Good morning. My name is Domniki Asimaki.
I am a professor at Caltech. And it is my great pleasure to
be today here and share with you the work we’ve been doing on
developing a sediment velocity model to improve the simulation
of basin amplification effects in southern California.
We have put a lot of effort in improving the algorithms and the
computer software and hardware that we use to simulate high frequencies
and the propagation from the source to the crust to the surface in original
ground motion simulations. The challenge now for the geotech
engineers like myself is to find ways to represent the fact that
high frequencies can actually see the near-surface soil.
So these complex three-dimensional, nonlinear heterogeneous anisotropic
features of the shallow crust cannot be captured anymore by correction
factors if we strive to propagate frequencies up to 10 hertz or more
through the shallow crust. And this is the same shallow crust
that will create conditions or will impose constraints through failure
on very large ground motions that we strive to simulate for very large
earthquakes yet to come. And so this shallow crust matters
to engineers and will significantly modify the very high frequencies
we are trying to propagate from source to surface.
And this is – was the motivation for the work I’m going to share.
So the previous iteration of the – of the shallow crust refinement in
ground motion simulations of SCEC is referred to as the geotechnical layer.
This was a smooth – is a smooth geometric representation of the shear
wave velocity down to 350 meters, which merges the Vs30 from geologic
max linear surface to the velocity models that 350 meters.
And this merging had definite benefits because we were able to refine
the shallow layering and therefore propagate high frequencies through
a more refined presentation of the shallow crust.
But, by imposing constraint at 350 meters connection point
between shallow layers and CVM-S, this could mask impedance contrasts
that lie somewhere in between and also alter the basin geometry,
particularly in the basin edges. And so [inaudible] [inaudible]
and others say – in the recent years, have shown through simulations
that this requirement – geometric requirement or constraint deteriorated,
in some cases, rather than improved the ground surface predictions
compared to the classic model without using the layer.
So that was the motivation for the – for the development of the sediment
velocity model. We wanted to develop an idealized model based on
observations. So also look at how actual profiles, Quaternary sediments,
vary in – deposits vary in shear velocity with depth.
And try to simulate – to capture, in an idealized fashion, the natural
deposits of shear wave velocity. And we wanted it to be function of
available physical properties, so properties that are already
embedded in the – in the velocity models so that we would have a
seamless integration of the velocity models we develop with the existing
community velocity model of SCEC. And we also wanted to find rules
to preserve the basin geometry while refining the stratigraphy
inside the basin structures.
The database that we used to perform this work was adopted from a series
of [inaudible] shown here. We used about 1,000 different profiles.
Merging those profiles into a unified database was
not always straightforward. An example I’m going to show you
here is from the near-surface structure and how different methodologies –
invasive versus non-invasive can lead to schematic differences
in the profile representation. So these are four different examples
from a narrowly defined Vs30 ranges. And you can see that, overall,
the comparison between the different databases is very good
within the same Vs30. This is because we chose to
stay within a certain geologic – set of geologic observations.
But, when we look at the near-surface, then the non-invasive profiles,
which are the black lines from the – a profile database shows us the
schematic reduction in the near-surface because these are inverted profiles.
The discretization is here, and the – and the inversion algorithm allows for
this reduction. Whereas, in the – in the invasive cases, the first
measurement is usually taken at 2.5 meters’ depth, and that explains
why the shallow presentation of the – of the near-surface layers is
so uniform in the invasive cases. So we found a way to map one set
to the other by trying to understand how the different methodologies
of measurement affect the measurement of the shear velocity profile.
And choosing an average variation with depth.
Thankfully the differences were only concentrated in the near-surface
down to about 2, 2.5 meters, which requires very low velocity
[inaudible] hertz frequencies can see it.
We were able to merge all those databases to one unified profile
and then come up with an idealized variation of shear velocity with depth
based on [inaudible] [inaudible] original scale input parameters.
So the parameters were idealized models Vs-zero, which is basically
the average velocity of the top 2.5 meters of the crust.
And then this – multiply with k and the exponent 1 over n.
The range of the profiles has been [inaudible] ranged from a Vs30
between probably 100 meters and 1,200 or more.
We reliably found that we were able to capture Vs30 up to 1,000 meters
per second. The training model that we used, we chose to split the shear
velocity profiles to Vs30 bins that were statistically equivalent.
These are the empirical variation of the mean and the standard deviation and
the idealized fitting based on these profiles here – this model here.
The parameters Vs-zero, k, and n, their variation with Vs30 shown
in this location. The input parameter for the velocity profile is Vs30.
The decision of where the sediment profile stops and the
subsurface rock starts is based on z-1,000.
Data didn’t only show us how the Vs30 varies at the near surface
as a function of depth, but they also showed us how we could –
helped us understand how to randomize the shallow layers. This is the variation
of the thickness of the layer profiles as mapped from the measurements.
So, when we had the smoother presentation of the velocity, we had to
break it down into thinner layers and then randomize each layer.
The way that we broke it down was on the basis of data.
I’ll show you an example right away. And, on the right-hand side, this is
the region-specific, geology-specific variation of z-1,000 with Vs30.
This was very useful for cases where the z-1,000 was shown to be zero.
The site was reported in the Community Velocity Model as being a rock site,
whereas, the geology suggested that Vs30 was low.
In that case, we have to find a way to marry those two – those two consistent
[inaudible] presentations. Then we define the z-1,000,
a function of Vs30, and so, at that location, we were able to then switch
to the actual rock properties of the Community Velocity Model.
So here’s an example for a site with 320 meters per second
and a z-1,000 of 120. You can see this is [inaudible] –
the homogenized – the smooth representation of the [inaudible] profile.
The discretization is of the basis of the data I showed you here.
And the randomization is by choosing – by selecting from the – from the
variation of the parameters Vs-zero, k, and n to perturb this profile according
to the statistics of the actual profiles we used to develop SVM.
The way that this model worked in implementation in a basin structure –
an example is shown here. This is a cross-section northeast
of Long Beach. And you can see that – you can see the smooth variation with
depth but also the respecting of the interface between soil and rock.
And you can see here, this is a location where z-1,000 was reported as zero.
The velocity at depth was higher than – I mean, at the surface was higher –
the z-1,000 than 1 kilometer per second.
But we were able to then merge the Vs30 of the geologic feature with the
z-1,000 of CVM by choosing the empirical defined depth to
1 kilometer per second, filling that very shallow layer
with SVM and then transitioning to the stiffer subsurface rock.
We validated SVM by comparing the goodness of fit – by evaluating
the goodness of fit of both 1D profiles and their corresponding
amplification factors. The comparison between –
was between SVM, CVM-S – so only the cluster the structure,
and then CVM-H – have our model with the geotechnical layer.
And the validation was performed on a hold-out data set of 43 profiles
that were not used for the training of our model.
Two examples shown here. This is a site where CVM-S had –
was mapped as a – as a rock. In that case, the geotechnical layer
does a very good job of approximating the shallow crust in model, and this is
also reflected in the comparison of the amplification factors.
In the next example, SVM clearly does a better job in capturing the
measured profile compared to GTL. But this is a case where CVM-S also
had a variation of shear wave velocity with depth in the –
in a comparable Vs30 range.
The ensemble of the comparison between measurement –
the simulation is shown here. The definition of the goodness of fit
that we gave was on the basis of [inaudible] function.
The measured profiles and the – and the transfer function, you can –
you can see here that the GTL spans a range of goodness of fit
from very poor to very good. CVM-S stands to have a lot more sites
that are sedimentary deposits mapped as rock,
which is why GTL tends to improve this presentation.
SVM is systematically better for the –
for the three hold-out profiles of the data set.
In transfer functions, the comparison is less contrasting, particularly because
the details of the near-surface layers have are very critical for the
high-frequency amplification. And therefore, once you don’t capture
those details, then the range of goodness of fit for amplification
factor of the three profiles is similar. Nonetheless, both the mean and the
scatter above the mean of SVM was improved compared to
the other two options.
Currently, we have – in blue, we have implemented the SVM in the
Unified Community Velocity Model. We are able to now generate a regional
velocity model that include the sediment velocity model
in the shallow layers. And we are now conducting
a forward simulation using Hercules at the [inaudible] Valley.
The choice of the site was because the location has – we have a lot of
information about properties. And you can see here the surface
velocity profiles of CVM-S with the geotechnical layer
compared to CVM-S with SVM.
The location of the – of the basins is similar, although you can see here,
the ones we are – for example, this location here is a contrast in the GTL,
whereas, in the SVM, there is a more smooth presentation.
Preliminary results show that we capture better the wave propagation,
particularly in the basin edges, compared to measurements of different
events. But stay tuned because the results will be published soon.
Future work – we would like to implement SVM at a site with a dense
array so that potentially we can couple the material property statistics with
the spatial statistics of the variation of the material properties.
Correlation structures and correlation length in X and Y.
We would like to test it for a larger region, so move from the
Garner Valley, we scale to a L.A. Basin scale.
And then this framework that I showed you might be specific for the geology
of the sedimentary deposits in southern California, but the framework is
transferable, and the potentially northern California would be a natural
next step for us to look at the geologic features, trying to cluster geologies
together, and then understand how the variation of the properties
with depth lies in each one of those features.
The SVM is available in Python routines and Jupyter notebooks
at the – our GitHub site. And a lot of this – of what I presented
today can be found in this publication, although there is [inaudible] with
the implementation of SVM and use CVM and [inaudible]
the ground motion simulations.