
Because this is a tensor, it can be fairly difficult to plot on a map.
And so we often plot invariants of the tensor because they are
more convenient. There are some standard invariants –
the first invariant and the second invariant that I’m showing here.
The first invariant is simply the trace of the tensor.
And it is also known as the dilatation. It’s a very physical quantity.
When it is positive, it means there is extension and the volume
of that domain is growing. And when it is negative, it means
there is shortening and the volume of the domain is shrinking.
The second invariant, however – we also plot the second invariant
on occasion, but it doesn’t have a catchy name.
We just call it the second invariant.
And it displays the overall magnitude of strain.
It does not tell you whether the strain is shortening or shear,
but it simply displays the overall magnitude.
We also occasionally view the principal strains, which are the
eigenvectors of the system. And they’re plotted as these
sort of crosshairs on certain plots.
So how do we compute strain from GPS velocities?
The first technique – the simplest technique
is known as Delaunay triangulation. It’s quite simple, but it is not smooth
or robust to outliers, and it’s not robust to oddly shaped networks,
as you can see in these elongated triangles.
So are there more robust ways to compute a strain rate?
It turns out there are quite a few ways that are smoother, or they incorporate
an interpolation scheme or a weighting scheme to produce a robust strain rate.
I have seen probably at least 10 in the literature, and so there’s
a number of ways that one can go about doing this.
And so what we decided to do for this project was to construct an ensemble
strain rate map by performing this calculation in a number of –
using a number of methods and then averaging their results.
The idea here is to give us an ensemble strain rate map
that displays the characteristics common to all of these methods
and does not display any of the artifacts of a single method.
This is similar to a strain exercise that was performed by SCEC
a number of years ago. So when we use four methods here, and we average
them together on the same grid, here are some of our results.
Here is our ensemble second invariant map.
And we can even calculate an uncertainty –
an empirical uncertainty on quantities like the second invariant by taking
the standard deviation of those four methods that we’ve tried.
So, to interpret this, near the triple junction, it appears that we have high
interseismic strain through the second invariant throughout the forearc faults.
We can tell that the empirical uncertainties are higher in
the forearc than they are around the San Andreas Fault.
Higher in this area than in these values.
The uncertainties in some places are on the order of magnitude
of the strain rates themselves. And this may be surprising,
but similar results were actually found in the SCEC exercise too.
We find similar rotation values in each of the methods that we tried.
To expand on our results, we can plot the first invariant in the dilatation.
And, again, the negative values are shortening, and the positive
values in the blue are extension. The dilatation map – the mean
dilatation map here shows a strong shortening feature
around the forearc faults, where the azimuth of shortening
is approximately given by these vectors.
So we see shortening perpendicular to the forearc faults.
When we look at the direction of shortening, we can actually plot
the direction of shortening in this very colorful plot here,
where it may be easiest to look at some of these colors by their little keys.
The blue, which is at about 50 degrees clockwise from north,
represents shortening along this axis. Purple – closer to 20 degrees
from north – represents this kind of tensor and is indicative
of the San Andreas shear system.
And red would indicate this kind of tensor.
So we can see, in the forearc, there’s agreement that the tensors are in this –
in this shortening direction, but there’s actually not as much
agreement in the methods compared to what we find
further south in the San Andreas. This is where the uncertainties are low,
and in the north in the triple junction is where the uncertainties
are a little bit higher. We can also study the maximum shear,
which is another type of – which is basically another invariant we can
pull from the tensor, whom we find, not surprisingly, a lot of shear strain
in the San Andreas Fault system and then a fair bit
of shear strain to the north.
And we find low uncertainties on each of these quantities.
To put some of this together, we can plot the dilatation
together with vertical velocities from geodetic measurements.
So, in this map here, the background color is the dilatation derived from
horizontal GPS velocities, and the symbol color – the triangles and the
circles – are the GPS and leveling vertical velocities from the earlier slide.
This map shows a reasonable degree of correlation between areas
where there is shortening and areas where there is vertical uplift.
And similarly, a correlation between areas where there’s extension and areas
where there’s vertical subsidence. And that’s the kind of pattern
we would expect from an elastic strain accumulation process.
However, there seems to be an interesting outlier in the Humboldt Bay
area, where there is subsidence in the same area that there is shortening.
And that is an interesting feature that we intend to look at further.
We can also plot the maximum shear zoomed in on the Humboldt Bay area,
and we can see this feature of shear strain extending to the north.
But we can expand this tensor and look at the plane on which that
maximum shear is experienced. And that is more a north-south
oriented plane. It’s not exactly aligned with these particular faults.
So it’s an interesting feature as well.
So what have we learned?
We’ve learned that, near the triple junction, at the latitude
of Humboldt Bay, we have high interseismic strain with
fairly large empirical uncertainties. So that makes it difficult for us to
use this exact calculation for slip rates or moment accumulation.
But it’s still useful, as we have identified that there is quite high
margin-perpendicular contraction around the faults north of
the triple junction. And there’s well-resolved
shear strain, as well, north of the San Andreas Fault.
So what are the implications of this result for fault activity?
We are interested in understanding further these implications through
our next steps, which would be fault modeling through dislocation models.
We would like to estimate slip rates on some of these faults by building
a suite of dislocation models. There has been previous work
in dislocation modeling in this area from Williams et al. and Pollitz et al.
And we would like to extend that work by including the leveling data,
the tide gauge data, and the continuous – as much continuous
and campaign GPS data as we can reasonably include.
And our goal is to incorporate both vertical and horizontal
deformation into these models.
We will also focus on the tradeoffs inherent in a network of closely spaced
faults in doing this type of modeling. So, to conclude, thus far, on this
ongoing project, we have shown that GPS and leveling, tide gauges,
display systematic vertical deformation near faults
north of the Mendocino Triple Junction.
And our analysis of horizontal GPS velocities and strain rates shows high
strain rates north of the triple junction with residual right-lateral shear,
active shortening in the forearc perpendicular to these forearc faults,
and we have derived empirical uncertainties on each of
these quantities. The dislocation modeling work is ongoing,
and we’re aiming to perform that working with vertical data.
So thank you for your attention, and I’m happy to take questions
and discussion. Thank you.