Wang-Wong-Paper2024.pdf

Determining the shear wave vel

ocity of

the

Los Angeles

Basin

Matthew Wong and Yuping Wang

Mark Keppel High School

Alhambra, California, 91801

March 31, 2024

Abstract

We use Rayleigh waves to determine the shear wave velocity of

a portion of the Los Angeles

region. Correlations were constructed for two sets of six stations aligned relatively in the north

south and east

west direction, respectively. The arrival time of surface waves was estimated

between the stations which was the

n used to determine the group velocity for different sets of

frequencies, which we plotted on a dispersion curve to visualize the velocities the wave travels at

different frequencies. Lastly, the dispersion curve was converted into an estimate of the shear

wave velocity as a function of depth.

Introduction

The Los Angeles Basin has millions of residents with a significant earthquake risk. It is

deeper than the other basins in the region such as the San Gabriel basin and the San Fernando

Basin, and has faults within the basin area and is adjacent to the San A

ndreas fault, which is

capable of an 8+ magnitude earthquake [1]. The basin itself is composed of several sedimentary

layers that enhance the level of strong

motion shaking during an earthquake [1]. The shape

(mainly depth) of the basins as well as th

e shear strength of the sedimentary material are the

important factors that control the level of amplification of ground motions from earthquakes [1].

As a proxy for the strength of the material, we use the shear

wave velocity.

To measure the shear velocity, we use Rayleigh surface waves. These waves travel along the

surface of the earth between the earthquake and the receiver [2]. In the study we present here, we

use Rayleigh waves generated by the cross

correlation of the

seismic recordings at two stations.

This method uses the ambient noise generated primarily by the ocean waves breaking on

California’s coast [1]. Fortunately in Los Angeles, this is a strong signal. This method obviates

the need for expensive and environme

ntally disturbing active sources such as large vibrator

trucks or explosions [3].

By cross

correlating different stations, waveforms can be detected and their travel times can

be measured, which can be used to determine their velocities. Understanding the velocities of

these waves is crucial to determining the level to which strong

ground motions are amplified.

Specifically, shear wave velocities are important because when the shear wave velocity is higher,

the material is stiffer, and less ground shaking will occur. Velocity is dependent on the medium

in which it travels through, a

nd shear wave velocity is lower in soft soil than in hard soil or rock.

Method and Analysis

Open

source code was modified and used to retrieve seismic data from the cloud portion of

the Southern California Earthquake Data Center (SCEDC), rather than using the webservices of a

Jupyter Notebook because the latter had significant data dropouts [5].

Cross

correlation utilizes

two seismic stations that are running synchronously, and enhances the seismic signals picked up

by both stations over the same period. It filters unnecessary noise that will not be used, allowing

us to have a clearer image w

hen picking points on a seismogram. All seismic stations chosen for

cross

correlation in this study are from the Southern California Seismic Network (SCSN). We

use the vertical component (BHZ channel) for the correlations because this channel is

particularly sensitive to Rayleigh waves.

We chose 6 stations in the north

south geographical orientation and 6 stations in the east

west

geographical orientation. The stations in the north

south geographical orientation are especially

important because ocean waves hit southern Los Angeles fr

om the south [], and thus these

stations will pick up signals from the ocean the best. One station in the middle of all the stations

aligned in a linear direction is chosen to be correlated with the other stations and act as the

virtual vertical source tha

t radiates waves to the other stations (See Figure 1 for a map showing

the locations of our stations chosen). In our study, station USC was chosen as the station for both

the north

south and east

west measurements. The correlation data was then filtered fr

om 0.05

0.15 Hz, 0.15

0.25 Hz, 0.35

0.45 Hz, etc. increasing in intervals of 0.1 Hz up to 1.45

1.55 Hz to

target the data for a specific range of frequencies, i.e.: the interval 0.05

0.15 Hz was used to

visualize the frequency of 0.10 Hz. A seismogram is t

hen generated to show the cross

correlation

results between two stations at that frequency, and we plot those seismograms near each other on

a distance vs time graph, with the source station being set at a distance of 0 meters. An example

is shown in Figur

e 2.

Figure 1

Map of stations (East

West and North

South)

These are maps indicating the locations of the

seismometers we used for the cross

correlations. The first image details the seismometers used for the east

west

correlations, while the second image details the seismometers used for the north

south correlati

ons.

Figure 2

Correlations across stations (0.35

0.45 Hz)

This is the plot of all the correlations between each of the

east

west and north

south stations from 0.35

0.45 Hz. Here, we have drawn points on each of the peaks of the

perturbations to visualize how we chose them. The arrival time is measured from the x

axis of the peak, and the

distance between the stations is measured directly from their coordinates.

Figure 3

Correlations across stations (0.75

0.85 Hz)

This is the plot of all the correlations between each of the

east

west and north

south stations from 0.65

0.75 Hz, where the peaks of the arrivals are difficult to discern to

because there are multiple waves at some stations. From the top to the bottom of

the graph, the east

west stations

were aligned from east to west geographically, while the north

south stations were aligned from north to south

geographically.

This allows us to see the velocities by calculating it through the time the station sees the

perturbation and the distance the station is from the source station. In frequency intervals where

the perturbations were difficult to discern, the data was n

ot used, assuming it was an outlier

caused by a scattered wave. Figure 3 is below showing an example when perturbations were

difficult to discern. While there is a general trend we can see, it was not enough for us to

accurately pick the peaks.

Figure 4.1

Dispersion Curve (East

West)

This is the

dispersion curve with the error bars plotted with the

east

west stations. Each point represents a different set

of correlations.

The velocities that each station had when the perturbations were received were then averaged for

that specific frequency; when all the frequency sets with viable data had velocities averaged, we

plotted the velocities on a velocity versus frequency graph,

known as a dispersion curve, which

allowed us to visualize how velocity changes as the frequency changes. The standard deviation

was calculated to plot the error bars, and the dispersion curves demonstrated a downward trend,

with decreasing velocities as t

he frequency increased. This is explained by the fact that the

further down you go on Earth, the more compact the medium becomes, which decreases velocity

[]. Based on the equation v=

f • λ, because velocity is only affected by the medium in which it

propagates through, wavelength decreases as you go deeper into earth, which then causes the

frequency of the waves to increase.

Figure 4.2

Dispersion Curve (North

South)

This is

the dispersion curve with the error bars plotted with the

north

south stations, with each point representing a

different set of correlations.

Figure 5

Phase Velocity

These are the phase velocities shown for the east

west and north

south waveforms. It is

shown that as the depth increases, the velocity increases as well. The blue plus

signs represents the observed trend

from the dispersion curve (based on the points we p

icked in Figure 4) and the red plus

signs represents the

modeled trend from Geogiga’s software. The thicker blue line is the velocity determined from points we picked,

while the red line shows velocities based on the modeled trend. The gray area shows the

range of velocities that

the velocity could have been or the standard deviation.

Discussions and Conclusion

Finally, the dispersion curve was transformed into a shear wave velocity versus depth graph,

which shows the velocity of the wave at different depths, which was done using the "Surface"

software from the Geogiga Technology Corporation [6].

To conclude, our data shows that the shear wave velocities in the Los Angeles basin travel up

to around 1500 m/s in both the east

west and north

south direction when the depth exceeds about

1500 m. And as the depth increased, the velocity of the waves

increased as well. In the east

west

graph, the reference model’s velocity was slower than the observed trend up until about 970 m in

depth. Afterwards, the reference model’s velocity is greater than the observed trend. For the

north

south graph, the refer

ence model’s velocity was slower than the observed trend until about

1560 m in depth. Afterwards, the reference model’s velocity is greater than the observed trend.

We believe that these differences are simply results of the algorithm rather than an actual

trend in

the subsurface.

Knowing these shear wave velocities are crucial because shear wave velocities are important

for site amplification of strong motion waves. We expect that when the San Andreas fault rupture

occurs or when other earthquakes in southern Los Angeles happe

n, the shear wave velocity will

be the main determining factor on the level of shaking. These results are helpful when

earthquake scientists prepare for upcoming earthquakes in southern California like the long

expected San Andreas fault rupture.

Acknowledgements

The authors thank Robert Clayton of the Caltech Seismological Laboratory who provided his

expertise and support with this research. The authors thanks Yan Yang and James Atterholt, both

PhD students at the Caltech Seismological Laboratory, for their a

ssistance with the code used for

cross

correlating seismic stations. The authors thank Michael Gurnis of the Caltech

Seismological Laboratory for introducing this research opportunity.

References

1. Schulz, S. S., & Wallace, R. E. (n.d.). The San Andreas Fault.

https://pubs.usgs.gov/gip/earthq3/safaultgip.html

2. Surface Waves

. Michigan Technological University. (n.d.).

https://www.mtu.edu/geo/community/seismology/learn/seismology

study/surface

wave/

(

2013, April 24).

Development of a low Cost Method to Estimate the Seismic Signature of a

Geothermal Field

[Presentation].

https://www.energy.gov/eere/geothermal/articles/develpment

low

cost

method

estimate

seismic

signiture

geothemal

field

Building Resonance: Structural stability during earthquakes

. Seismological Facility for the

Advancement of Geoscience. (n.d.).

https://www.iris.edu/hq/inclass/animation/building_resonance_the_resonant_frequency_of_differ

ent_seismic_waves

5. Hadziioannou, C., & Rijal, A. (n.d.). Seismo

Live

GitHub Pages. https://seismo

live.github.io/html/Ambient%20Seismic%20Noise/NoiseCorrelation_wrapper.html

Surface

. Geogiga Technology Corp. (n.d.). https://www.geogiga.com/products/surface/

Supplementary Information

Figure S1

Cross

correlations across stations (0.25

0.35 Hz, 0.35

0.45 Hz, 0.45

0.55 Hz,...

1.45

1.55 Hz)

Below are the plots of all the correlations between each of the east

west stations

from 0.25

0.35, increasing in intervals of 0.10 up to 1.45

1.55 Hz. Here, the peaks of the

perturbations are difficult to discern to draw the group velocity, as there were m

ultiple

perturbations for some stations. The blue graph represents the station SMF2, orange represents

LCG, green represents LGB, red represents RHC2,

and purple represents WLT.

Figure S2

Notice that for the north

south line, the peaks were picked going from the top right

to the bottom left because the waveforms come from the south, and thus it takes less time for the

waves to reach stations closer to the south than the north.

Figure S3

Peaks picked for the north

south direction and the east

west direction

correlations

The chart below shows the distance and the time for each peak that we picked that

forms a diagonal line based on figure S2. It also shows the average velocity and standard

deviation that we used to generate the phase velocity versus depth graph in figure 5