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Tuesday, February 27, 2001 Louie, Shear-Wave Velocities from Refraction Microtremo
r
http://quake.seismo.unr.edu/ftp/pub/louie/papers/disper/
refr-pp.html Page: 1
Faster, Better: Shear-Wave Velocity to 100 Meters Depth
From Refraction Microtremor Arrays
John N. Louie
Seismological Laboratory and Dept. of Geological Sciences
Mackay School of Mines, The University of Nevada, Reno, NV 89557-0141
Phone: 775-784-4219 Email: louie@seismo.unr.edu Web: www.seismo.unr.edu
Manuscript in press in the Bulletin of the Seismological Society of America.
Abstract
Current techniques of estimating shallow shear velocities for assessment of earthquake site response are too costly for use at
most construction sites. They require large sources to be effective in noisy urban settings, or specialized independent recorders
laid out in an extensive array. This work shows that microtremor noise recordings made on 200-m-long lines of seismic
refraction equipment can estimate shear velocity with 20% accuracy, often to 100 m depths. The combination of commonly
available equipment, simple recording with no source, a wavefield transformation data processing technique, and an interactive
Rayleigh-wave dispersion modeling tool exploits the most effective aspects of the microtremor, SASW, and MASW techniques.
The slowness-frequency wavefield transformation is particularly effective in allowing accurate picking of Rayleigh-wave
phase-velocity dispersion curves despite the presence of waves propagating across the linear array at high apparent velocities,
higher-mode Rayleigh waves, body waves, air waves, and incoherent noise. Two locations illustrate the application of this
technique in detail: coincident with a large accelerometer microtremor array in Reno, Nevada; and atop a borehole logged for
shear velocity in Newhall, Calif. Refraction equipment could duplicate microtremor results above 3 Hz, but could not estimate
velocities deeper than 100 m. Refraction microtremor cannot duplicate the detail in the velocity profile yielded by a suspension
logger, but can match the average velocity of 10-20 m depth intervals and suggest structure below the 100 m logged depth of the
hole. Eight additional examples from southern California and New Zealand demonstrate the refraction microtremor technique
quickly produces good results from a wide range of hard and soft sites.
Motivation
Comprehensive earthquake preparedness requires methods to rapidly assess the possibility of unusually strong shaking at a large number of sites.
Estimating shallow shear velocity structure can be an important component of site-response estimates of possible shaking (Borcherdt and
Glassmoyer, 1992; Anderson et al., 1996). The data and analysis here show how multichannel arrays of lightweight single 8-Hz vertical seismic
refraction geophones can estimate surface-wave velocities to 100 m depths, with very little field effort.
Such seismometers for refraction exploration weigh less than one kilogram each. Most universities and engineering consultants already possess
seismic refraction systems that can digitally record between 12 and 48 geophones, or channels, simultaneously. This paper shows how to easily
deploy such commonplace equipment to record background noise, or ``microtremor,'' and how the data can yield surface-wave velocity
dispersion measurements that constrain shallow shear-velocity structure. The success of these tests suggests that this technique will efficiently
contribute to site-response assessments.
The refraction microtremor technique can only resolve velocity structure to 100 meters depth. Deeper constraints may require more conventional
seismic survey methods and microtremor recordings by broader arrays of more sophisticated instruments (Horike, 1985). Satoh et al. (1997)
made such analyses at the locations of unexpected damage from the 1994 Northridge earthquake. Liu et al. (2000) compared array results against
deep borehole measurements at two California sites, finding that array aperture was the limiting factor in the depth resolution of surface-wave
measurements.
A need for the rapid and inexpensive assessment of earthquake hazard at large numbers of sites has led to the development of several geophysical
testing methods that do not require drilling. The well-known Spectral Analysis of Surface Waves (SASW) and microtremor array techniques both
use surface-wave phase information to interpret shear-velocity or rigidity profiles. Other techniques that tried to employ P waves or S body
waves, for example as in Williams et al. (1994), have not been as successful in matching ground-shaking or borehole data.
The SASW and MASW Techniques
Nazarian and Stokoe (1984) first described the SASW method to the earthquake engineering community. Sometimes referred to as ``CXW''
(Boore and Brown, 1998), SASW uses an active source of seismic energy, recorded repeatedly by a pair of 1 Hz seismometers at small (1 m) to
large (500 m) distances (Nazarian and Desai, 1993). The seismometers are vertical particle-velocity sensors, so shear-velocity profiles are
analyzed on the basis of Rayleigh-wave phase velocities interpreted from the recordings. The phase velocities are derived purely from a
comparison of amplitude and differential phase spectra computed from each seismometer pair for each source activation, within an FFT
oscilloscope (Gucunski and Woods, 1991).
Since the original seismograms are not saved and all interpretation is done in the frequency domain, the SASW method assumes that the most
energetic arrivals recorded are Rayleigh waves. Where noise overwhelms the power of the artificial source, as is common in urban areas, or
where body-wave phases are more energetic than the Rayleigh waves, SASW will not yield reliable results (Brown, 1998; Sutherland and
Logan, 1998). The velocities of Rayleigh waves cannot be separated from those of other wave types in the frequency domain. Boore and Brown
(1998) found that SASW models consistently under-predicted shallow velocities, at the sites of six southern California borehole shear-velocity
profiles, thus over-predicting ground motions by 10% to 50%.
The Multichannel Analysis of Surface Waves (MASW) technique (Park et al., 1999) has been developed in response to the shortcomings of
SASW in the presence of noise. The simultaneous recording of 12 or more receivers at short (1-2 m) to long (50-100 m) distances from an
impulsive or vibratory source gives statistical redundancy to measurements of phase velocities. Multichannel data displays in a time-variable
frequency format also allow identification and rejection of non-fundamental-mode Rayleigh waves and other coherent noise from the analysis.
Tuesday, February 27, 2001 Louie, Shear-Wave Velocities from Refraction Microtremo
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M
ill
er et a
l
.
(2000)
were a
bl
e to o
b
ta
i
n exce
ll
ent M
AS
W resu
l
ts
i
n t
h
e no
i
sy env
i
ronment o
f
an operat
i
ng o
il
re
fi
nery. Us
i
ng
b
ot
h
l
arge an
d
stacked small sources, they could acquire records dominated by fundamental-mode Rayleigh waves. They also attempt 2-dimensional profiling
for lateral anomalies in shear velocity by inverting many records along a profile. Such a profile represents much costly effort, similar to that
needed for a high-resolution reflection survey, as a large source must be moved along and activated repeatedly at a large number of locations.
Simpler Acquisition, More Robust Analysis
The refraction microtremor method combines the urban utility and ease of microtremor array techniques with the operational simplicity of the
SASW technique, and the shallow accuracy of the MASW technique. By recording urban microtremor on a linear array of a large number of
lightweight seismometers, the method achieves fast and easy field data collection without any need for the time-consuming heavy source required
for SASW and MASW work. By retaining all the original seismograms, and by applying a time-domain velocity analysis technique as is done in
MASW, the analysis described here can separate Rayleigh waves from body waves, air waves, and other coherent noise. Transforming the
time-domain velocity results into the frequency domain allows combination of many arrivals over a long time period, and yields easy recognition
of dispersive surface waves.
With sponsorship by the U.S. Geological Survey, the Southern California Earthquake Center, and the U.S. National Science Foundation; and
through collaboration with colleagues from the Victoria University of Wellington, Shimizu Corporation, Kobe University, and the Disaster
Prevention Research Institute of Kyoto University, this project carried out noise surveys at ten locations in Nevada, southern California, and
New Zealand. Three of these surveys were blind tests against other techniques. The Reno survey combined 1-km-wide arrays of 1-Hz sensors as
used by Horike (1985) with 358-m linear arrays of 8-Hz and 4.5-Hz sensors at the northeast corner of the Reno/Tahoe International Airport. A
200-m linear noise and refraction array of 8-Hz sensors surveyed a ROSRINE borehole at the Newhall Fire Station in southern California. Also,
linear analysis of existing 1-Hz array data compared favorably against SASW and seismic-cone-penetrometer profiles in the Parkway
neighborhood of Wellington, New Zealand.
Method
The refraction microtremor technique is based on two fundamental ideas. The first is that common seismic-refraction recording equipment, set out
in a way almost identical to shallow P-wave refraction surveys, can effectively record surface waves at frequencies as low as 2 Hz. The second
idea is that a simple, two-dimensional slowness-frequency (p-f) transform of a microtremor record can separate Rayleigh waves from other
seismic arrivals, and allow recognition of true phase velocity against apparent velocities.
Use of Seismic Refraction Recording Equipment
Two essential factors that allow exploration equipment to record surface-wave velocity dispersion, with a minimum of field effort, are 1) the use
of a single geophone sensor at each channel, rather than a geophone ``group array,'' and 2) the use of a linear spread of 12 or more geophone
sensor channels. Single geophones are the most commonly available type, and are typically used for refraction rather than reflection surveying.
The geophones with 8 Hz resonant frequency used at most of the ten sites tested here are on the low end of the frequencies commonly found.
They are not unusual among refraction equipment, however.
A geophone group array consists of several sensors wired together to sum electrically, producing a single recorder input channel.
Petroleum-industry seismic-reflection surveys use geophone group arrays to cancel surface waves and other horizontally propagating energy, and
emphasize vertically propagating reflections. Because of the widespread use of group arrays, existing reflection records may not yield good
results from these surface-wave analysis techniques. New data may have to be taken. If only geophone group array strings are available for new
recording, they can be set in a cluster or ``potted,'' at one effective surface location. Alternatively, the strings might be stretched out
perpendicularly to the trend of the refraction line, thus mitigating energy propagating across the line while enhancing the recording of waves
travelling along the line.
A cluster test showed that common, compact seismic refraction sensors perform very well even if they are set as much as 20° off vertical. With no
leveling needed, the setting of a 24-channel line of such geophones can take as little as one person-hour. Geophones are usually set below loose
surface materials and buried under about 10 cm of tamped soil, or set into the base of a slice cut into turf and pried open with a spade. It is easy to
pound holes in asphalt pavement with a short length of 3/8-inch rebar to set the geophone spikes into, if unpaved areas are not available. These
small holes are easily repaired with a quick-setting asphalt patching compound.
Another important component of this experimental setup was the use of a relatively long (8 to 20 m) interval between each geophone along the
multichannel spread. The so-called ``takeout interval'' of the cables used for these tests is on the long side of those already in the market, but not
unusual. The use of hundreds of meters of multichannel seismic recording cable can make deployment of this technique difficult in congested
urban areas, where the cable would have to be protected at every vehicle crossing. An array of independent, stand-alone recorders is easier to
deploy over a grid of streets. With careful examination of maps and some scouting, however, at least 200 m lengths of single blocks without
cross streets can be found near almost any desired site.
The discussion here is restricted to recordings of single straight lines of geophones, to evaluate the utility of the simplest deployment geometry.
As a result, these analyses will contain energy at apparent phase velocities that are higher than the true phase velocities. The examples here
demonstrate that the lower limit of the apparent phase velocities on these analyses can be recognized as the true phase velocity. With this ability, it
is possible to record with a 200-m refraction cable at almost any site, even in very heavily urbanized areas.
Sensor accuracy below their resonant frequency - Many of the experiments reported here used a Bison Galileo-21 48-channel recorder and 8-Hz
compact geophones. The Galileo-21 employs an instantaneous floating-point digitizer to 21-bit floating-point samples. Before digitization, the
analog signals from the geophones pass through pre-amplifiers with configurable gain and filter settings. During tests of the system's response to
low frequencies, using the 8-Hz geophones clustered together, setting the higher ranges of pre-amplifier gain yielded the most coherent recording
of noise and microtremor frequencies below 5 Hz.
Table 1 gives representative correlation coefficients of combinations of preamp gain and frequency range for cluster noise records taken on the
University of Nevada, Reno campus. The three columns of table 1 list average correlation coefficients, and their standard deviations, between the
24 traces of cluster noise records after 0-5 Hz and 0-25 Hz low-pass filtering, and raw without filtering. These data show that all instrument
preamp gain settings except zero can accurately record data above 5 Hz; including urban background noise and nearby sledgehammer impacts.
Tuesday, February 27, 2001 Louie, Shear-Wave Velocities from Refraction Microtremo
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refr-pp.html Page: 3
C
o
h
erent m
i
crotremor at
4
Hz
d
om
i
nates t
h
e
0
-
5
Hz
fil
tere
d
no
i
se recor
d
s.
A
preamp ga
i
n o
f
40
or a
b
ove w
ill
accurate
l
y recor
d
b
e
l
ow
5
Hz,
although raw or higher-frequency data will show digitizer clipping from nearby impacts.
A sledgehammer impact closer than 10 m from the geophone will cause physical clipping (or ``pin the seismometer to the stops''). No clipping
was observed at lower gain for impacts more than 10 m from the cluster. The custer records show poor but visible coherency below 5 Hz at 20
dB, suggesting that any data recorded with similar instruments might yield low-frequency velocities. Table 1 shows cross-correlation tests
yielding correlation coefficients of 97.8±2.0% among geophones in the cluster, at 0-5 Hz with a 60 dB gain. Background noise did not saturate
digitally at such a gain, although hammer-blow recordings would.
(table 1 here)
Other recordings made under similar conditions with a Geometrics R24 seismograph yielding 24-bit integer samples and 12-Hz compact
geophones (with the generous cooperation of J. Taber and T. Haver of the Victoria University of Wellington, New Zealand) did not need high
pre-amplifier gain to record low-frequency microtremor accurately. These tests show that modern refraction geophone transducers, when
properly coupled to the ground, can coherently record frequencies less than half their resonance frequency. Seismographs producing 12- and
even 16-bit integer data, on the other hand, probably cannot record low-frequency microtremor without an analog high-cut filter.
The very great advantage of the refraction microtremor technique, from a seismic surveying point of view, is fourfold: it is very fast and
inexpensive; it requires only standard refraction equipment already owned by most consultants and universities; it requires no triggered source of
wave energy; and it will work best in a seismically noisy urban setting. Traffic and other vehicles, and possibly the wind responses of trees,
buildings, and utility standards provide the surface waves this method analyzes.
Velocity Spectral (p-f) Analysis
The basis of the velocity spectral analysis is the p-tau transformation, or ``slantstack,'' described by Thorson and Claerbout (1985). This
transformation takes a record section of multiple seismograms, with seismogram amplitudes relative to distance and time (x-t), and converts it to
amplitudes relative to the ray parameter p (the inverse of apparent velocity) and an intercept time tau . It is familiar to array analysts as ``beam
forming,'' and has similar objectives to a two-dimensional Fourier-spectrum or ``F-K'' analysis as described by Horike (1985). Clayton and
McMechan (1981) and Fuis et al. (1984) used the p-tau transformation as an initial step in P-wave refraction velocity analysis.
The p-tau transform is a simple line integral across a seismic record A(x,t) in distance x and time t
A(p,tau) =
∫
xA(x,t=tau+p x) dx (1)
where the slope of the line p = dt/dx is the inverse of the apparent velocity Va in the x direction. In practice x is discretized into nx intervals at
a finite spacing dx (here usually 8-20 meters) so x = j dx with an integer j. Likewise time is discretized with t = i dt (with dt usually
0.001-0.01 second), giving a discrete form of the p-tau transform for negative and positive p = p0+l dp and tau = k dt called the slantstack:
A(p=p0+l dp,tau=k dt) =
∑
j=0,nx-1 A(x=j dx,t=i dt=tau+p x) (2)
starting with a p0 = -p max . pmax defines the inverse of the minimum velocity that will be found, usually set at 200 m/s but searched at 100 m/s
or less for particularly soft sites. np is effectively set to be one to two times nx . Here dp may range from 0.0001-0.0005 sec/m, and is set to
cover the interval from -p max to pmax in 2np slowness steps. This will analyze energy propagating in both directions along the refraction
receiver line. Amplitudes at times t = tau+p x falling between sampled time points are estimated by linear interpolation.
The distances used in refraction microtremor analysis are simply distances of geophones from one end of the array. As described by Thorson and
Claerbout (1985), the traces do not have to sample distance evenly, so the straight arrays analyzed here are for the convenience of field layout,
not for the convenience of analysis. The intercept times after transformation are thus simply arrival times at one end of the array.
The p-tau transformed records contain, in the work here, 24 or 48 slowness traces, one or more per offset trace in the original x-t records. Each
of these traces contains the linear sum across a record at all intercept times, at a single slowness or velocity value. The next step takes each p-tau
trace in A(p,tau) (equation 2) and computes its complex Fourier transform FA(p,f) in the tau or intercept time direction:
FA(p,f) =
∫
tau A(p,tau)e -i 2 pi f tau dtau (3)
for which the discrete Fourier Transform with f = m df is
FA(p,f=m df) =
∑
k=0,nt-1 A(p,tau=k dt)e -i 2 pi m df k dt (4)
although in practice the Fast Fourier Transform is mathematically equivalent but more efficient. Note that this is a one-dimensional transform that
does not affect the slowness or p axis. Achieving good frequency resolution requires recording times longer than those typically used in seismic
refraction work. For example, a time sampling dt of 0.001 sec requires a record length nt of at least 4000 samples, or 4 sec, for df = 0.25 Hz
frequency resolution. In this work the refraction microtremor records range from 20 to 50 seconds in length.
The power spectrum SA(p,f) is the magnitude squared of the complex Fourier transform:
SA(p,f) = F A*(p,f) F A(p,f) (5)
where the * denotes the complex conjugate. This method sums together two p-tau transforms of a record, in both forward and reverse directions
along the receiver line. To sum energy from the foward and reverse directions into one slowness axis that represents the absolute value of p, |p| ,
the slowness axis is folded and summed about p=0 with
SA(|p|,f) = [ S A(p,f) ] p
≥
0 + [ S A(-p,f) ] p<0 (6)
This completes the tranform of a record from distance-time (x-t) into p-frequency (p-f) space. The ray parameter p for these records is the
horizontal component of slowness (inverse velocity) along the array. In analyzing more than one record from a refraction microtremor
deployment the individual records' p-f images SAn(|p|,f) are added point-by-point into an image of summed power:
Stotal (|p|,f) =
∑
nSAn(|p|,f) (7)
Tuesday, February 27, 2001 Louie, Shear-Wave Velocities from Refraction Microtremo
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S
o t
h
e s
l
owness-
f
requency ana
l
ys
i
s
h
as pro
d
uce
d
a recor
d
o
f
t
h
e tota
l
spectra
l
power
i
n a
ll
recor
d
s
f
rom a s
i
te, w
hi
c
h
p
l
ots w
i
t
hi
n
slowness-frequency (p-f) axes. If one identifies trends within these axes where a coherent phase has significant power, then the
slowness-frequency picks can be plotted on a typical period-velocity diagram for dispersion analysis.
The p-tau transform is linear and invertible, and can in fact be completed equivalently in the spatial and temporal frequency domains (Thorson and
Claerbout, 1985). The transform does act as a low-pass 1/frequency filter on the amplitudes in the data. However, this filtering does not distort
or bias frequencies. The transform stacks along parallel lines to each intercept time, so there is no ``stretch'' or frequency distortion as there is for
the ``normal-moveout'' or velocity stack along hyperbolae (Thorson and Claerbout, 1985). The transform does produce artifacts, however,
smearing distance-limited or spatially aliased large amplitude waves over a large range of slownesses. This artifact does not prevent the
identification of surface-wave dispersion, however.
McMechan and Yedlin (1981) developed the p-f technique and tested it against synthetic surface waves, and reverberations seen on
controlled-source multichannel seismic records. Park et al. (1998) applied the p-f technique to active-source MASW records. All phases in the
record are present in the resulting (p-f) image that shows the power at each combination of phase slowness and frequency. Dispersive phases
show the distinct curve of normal modes in low-velocity surface layers: sloping down from high phase velocities (low slowness) at low
frequencies, to lower phase velocities (high slowness) at higher frequencies. Miller et al. (2000) examine p-f-domain power spectra of MASW
records along a profile to define lateral variations in dispersion curves and thus in shear velocities.
The distinctive slope of dispersive waves is a real advantage of the p-f analysis. Other arrivals that appear in microtremor records, such as body
waves and air waves, cannot have such a slope. The p-f spectral power image will show where such waves have significant energy. Even if most
of the energy in a seismic record is a phase other than Rayleigh waves, the p-f analysis will separate that energy in the slowness-frequency plot
away from the dispersion curves this technique interprets. By recording many channels, retaining complete vertical seismograms, and employing
the p-f transform, this method can successfully analyze Rayleigh dispersion where SASW techniques cannot.
Rayleigh Phase-Velocity Dispersion Picking
This analysis adds only a spectral power-ratio calculation to McMechan and Yedlin's (1981) technique, for spectral normalization of the noise
records. The average power over all the slownesses may be orders of magnitude different from one frequency to another. This method takes the
spectral ratio R(|p|,f) of the power at each slowness-frequency combination against the average power across all slownesses at that frequency in
individual p-f images SA(|p|,f), or in a summed image Stotal(|p|,f).
R(|p|,f) = S(|p|,f) np / [
∑
j=0,np-1 S(|p|=l dp, f) ] (8)
(with np being half of the original number of slowness steps 2np ). In most cases the resulting spectral-ratio image shows maxima clearly
aligned along a dispersion curve.
The ability to pick and interpret dispersion curves directly from the p-f images of spectral ratio parallels the coherence checks in the SASW
technique (Nazarian and Stokoe, 1984) and the power criterion in the MASW technique (Park et al., 1999). Picking phase velocities at the
frequencies where a slope or a peak in spectral ratio clearly locates the dispersion curve. Picks are not made at frequencies without a definite peak
in spectral ratio, often below 4 Hz and above 14 Hz where an identifiable dispersive surface wave does not appear. Often, the p-f image directly
shows the average velocity to 30 meters depth, from the phase velocity of a strong peak ratio appearing at 4 Hz, for soft sites, or nearer to 8 Hz,
at harder sites.
Avoiding high apparent velocities - The use of linear geophone arrays in this technique means that an interpreter cannot just pick the phase
velocity of the largest spectral ratio at each frequency as a dispersion curve, as MASW analyses effectively do. An interpreter must try to pick the
lower edge of the lowest-velocity but still reasonable peak ratio. Since the arrays are linear and do not record an on-line triggered source, some
noise energy will arrive obliquely and appear on the slowness-frequency images as peaks at apparent velocities Va higher than the real in-line
phase velocity v:
Va = v/cos(a) = 1/p (9)
or: a = cos -1 (vp) (10)
with a being the propagation angle off the line direction.
The highly nonlinear relationship between a and p works in favor of interpreting accurate slowness (and velocity) from the appearance of wave
energy in the S(|p|,f) or R(|p|,f) images. Energy within the images is arranged according to linear slowness p. Table 2 shows how energy
arriving from different azimuthal angle a ranges will appear on a linear slowness p axis.
(table 2 here)
Each range of propagation angle a in the center column of table 2 is the range within each of the four quadrants of the circle. Arrivals from
azimuths a, -a , 180°-a , and 180°+a will all be summed into the same |p| trace of the S(|p|,f) spectral-power image.
Assuming horizontally-propagating energy arrives equally from all directions, table 2 shows that 40.9% of the energy will be slantstacked into
the p slowness traces that have 80-100% of the true slowness 1/v . In other words, 40.9% of the energy will appear at an apparent velocity Va
= 1/p that is less than 1/0.80 = 125% of the true phase velocity. The rest of the energy is smeared thinly over the lower slowness ranges. Thus,
at a particular frequency f within an S(|p|,f) or R(|p|,f) image, this technique tries to pick the phase velocity at the largest slowness |p| (or
smallest velocity) at which significant energy appears. Picking is done along a ``lowest-velocity envelope'' bounding the energy appearing in the
R(|p|,f) image.
It is possible to pick this lowest-velocity envelope in a way that puts confidence limits on the phase velocities, as well as on the inverted velocity
profile. Making three picks at each frequency accomplishes this: first at a low phase velocity where the spectral ratio just begins to depart from the
low ratios of incoherent noise; second at a ``best guess'' velocity where the ratio is rising steeply or has just leveled out; and third at a high
velocity atop a spectral-ratio peak, which may be centered on an apparent velocity above the true phase velocity.
In crucial parts of the p-f images in the examples detailed below, use of the discretized slowness values dp results in only 10% velocity change
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f
rom one constant-s
l
owness row to t
h
e next.
S
o one row can
i
nc
l
u
d
e az
i
mut
h
s
30°
away
f
rom t
h
e
li
ne
di
rect
i
on
(
as at t
h
e
b
ottom o
f
ta
bl
e
2)
,
summing all energy arriving from nearly one-third of the full azimuthal circle. The remaining two-thirds is spread much more widely in slowness
above the minimum-velocity envelope on the p-f image.
Picking a surface-wave dispersion curve along an envelope of the lowest phase velocities having high spectral ratio at each frequency has a
further desirable effect. Since higher-mode Rayleigh waves have phase velocities above those of the fundamental mode, the refraction
microtremor technique preferentially yields the fundamental-mode velocities. Higher modes may appear as separate dispersion trends on the p-f
images, if they are nearly as energetic as the fundamental. Noticeable higher modes have appeared on the p-f analysis of an explosion refraction
survey shot on a shallow, dipping pediment surface with a 2:1 velocity contrast (not shown).
Spatial aliasing will contribute to artifacts in the slowness-frequency spectral-ratio images. The artifacts slope on the p-f images in a direction
opposite to normal-mode dispersion. The p-tau transform is done in the space and time domain, however, so even the aliased frequencies
preserve some information. The seismic waves are not continuously harmonic, but arrive in groups. Further, the refraction microtremor analysis
has not just two seismograms, but 12 or more, so severe slowness wraparound does not occur until well above the spatial Nyquist frequency,
about twice the Nyquist in most cases.
Shear-Velocity Modeling
The refraction microtremor method interactively forward-models the normal-mode dispersion data picked from the p-f images with a code adapted
from Saito (1979, 1988) in 1992 by Yuehua Zeng. This code produces results identical to those of the forward-modeling codes used by Iwata et
al. (1998), and by Xia et al. (1999) within their inversion procedure. The modeling iterates on phase velocity at each period (or frequency),
reports when a solution has not been found within the iteration parameters, and can model velocity reversals with depth.
A graphical model-adjustment capability implemented around the modeling code allows rapid fitting of dispersion curves while adjusting the
model with a computer mouse. This strategy results in quick testing of what model features are constrained by the dispersion-curve picks, and
what depth-velocity trade-offs may exist. An interpreter can also interactively estimate the maximum depth of velocity constraint, and whether the
data might rule out high-velocity transitions just below this depth. Because the refraction microtremor method does not rely on an inversion of
dispersion picks for velocity structure, the forward-modeling part of the technique is the most dependent on the interpreter's skill and experience.
One way to lessen the modeling's dependence on the interpreter is to estimate the confidence limits of the velocity profile resulting from
modeling, by developing two models that fit the dispersion picks equally well. Shear-velocity profiles determined from dispersion picks are
highly non-unique, and the interpreter should try to find at least two canonically different models giving the same dispersion curve. This
approach is taken at the Reno site, below. However, defining canonical velocity profiles may be troublesome in engineering practice.
The interactive forward-modeling of a dispersion curve by an experienced practitioner can yield more information about velocity constraints on a
site than can an automated inversion procedure, such as that of Xia et al. (1999). The interactive modeling can avoid local minima in the objective
error function that often result in false velocity inversions with depth, due to the equivalence problem that is inherent in the integrative nature of
surface-wave velocities. Automatic inversions may be very effective in showing lateral variations along a profile, as in Miller et al. (2000), but
often show oscillatory velocity anomalies that have artificially large magnitude.
In geophysical exploration work using other integrative fields such as gravity, magnetics, and resistivity, problems with automated inversions
exaggerating anomalies have led to the widespread current practice of interactive forward modeling. Microtremor analysis done by Liu et al.
(2000) completely avoids modeling of picked dispersions, by simply comparing array dispersion data against dispersions forward modeled from
borehole data. The interactive forward modeling of dispersion curves, though, is no slower than inversion procedures, and allows the fitting of a
simple model in less than a minute using popular computer platforms. The main difficulty with interactive modeling is to reduce the process of
testing hypotheses and estimating confidence limits to a set of practical procedures that will not require extensive re-training by practitioners.
A simple method, more independent of the observer than developing a set of canonical models, is to fit models to the high- and low-velocity
confidence limits of the dispersion picks. This procedure will produce extremal velocity profiles at the limits of the velocity range allowed by the
dispersion data, a technique discussed for the Reno and Newhall examples below. With 95-99% of the minimum-velocity energy in the p-f
images usually falling between the picked velocity extremes, there is similar confidence in the velocity ranges produced.
If higher-mode Rayleigh dispersion picks have been made, those can be modeled as well with the codes employed here. Another possible
problem is the lack of information on P-wave velocities or densities in modeling Rayleigh dispersion curves. All of the modeling done to date has
assumed a Poisson's ratio of 0.25, which is often far from the truth in shallow soils. Experimentation with the interactive modeling tool suggests
that even huge changes in Poisson's ratio or density will only change modeled shear velocities by less than 10% in the process of fitting
Rayleigh-wave velocity spectra. Lay and Wallace (1995, p. 122) show that the Rayleigh phase velocity in a half space will change only from
89% to 95% of the shear velocity, as Poisson's ratio ranges from 0.1 to 0.4.
These factors suggest that Rayleigh dispersion curves are good indicators of shear-velocity structure and poor indicators of shallow P-velocity
structure. A Jacobian analysis of Rayleigh dispersion inversion by Xia et al. (1999) supports this suggestion. Liu et al. (2000) also maintain that
Rayleigh phase-velocity measurements can only constrain shear velocity. Since the refraction microtremor method uses essentially phase
information from multichannel seismic recordings to estimate surface-wave phase velocities, determination of near-surface shear velocities is an
attainable goal.
Results
Described here in detail are two tests of the refraction microtremor technique, done at locations where the most definitive corroborating data exist.
The first test was against a more traditional accelerometer microtremor array (as in Horike, 1985; or Liu et al., 2000) in Reno, Nevada. The
second test was against the shear-velocity suspension log of a 100-m-deep borehole in Newhall, California. Described in less detail below will be
the application of this technique at eight other locations in Wellington, New Zealand, and in southern California. This p-f analysis technique has
also been applied extensively to explosion refraction records.
In all trials the method has produced reasonable shear-velocity results to 50-150 m depth, in good agreement with all available data. However, the
two cases discussed first are those for which the best shear-velocity data from independent measurements were available. They were effectively
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bli
n
d
pre
di
ct
i
on tests, as was t
h
e wor
k
o
f
L
i
u et a
l
.
(2000)
, s
i
nce t
h
e
i
n
d
epen
d
ent
d
ata were not exam
i
ne
d
b
e
f
ore re
f
ract
i
on m
i
crotremor resu
l
ts
were developed. True blind prediction has not been attempted, however, since that would require drilling and logging of a borehole only after
refraction microtremor results had been published.
Tests Against a Microtremor Accelerometer Array in Reno, Nevada
On 22 July 1997, and 18 Oct. 2000, University of Nevada, Reno staff and students performed linear refraction array recording tests on the
property of the Reno/Tahoe International Airport, at the southwest corner of Rock Blvd. and Mill Street in Reno, Nevada (figure 1). The site is
next to the north end of the airport's main runways, and about 1 km north of a site at which the UNR Seismological Lab made recordings of
aftershocks of the Sept. 12, 1994 Double Spring Flat event (Ni et al., 1995). The site is bladed soil and gravel fill, covered by organic materials
and silt deposited by a major Truckee River flood in January 1997. The site is about 300 m south of the river.
In the 1997 test two arrays of 24 8-Hz geophones spaced at 15.24 m were spread out in approximately W-E and N-S directions from the
intersection. Each geophone was planted in a hole 10 cm deep, covered with soil, and tamped lightly. The several 48-second noise records
recorded by the Bison Galileo-21 had a 4 ms sampling interval and a 60 dB pre-amplifier gain. Fieldwork for that test required more than 8
person-hours, because of the use of 48 channels over a 720 m total array length.
The 2000 test placed one N-S array of 15 RefTek RT-125 ``Texan'' recorders, with 24-bit fixed-point digitizers and 4.5-Hz geophones (figure
1). The geophones were spaced at 20 m for an overall array length of 280 m. Geophone plants were similar, and five 50-second noise records
were taken. Fieldwork for that test required only 4 person-hours.
Wave sources - One of the records triggered in 1997 was at the time of an approximately 3,000 kg ripple-fired excavation blast 16 km to the
south. Synchronizing watches over a cell phone link with an observer at the Caithness site provided timing to ±2 seconds. The N-S channel 1-18
section of the array (figure 1) pointed within 10° of the direction of the blast site. This record also used a high 60 dB pre-amplifier gain.
During both deployments traffic was heavy through the adjacent major intersection, and included all types of light and heavy vehicles. Vehicle
speeds up to 20 m/s can be identified on the records (not shown). In addition, the touchdown point of frequently landing Boeing 727 and 737
aircraft was only about 300-500 m distant. Some of the 1997 records were triggered to include aircraft landing and taking off (when the
low-frequency engine rumble was loud). A 1.5-meter-deep irrigation ditch was flowing vigorously at the site, less than 5 m from the 1997 W-E
channels 25-36 (figure 1). A transcontinental freight rail line and Interstate Highway 80 are also <500 m north of the array.
Most of the energy in the 1997 microtremor records, appears between 2 and 10 Hz, with the peak at 4.7 Hz. This result is surprising; considering
the 8 Hz resonant frequency of the Mark Products geophones used, and the expected rapid decrease in their response at lower frequencies. It is
consistent, however, with the low-frequency cluster test discussed above, and required the use of a high 60 dB pre-amplifier gain. The 2000
records using 4.5-Hz instruments recorded significant energy between 2.5 and 5.5 Hz, but most energy between 8 and 20 Hz.
The 1997 deployment included sledgehammer refraction records taken from the intersection of the two 24-channel arrays. The high level of noise
at this site together with the long spacing between geophones made the refraction times extremely difficult to pick. The only conclusion that can
be made from them is that the average P velocity to 30 m depth is 890±200 m/s.
(figure 1 here)
Analysis - Figure 2a shows results from the p-tau and Fourier transformation of five 48-second noise records on the 1997 8-Hz refraction
arrays, including the record from the 16-km-distant blast. Higher spectral ratios are darker in the images. Figure 2a shows dispersion p-f picks
and slowness errors. That case, as explained below, used picks on the centers of spectral-ratio peaks. The errors represent the ranges of
slowness within which the spectral-ratio peaks have a 95% chance of occurring. Each peak can be regarded as a Gaussian curve of relative power
against frequaency, so the error bars cover the range where the spectral ratio is significantly elevated above the background. Note that the error
bars must be at least two slowness rows in height on the p-f image, for a minimum slowness uncertainty of ±0.213 s/km. Since the vertical axis
of the p-f plot is linear in slowness and nonlinear in velocity, the interpreted velocity error will be small for low-velocity picks and can be very
large for high-velocity picks. The picks above 16 Hz have additional uncertainty.
Figure 2b shows the summed p-f power-ratio image from the five 4.5-Hz records taken in 2000. This image has less clear power-ratio peaking
than the 8-Hz records image. It resembles more the concentration of power ratio along the lowest-velocity envelope, with energy smeared along
higher velocities as demonstrated in table 2. Note that both the 8-Hz and 4.5-Hz p-f images (figures 2a and 2b) have a distinct peak at a high
apparent velocity at 6 Hz, labeled Va. At about 40% of maximum slowness, table 2 suggests the source of that peak will be found at an angle a
of 60° from the array trend. Iwata et al. (1998) saw energy arriving from the same azimuth and interpreted it as coming from the Interstate 80-US
395 freeway interchange 3 km distant. As a result figure 2b is picked along a lowest-velocity envelope, with three picks at each frequency. As
described above, one is at the first rise of spectral ratio over the background at lower apparent velocities; the central pick is at the maximum slope
in ratio versus slowness; and the third is atop a ratio peak. Clearly it was much more difficult to make picks below 3 Hz or above 15 Hz.
The normal-mode dispersion, down to the right, is clear on both p-f images below the aliasing or Nyquist frequency (left of the heavy dots),
where an F-K analysis such as Liu et al. (2000) would be spatially aliased. In the 1997 data from 8-Hz sensors (figure 2a) a spectral-ratio peak
can be interpreted at frequencies as low as 3 Hz, but not below. In the 2000 data from 4.5-Hz sensors (figure 2b), both ratio peaks and the
lowest-velocity envelope are clear down to 2.5 Hz, and the figure shows the less clear dispersion picks down to just below 2 Hz. The 4.5-Hz
data allows picks to be made at each frequency column between 2 and 5.5 Hz, which much improves the low-frequency interpretation over that
from the 8-Hz sensors.
Above the Nyquist frequencies the picks also have larger slowness uncertainties. The trend of spectral-ratio peaks continues downward to the
right, suggesting the typical surface-wave dispersion to lower velocities at higher frequencies. Spectral-ratio peaks trend up to 26 Hz in the
analysis of 8-Hz data (figure 2a), and up to 16 Hz in the 4.5-Hz data (figure 2b). The refraction microtremor technique's p-f transform never
applies a Fourier transform to the spatial x axis. Thus, the images show that some information can be recovered at high frequencies where F-K
analyses would fail.
The strongest peaks of spectral ratio are at 12 Hz in figure 2a and 10 Hz in figure 2b. These peaks arise from waves that are spatially truncated by
the edges of the arrays. The truncation leaves the smeared and frequency-shifted artifacts that arch up and to the right in both images, essentially
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art
if
acts o
f
t
h
e p-tau trans
f
orm
(
equat
i
ons
1
an
d
2)
. Frequency wraparoun
d
smears t
h
e
hi
g
h
-spectra
l
rat
i
o po
i
nts
i
n
b
ot
h
p
l
ots su
b
-para
ll
e
l
to t
h
e
dotted Nyquist curves. Clearly, however, these artifacts slope down to the left on the p-f plots and do not interfere with picking normal-mode
dispersion trends.
In the areas of the p-f plots that would be aliased in an F-K analysis, the slantstack is still sensitive to the energy concentration of the group
arrival across 12 or more traces in the record. This factor keeps the velocity range of the aliased, smeared peaks limited. The frequency
wraparound and smearing show the frequency shift error of the peaks. These shifts do not extend beyond the limited shifts of the strong group
arrival on figure 2a at 12 Hz, or on figure 2b at 10 Hz. In this way, picks from the aliased areas of the velocity spectral plots could have 4-8 Hz
of frequency error, up to 25%.
Examination of the 1997 raw blast record after 0-5 Hz low-pass filtering (not shown) identified surface wave arrivals with a 0.43±0.03 km/s
group velocity and 0.86 to 1.3 km/s phase velocity. These arrivals are not clearly separable in figure 2a, although they contribute to a smear of
moderately high spectral ratios at 6 Hz and below.
(figure 2 here)
Apparent phase velocities - Figure 2a includes the spectral sum of four noise records and the 16-km distant blast record. The minimum apparent
velocity, or true phase velocity, of the dispersed surface wave sums well. The sum included both the E-W and N-S parts of the arrays, showing
the resulting coherence and preponderance of waves travelling near the true velocities. On both p-f images, Va labels a significant spectral-ratio
peak that does not contribute to the minimum-velocity interpretation. But the Va peaks do not interfere with making the correct interpretation.
If one assumes an even distribution of energy arriving from all directions, over all these 48-second records, then table 2 makes clear the reason
for the coherent summation at the true velocity. The non-linearity of the cosine that divides the real velocity to produce the apparent velocity
allows a third of the energy from many random directions to contribute to the observed peak, no more than 20% higher than the true velocity. The
remaining two-thirds is spread much more widely in slowness, and is visible in figures 2a and 2b as a background of slightly higher spectral
ratios, at velocities above the true dispersion curve. With the summing of spectra from records of two perpendicular linear arrays in figure 2a, the
non-linear concentration of energy toward the true velocities on the p-f image is even more pronounced.
The superimposed line on figure 2a traces the dispersion trend from 0.50 km/s at 4 Hz down to 0.25 km/s at 26 Hz. The slowness accuracy of
this trend appears to be about the slowness sample interval of the p-tau transform (0.213 s/km in that image). Thus at the low-velocity end the
phase-velocity estimates should be accurate to within ±0.015 km/s. Frequency accuracy within this plot is not as good as the frequency sampling,
but can be ±0.25 Hz or better, in picking spectral-ratio peaks outside the aliased area.
Velocity modeling - Figure 2c graphs the picked dispersions, error bars, and extremal picks from both p-f images. It also shows the fits within
the errors and extremes of synthetic dispersion curves from the models in figure 2d. Extensive interactive testing with the forward-modeling
application shows that picks constrain the 0-9 m depth shear velocity very well at 0.28 km/s, the 9-40 m depth at 0.52 km/s, as well as the 9 and
40 m depths of the velocity increases. The 0.68 km/s velocity below 40 m can trade off against the depth and velocity of the deeper interface at
77-156 m (figure 2d). The aliasing and resulting frequency shifts of the picks above 12 Hz do not have a significant effect on the modeling.
The picks from the 8-Hz-sensor data, at 4 Hz minimum frequency, cannot constrain velocity below 75 m depth. The interpreter, in the absence of
other data, placed a 1.55 km/s layer at 77 m depth. The picks from the 4.5-Hz-sensor data extend down to 2 Hz, allowing the interpreter to place
a higher-velocity 1.98 km/s interface deeper, at 156 m. Thus using lower-frequency sensors probably doubled the maximum depth of velocity
constraint, to about 150 m (question marks on figure 2d). In both cases, the higher phase velocities picked at the lower frequencies demand a
velocity increase at some depth below the depth of constraint. Being in essence depth-averaged velocities, the higher phase velocities constrain
the ratio of the depth and velocity, but not either one individually.
In modeling the dispersion-curve picks of figure 2c the interpreter attempted to develop canonically different models that fit the data equally well.
The differences in the two models presented in figure 2d is in the number of shallow layers and in the depth and velocity of the deepest layer. The
3-layer model presents an extreme hypothesis for the deepest layer, showing it at the minimum possible depth and minimum possible velocity.
Both the test models, plus the models fitting the extremal picks, fit to nearly the same velocity at 9-77 m depths, and also give a narrow velocity
range for the shallowest 0-9 m layer. The 3- and 4-layer models have almost identical average velocities for the 0-30 m depth range, of 456 and
448 m/s, respectively.
Comparison with accelerometer results - In December 1997 colleagues from Shimizu Corp. and Kyoto and Kobe Universities tested at the
Reno/Tahoe Airport site a nested-triangle array of seven 1-Hz, 3-component accelerometers. This is the type of accelerometer array they have
deployed for microtremor noise recording in Japan and California (for example: Satoh et al., 1997), and is almost identical to the techniques of
Liu et al. (2000). They recorded both 100-m and 1-km-aperture arrays at the Reno/Tahoe Airport site (figure 1).
Each seismometer recorded independently, with timing provided by GPS clocks, so distributing the array over an area of several blocks was not
difficult. Setting out each receiver, however, required a painstaking leveling process, as the 1-Hz accelerometers are far more sensitive to leveling
errors than are the velocity sensors of the refraction equipment. The fieldwork for each array required more than 10 person-hours, and used
custom equipment costing more than $100,000.
Iwata et al. (1998) showed the results of their analysis for the Airport site. They analyzed only vertical-component noise records. Total recorded
time was about one hour; certain slices of their data several minutes long yielded good results in their moving-window F-K domain analysis (very
like the analysis presented by Liu et al. (2000). The frequency range of their phase velocity estimates (figure 3) overlaps that of the refraction
experiments (from figure 2) between 2 and 7 Hz. At 3 Hz they determined a 0.475±0.05 km/s velocity, and at 7 Hz it was 0.45±0.02 km/s.
From figure 2a, the 8-Hz-sensor refraction microtremor pick at 4 Hz agrees with their results at 0.47 km/s (figure 3). From figure 2b, the
4.5-Hz-sensor refraction microtremor pick is higher at 0.51 km/s, with extremes at 0.46 and 0.60 km/s. At 8 Hz, the refraction microtremor
picks are at 0.42±0.02 km/s. The lack of lower-frequency data prevents comparison against their results below 2 Hz. The data of interest for the
prediction of shallow site amplification, from 4 Hz and up, are virtually identical.
Because of the close spacing and large number of channels allowed by the refraction equipment, it produces surface-wave dispersion most easily
interpreted between about 7 and 16 Hz, as figure 2 shows. The modeling in figures 2c and 2d suggested that this range puts good constraints on
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s
h
ear ve
l
oc
i
t
i
es w
i
t
hi
n 7
5
m o
f
t
h
e sur
f
ace. D
i
spers
i
on
i
s o
f
ten
i
nterpreta
bl
e
i
n t
h
e p-
f
resu
l
ts at
hi
g
h
er
f
requenc
i
es w
h
ere an F-K ana
l
ys
i
s
i
s
impossible due to spatial aliasing. The refraction equipment could more accurately assess shear velocity at very shallow 1-10 m depths, while the
2-d array of 1 Hz instruments was needed to estimate the velocity profile from 100 m to 1 km depth.
The amplification analysis of Ni et al. (1995), based on a nearby 30-m-deep acoustic log and weak-motion records, suggests similar shallow
velocities, with modeled dispersion curves matching those of Iwata et al. (1998) above 3 Hz. Gravity work across the Reno basin by Abbott and
Louie (2000a) shows a depth to andesite basement at the Reno Airport site of 400 m. Nearby water wells penetrating 200-300 m make it unlikely
that the 77-156 m interface could be basement. It is more likely the base of Quaternary alluvium and the top of a Miocene-Pliocene diatomaceous
sandstone that underlies the entire basin (Abbott and Louie, 2000a). Shallow models from noise recorded on refraction equipment could not
derive basin sediment thickness here, although the lower-frequency accelerometer data of Iwata et al. (1998) could do so.
(figure 3 here)
Test at the ROSRINE Borehole in Newhall, California
On Sept. 13, 1996 the Resolution of Site Response Issues from the Northridge Earthquake (ROSRINE) project (http://geoinfo.usc.edu/rosrine;
Nigbor et al., 1997) collected an OYO suspension P- and S-wave velocity log at the Los Angeles County Fire Station in Newhall, Calif. In Feb.
2000, with sponsorship from the Southern California Earthquake Center, and assistance from Los Angeles County Fire Dept. personnel and the
County Flood Control District, University of Nevada, Reno staff located the site of the ROSRINE borehole and performed refraction and
microtremor experiments.
The refraction microtremor experiment employed a 200-m-long array of 24 8-Hz refraction geophones along the asphalt-paved access road at the
side of a 4-m-deep concrete-lined flood channel. The 200 m array was centered 4 m from the ROSRINE hole. Noise records 30 and 60 seconds
long and a reversed sledgehammer refraction profile were recorded. A 10-second section of the first noise record taken appears in figure 4a.
Using the same equipment as with the 8-Hz Reno/Tahoe Airport deployment, the microtremor fieldwork in Newhall required less than 6
person-hours, with a field crew of three. Time at the site was extended, however, by rain showers, recording of a large number of noise records,
and by the hammer refraction recording.
Noise sources - This part of Newhall is densely suburban, with heavily trafficked streets only 100-200 m apart, and fully built up. San Fernando
Road, a six-lane artery, is only 75 m from the array. Frequent commuter trains were running 100 m away. The raw microtremor record in figure
4a shows identifiable Rayleigh groups with 100-200 m/s velocities, at a relatively high frequency of 18 Hz. The surface wave marked on figure
4a, one example of the many present, probably originated close to the array. The lower-frequency microtremor is not easily seen in the figure,
which includes frequencies up to 20 Hz.
(figure 4 here)
Analysis - For the Newhall example just the analysis of the first 30-second noise record taken is shown here. If the refraction microtremor
techniques can be sufficiently accurate on just one record, then prolonged field recording efforts are not needed. The p-f analysis of this
30-second noise record is figure 4b. From 3-12 Hz, the p-f image shows a clear energy cutoff at a minimum-velocity envelope. The energy of
obliquely-propagating waves is broadly distributed across high apparent velocities above this envelope. Arrivals at many different apparent
velocities form a broad ramp in spectral ratio, but the cutoff of high spectral-ratio values against the true phase-velocity envelope is clear from
3-12 Hz (as shown by table 2). At frequencies below 3 Hz, and in the area of F-K aliasing, this envelope is not as clear. There are a few
spectral-ratio peaks in these areas still aligned with the dispersion envelope.
The dispersion picks follow the lowest-velocity envelope at the base of the high spectral ratios in the image (figure 4b). The area of pick
confidence is between the lowest velocity where spectral ratios rise above those of uncorrelated noise (white in figure 4b) and the higher velocity
at the top of the ratio peak (black in figure 4b). The ``best pick'' was made within this range where the ratio slope is steepest, as for the Reno
4.5-Hz data in figure 2b. The three phase-velocity values at one frequency constitute the dispersion pick (filled squares in figure 4c) and its
uncertainty within extremal values (open squares in figure 4c). Dispersion picking is possible where an F-K analysis would spatially alias (right
of the thick dashed line in figure 4b), although the p-f artifacts produce larger uncertainties there.
Velocity modeling - Figure 4c shows just the dispersion curve with increasing uncertainty at larger periods, interactively modeled with the
velocity profile of figure 4d (bold line). The modeled profile is an excellent match to the ROSRINE logged shear velocity (thick gray line). The
8-m-thick shallowest layer with 210 m/s shear velocity compares well with the log, which starts at 2 m depth and varies from 178-238 m/s to 8 m
depth. The 370 m/s modeled layer from 8-34 m depth averages across a strong gradient in the log from 219-685 m/s over the same depth range.
Below 34 m, the shear-velocity log has about 10% variability with a standard deviation of 77 m/s, but maintains to the 105.2 m maximum logged
depth a 741 m/s average. The 34-125-m-depth model layer has a velocity of 620 m/s, which is just 16% low.
The bias of the interactive modeling process toward fewer layers 7-100 m thick is clear in this comparison. Since the phase-velocity dispersion
data effectively integrate velocities over substantial depth ranges, modeling results could never match the detail of the shear-velocity log. In the
log velocities can change by 30% over a few meters. This lack of detail in the modeled velocity profile is no impediment to site-response
evaluation, however. The amplification of earthquake waves by site conditions is also an integrative process. As long as the velocity results are
accurate in terms of averages over 5-100 m depth ranges, accurate prediction of linear site amplification effects is assured (Borcherdt and
Glassmoyer, 1992; Boore and Brown, 1998; Brown, 1998).
The uncertain longest-period picks of the dispersion curve (figure 4c) suggest a velocity increase at an interface below the 100 m maximum
logged depth (question mark in figure 4d). However, the low-frequency dispersion picks cannot control the trade-off between the depth and
velocity of this interface. Experimentation shows that many models could match the dispersions in figure 4c. Both the depth and the velocity of
the deepest layer are highly non-unique, and very poorly determined at this site by the dispersions down only to 2 Hz. In this case, at least the
ROSRINE log shows that the interface is deeper than 100 m. This fact suggests the refraction microtremor method could estimate velocity
accurately to 100 m at this site.
The Newhall example demonstrates a simpler method of finding velocity constraints than that used for the Reno site. Developing a set of
canonical models, essentially independent geological hypotheses, is too time-consuming for practical use. Modeling a single dispersion curve
with the interactive tool is still a task that relies on some training, and tutorial exercises have been written to teach undergraduates how to perform
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t
h
e mo
d
e
li
ng e
ff
ect
i
ve
l
y.
A ``top-down'' approach is most effective, matching phase velocities with layer velocity adjustments, starting at the surface layer (e.g. fitting the
picks on figure 4c below 0.1 second period first). Cusps and increases in slope of the dispersion curve (as at 0.12 s, 0.25 s, and 0.45 s in figure
4c) are matched by adjusting layer thicknesses. Following such a procedure, it is possible to model velocities in about one minute, since only a
small number of layers is used.
Here the extremal velocity limits are found by fitting not only the ``best picks'' (filled boxes on figure 4c) but also, separately, the
highest-velocity picks, and the lowest-velocity picks of the confidence limits (open squares on figure 4c). This procedure results in three models,
one central and two that represent the upper and lower-velocity extremes of confidence in the pick of the central model. The thin lines on figure
4d show the velocity profiles that result from this procedure. For the poorly constrained deepest layer (question mark on figure 4d) the minimum
extremal model had the same velocity as the central model, while the maximum extremal model had a velocity of 3.5 km/s, off the plot. For these
data adjustment of layer thicknesses was not necessary in the process of creating the extremal models.
P-wave refraction results - The refraction experiments conducted at Newhall show a shallow P-wave velocity of 328-408 m/s. At 23 m depth the
P-wave velocity increases to 970 m/s (thin black line in figure 4d). These values also agree well with the OYO suspension P-velocity log (thin
gray line in figure 4d). Naturally a simple refraction interpretation cannot yield the detail of the suspension log. But the velocities and refractor
depth agree well with the log, especially the steep velocity gradient in the log from 26 to 34 m depth.
Both the 23-m-deep P-wave refractor and the 34-m-deep increase in shear velocity may represent the same interface, possibly a transition to more
consolidated or clay-rich Quaternary alluvium. The interface is seen as both P- and S-wave velocity gradients over the 23-34 m depth range in the
logs. The 11 m mismatch in depth between the refraction and shear-velocity modeling could be eliminated by biasing the refraction interpretation
within its confidence limits, or by inserting another layer into the shear-velocity model. First arrivals from 50 stacked hammer blows could only
be seen to 130 m distances in this noisy area. As a result, the refraction data were not sensitive to either the logged P-velocity increase at 60 m
depth, or the bottom of Quaternary sediments at 125 m (or deeper) interpreted from the Rayleigh dispersion.
Stability of data and analysis - The record analyzed above in figure 4 is only the first of 14 noise records taken at the Newhall site. The
experiment recorded 10 records 30 seconds long, 5 with 2 ms sampling and 5 with 1 ms sampling. Four additional records were 60 s long, with
1 ms time sampling. Summed p-f images were computed of the five 2-ms-sampled 30 s records, of the five 1-ms sampled 30 s records, and of
the four 60 s records. The p-f images are very similar to the single-record image, except for the increased concentration of energy close to the true
phase velocity as was seen in the Reno summed-record analysis.
Each summed p-f image was picked independently. The picks all agree well with the single-record picks of figure 4c, with two exceptions. The
summed-record picks show phase velocities 15% to 30% higher than the single-record picks between periods of 0.3 and 0.42 s. This is the
period range most sensitive to the velocity of the 34-125-m-deep layer, which was 16% slower in the single-record analysis than in the
shear-velocity log. Modeling the picks from this summed-record p-f image gave the layer a 707 m/s velocity, only 5% lower than the 741 m/s
average in the log.
The other exception arose in trying to alter how one of the summed-record p-f images was picked. The five 30 s records with 1 ms sampling
produced a p-f image that seemed more distinctly peaked along the true-velocity dispersion curve than the other images. Accordingly it was
picked not along the low-velocity envelope but atop the center of its spectral-ratio peaks (not shown). At periods between 0.22 and 0.38 s, this
procedure yielded phase velocities that were up to two times larger than the velocities picked from all other Newhall p-f images. Fitting the ``best
picks'' at the ratio peaks yielded a velocity for the 34-125-m-deep layer of 993 m/s, 34% higher than the 741 m/s average of the shear-velocity
log for that depth range. For a randomly oriented single, straight-line noise array, picking the lowest-velocity envelope appears to be the most
accurate procedure.
Extremal models matching the dispersion-envelope pick confidence limits show high confidence that modeling has estimated velocities to 100 m
depth with 15% accuracy at Newhall, comparable to the total variability of the logged shear velocity over 5 m depth ranges. Rayleigh
phase-velocity dispersion modeling matches the logged shear velocity despite a significant increase in Poisson's ratio at 50 m depth. With the
match to logged velocities shown in figure 4, the cheap and rapid linear-array microtremor technique promises almost the depth and velocity
resolution of the SASW and MASW techniques, but at lower cost since no artificial energy source is needed.
Additional Tests
Wellington, New Zealand - Ground-shaking hazard assessments have been underway for some years in New Zealand's Wellington metropolitan
area (e.g.: Van Dissen et al., 1992). Geotechnical surveys of shear-velocity profiles have only taken place in two suburbs underlain by
particularly soft sediments, known as Parkway and Porirua. In the Parkway suburb, Duggan (1997) conducted gravity and triggered-source
seismic-refraction and reflection surveys, but not noise recordings. These techniques revealed 75 m of low-velocity lacustrine sediments
overlying Mesozoic greywacke basement. Yu and Taber (1998) recorded noise and local events on a temporary network of 24 1-Hz stations
about 0.5 km across. Barker (1996) made seismic cone-penetrometer profiles at 3 sites in Parkway. Sutherland and Logan (1998) provide shear
velocities to 20 m depth from SASW surveys from a site in Parkway.
Figure 5 compares a model developed from p-f analysis of noise records from Yu and Taber's (1998) 0.5 km array of 1 Hz stations, against the
geotechnical results. Arranging the 12 soft-site stations available from the array with x distances appropriate for detecting waves propagating to
the north showed clear Rayleigh-wave dispersion between 1 and 5 Hz. The velocities fitting the dispersion give a 30-m average shear velocities
of 305 m/s, with a good match, at 90 m depth, to Duggan's (1997) 75 m basin depth from gravity and reflection.
Figure 5 also shows the SASW and seismic cone-penetrometer results (from Sutherland and Logan, 1998). Given the large aperture of the 1-Hz
array and the poor resolution of the refraction data, the microtremor result could not match the 17.5 m thickness of the low-velocity surface layer.
But the microtremor surface-layer velocities just below 200 m/s are a good match.
(figure 5 here)
Taber and Richardson (1992) reported the highest strong-motion amplification measurement from Wellington in its Seatoun suburb. Although
corroborating geotechnical measurements of velocity are not available from Seatoun, gravity measurements suggest a soft basin with 100 m
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max
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.
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,
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1999
.
Analysis of 16- and 32-second noise records taken during the arrival of a southerly storm, with winds to 90 km/hr reported elsewhere in the city,
yielded a clear dispersion curve from 22-10 Hz, with less clear but still interpretable dispersion from 10 Hz down to 4 Hz (not shown). Fitting
the dispersion picks with two alternative velocity models found the end members of the range of models that will fit the data. Both end-member
models agree with the prediction of 100 m basin depth by gravity (McLoughlin, 1998). The 30-m averaged shear velocities from the models
range from 300-324 m/s. Hammer refraction data taken before the arrival of the storm show a 30-m averaged P velocity of 1488 m/s. Despite the
low-rigidity condition of the Seatoun soils, the beach location guarantees their saturation with water. Thus, the P velocity could not be less than
about 1500 m/s.
With sponsorship by the Southern California Earthquake Center, refraction microtremor measurements have been made at six additional sites in
southern California. Most of these sites are on outcrops of hard rock hosting precariously balanced stones that have not been toppled by several
of the most recent magnitude 8 earthquakes on the nearby San Andreas fault (Brune, 1999). The measurements were made to quantify the amount
of de-amplification that could be assigned to the higher velocities of precarious-rock sites. As a result, these measurements have tested the
refraction microtremor technique across a very wide range of shallow velocity values. The linear-array noise recording technique, p-f analysis,
and dispersion modeling techniques detailed above all yielded well-constrained results at all six additional sites. The conclusions of the
earthquake-shaking study are presented elsewhere (Abbott and Louie, 2000b).
Being on hard rock, the additional six measurement sites are expected to be fast, but have not been drilled. Although they cannot be compared
against other shear-wave measurement techniques, as with Seatoun, a P-wave refraction result can be compared against the shear-wave modeling
result. Sledgehammer refraction data were recorded at all the sites, and analyzed for P velocity to 30 m depth using long-standing and simple
techniques.
Figure 6 compares the P-wave refraction result against the shear-velocity models at all ten sites discussed in this paper. Figure 6 only compares
30-m-depth average velocities. For the graph, P velocities were divided by the square root of three. Thus, if Poisson's ratio at a site is exactly
0.25, and the P-wave and shear-wave results agree perfectly, the site would plot on the 45° line angling up the middle of the graph.
In figure 6 the hard-rock sites seem consistent with higher Poisson's ratios, approaching 0.37. An alternative explanation would be that the
linear-array microtremor analysis is underestimating the higher shear velocities by up to 20%. The soft-rock and soil sites, including those in
Nevada, southern California, and New Zealand, all plot at a Poisson's ratio indistinguishable from 0.25 (or with less than 10% shear-velocity
error), except for Seatoun. That entirely water-saturated site cannot have a P velocity much below 1500 m/s, and so plots at a high, nearly fluid
Poisson's ratio. All the other sites are either in semi-arid regions, or have been drained to some degree by water wells, and are not entirely
saturated.
One way to interpret figure 6 is that it shows that the refraction microtremor method will produce shear velocities accurate to 20% across an
enormous range of velocity and Poisson's ratio. The technique is most accurate within 30 m of the surface, where most of the engineering
interest in site conditions lies. Refraction microtremor will go beyond 30 m depth, however, to produce useful constraints on shear velocity to
100 m depth at most sites.
(figure 6 here)
Conclusions
The ten sites described here are all those tested with refraction microtremor to date, for which a corroborating velocity estimate is available from
any other technique. Quiet rural sites (such as Piute Butte) do not yield refraction microtremor results as easily interpreted as results from noisy
urban sites. Despite this variation in quality, every data set collected with this technique has yielded interpretable velocities. No site has been
culled from the analysis here, and every data set collected has been analyzed.
The refraction microtremor method does not explicitly correct the apparent velocities of waves traveling obliquely to the array. Instead it relies on
the stacking of waves traveling in all directions, the greater precision of the array for velocities along its length, and a procedure for picking the
dispersion curve along a lowest-velocity envelope in the p-f images. This technique matched the shallower part of the results from microtremor
recording in Reno of the type originated by Horike (1985), and yielded better shear-velocity estimates within 30 m of the surface. Comparison of
these results against the shear-velocity log of the ROSRINE borehole at the Newhall County Fire Station proved the technique to be accurate,
matching the log to within 15%. Eight additional tests in southern California and New Zealand show the refraction microtremor technique can
quickly find the 30-m-average shear velocity to better than 20% accuracy.
These tests show that common seismic refraction equipment can yield accurate surface-wave dispersion information from microtremor noise.
Configurations of 12 to 48 single vertical, 8-12 Hz exploration geophones can give surface-wave phase velocities at frequencies as low as 2 Hz,
and as high as 26 Hz. This range is appropriate for constraining shear velocity profiles from the surface to 100 m depths. The heavy triggered
sources of seismic waves used by the SASW and MASW techniques to overcome noise are not needed, saving considerable survey effort. This
microtremor technique may be most fruitful, in fact, where noise is most severe. Proof of this technique suggests that rapid and very inexpensive
shear-velocity evaluations are now possible at the most heavily urbanized sites, and at sites within busy transportation corridors.
In addition, limited resources for earthquake-hazard evaluation can now be stretched to measure at three to ten times as many sites as was
possible in the past. A possible application of this method would be to gather large numbers of 100-m shear-velocity profiles across mapped soil
types used to predict regional shaking hazards (as by Borcherdt and Glassmoyer, 1992). Hazard classification schemes and hazard maps based
on soil mapping could be verified against the velocity profiles. In addition, the multiple velocity measurements for each soil type would contribute
a velocity variance to soil-type-based probabilistic seismic hazard mapping efforts.
Another possible application of this technique is that it is now possible to estimate shear velocities at one site for 10-30% of the cost of SASW,
MASW, borehole, or cone-penetrometer evaluations. In regions where the earthquake hazard or risk is not high enough to justify the cost of
existing methods for site evaluation, this technique will allow a quick and affordable site study. The refraction microtremor technique requires as
few as two person-hours, including all analysis, and equipmment with a capital cost now as low as $10,000 (for a 12-channel refraction system).
Even home builders might now be able to afford a shear-velocity evaluation at every home site. If engineers and builders find this technique
useful, seismologists can look forward to an explosion in the number of available shallow site characterizations.
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Acknowledgments
This research was supported in part by the U.S. Geological Survey National Earthquake Hazards Reduction Program under contract #NI17292,
with co-investigators J. G. Anderson, F. Su, and Y. Zeng; as well as by the Southern California Earthquake Center, with co-investigators R.
Anooshehpoor and J. Brune. The W. M. Keck Foundation generously donated the seismic refraction equipment to the Mackay School of Mines,
University of Nevada, Reno. Reftek 4.5-Hz ``Texan'' recorders and software were loaned by the IRIS/PASSCAL instrument center at New
Mexico Tech, with training provided by S. Azevedo. T. Iwata, H. Kawase, T. Satoh, Y. Kakehi, and K. Irikura of the DPRI, Kyoto University,
Kobe University, and Shimizu Corporation graciously made the accelerometer deployments, performed data analyses, and also helped support
the author's sabbatical research. Further crucial sabbatical assistance and collaboration were generously provided by E. Smith, M. Savage, J.
Taber, T. Haver, M. Robertson, and R. Neal of the Victoria University of Wellington, New Zealand. Refraction instruments were deployed in
Reno and southern California with valuable assistance from K. Smith, R. Anooshehpoor, R. E. Abbott, G. Ichinose, M. Herrick, M. Engle, A.
Pancha, J. Skalbeck, and C. Mann. Caithness Power Corp. and Mike Tyler of Cal-Neva Drilling And Blasting kindly provided timing
information on their 3000 kg construction blast. The Reno/Tahoe International Airport Authority generously provided access to the Reno site.
The Los Angeles County Flood Control District and the Los Angeles County Fire Station in Newhall were very helpful in providing access to the
ROSRINE site in Newhall, Calif.
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ut
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A
. J., an
d
Logan, T.
C
.,
1998
,
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W measurement
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or t
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f
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te amp
lifi
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Research Project 97/276: unpub. Central Laboratories Report 98-522422, Lower Hutt, New Zealand, 22 pp.
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Kapiti coast: Client report to Wellington Regional Council, New Zealand, 53 pp.
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Table 1: Low-Frequency Coherency Results from 8-Hz Geophones
Preamp Gain 0-5 Hz Filtered 0-25 Hz Filtered Raw
20 dB 32.1 ± 10.2% 94.4 ± 1.6% 92.2 ± 1.6%
40 dB 92.9 ± 2.2% 96.4 ± 3.4% 96.3 ± 3.3%
60 dB 97.8 ± 2.0% 97.2 ± 2.4% 96.6 ± 2.4%
Table 2: Angular Coverage of Slowness Intervals
Proportion of Inverse
Velocity vp, % Propagation Angle
a, degrees Coverage of 360°
Energy, %
0-10% 90.0°-84.2° 6.3%
10-20% 84.2°-78.4° 6.4%
20-30% 78.4°-72.5° 6.6%
30-40% 72.5°-66.4° 6.8%
40-50% 66.4°-60.0° 7.1%
50-60% 60.0°-53.1° 7.6%
60-70% 53.1°-45.5° 8.4%
70-80% 45.5°-36.8° 9.7%
80-90% 36.8°-25.8° 12.2%
90-100% 25.8°-0° 28.7%
Total: 100.0%
Figure Captions
Figure 1: Map of microtremor experiment deployments near the Reno/Tahoe International Airport, western Nevada. The lines of 48 dots total
show the 1997 placement of the 8-Hz single refraction geophones. Channels 1-18 extend south from the Rock and Mill intersection along Rock
Blvd., with 19-24 turning west. Channels 25-48 extend west from the intersection along Mill St. The line of 15 rectangles shows the 2000
placement of the 4.5-Hz refraction geophones. The dots in triangular arrays show the locations of 3-component accelerometers deployed by Iwata
et al. (1998). The words labeling the airport are aligned with the location of the main runways in use during all the experiments. The major
intersection between Rock Blvd. and Mill St., the nearby Truckee River, and the irrigation ditch flowing along the site also appear.
Figure 2: Analysis of shallow shear velocity near the Reno/Tahoe Airport, using recordings of microtremor noise on two arrays. The p-f
images are linear from a slowness of zero (top edges) to 0.005 s/m (200 m/s minimum phase velocity, along the bottom edges). Higher spectral
ratios are darker in the images. a) Summed p-f transformation of five 48-sec 1997 records from the 8-Hz sensor arrays, with well-established p-f
picks and errors (white circles and bars). b) Summed p-f transformation of five 50-sec 2000 records from the 4.5-Hz sensor array, with picks
and extremal picks along the lowest-velocity envelope (small squares). F-K analyses would be spatially aliased below the dotted curves; but the
p-tau transform can with care still yield useful phase velocities from this region. c) Dispersion curves for all the picks, and matching fits. d) Fit
shallow shear-velocity models. The 8-Hz records picked to 4 Hz minimum frequency constrain velocities to 75 m depth. The 4.5-Hz records
picked to 2 Hz constrain velocities to 150 m.
Figure 3: Comparison of phase-velocity spectra near the Reno/Tahoe Airport from three microtremor noise recording techniques. Triangles with
error bars were picked from F-K analysis of broadband accelerometer array records by Iwata et al. (1998), yielding the model plotted with a thin
solid line. Open circles and the thick dashed lines show the lower-frequency part of microtremor analysis using 8-Hz refraction equipment and
the p-tau and Fourier transformation method, from figure 2. Squares and a thick solid line show the results of the same analysis on the coincident
array of 4.5-Hz refraction recorders. The thin dashed line is a model computed from a 30 m borehole log by Ni et al. (1997).
Figure 4: Demonstration of a 200-m linear array of 8-Hz seismic-refraction geophones, recording microtremor noise (a) at the Newhall Fire
Station, southern California, and analyzed with the slowness-frequency (p-f) technique (b). The arrows on (a) point to one example of the many
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sur
f
ace waves t
h
at can
b
e seen
i
n t
h
e recor
d
. Ray
l
e
i
g
h
-wave p
h
ase-ve
l
oc
i
ty
di
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i
ons
(
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)
l
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e
l
ve
l
oc
i
ty pro
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(d)
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at can matc
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suspension-logger shear-velocity results from the ROSRINE borehole there. Refraction P velocity below 30 m and microtremor shear velocity
below 110 m are very poorly constrained (question marks).
Figure 5: Comparison of velocity profiles estimated in the Parkway neighborhood of Wellington, New Zealand. SASW results from Sutherland
and Logan (1998); seismic cone-penetrometer results from Barker (1996); and P-wave refraction velocities from Duggan (1997). The
microtremor profile results from modeling of the p-f dispersion analysis (not shown) of records from a 1-Hz array deployed by Yu and Taber
(1998). Dispersion analysis also finds the basin bottom at 75-90 m, beyond this plot to just 20 meters depth.
Figure 6: Comparison of 30-m averaged velocity estimates at ten sites. Shear velocities derived from microtremor modeling are plotted on the
horizontal axis. Shear velocities estimated from coincident P-wave refraction results are plotted on the vertical, after assuming a Poisson's ratio of
0.25 in converting to a shear velocity. In the Santa Clarita Valley and western Mojave Desert of southern California NFS is from the Newhall
Fire Station (figure 4); MCS from Mill Creek Summit; GLR from Gleason Road 0.5 km from MCS; ANB from Antelope Buttes; LJB from
Lovejoy Buttes; ALC from Aliso Canyon; and PIB from Piute Butte. In Nevada RNO is from the Reno/Tahoe Airport (figures 1 and 2). In
Wellington, New Zealand, PKY is from Parkway (figure 5) and STN is from Seatoun.
DSF
Record
1 km
1-Hz Accel.
Array
100 m
1-Hz Accel.
Array
8-Hz 24-Chan. Arrays
Reno/Tahoe International Airport
4.5-Hz
15-Chan.
Array
Scale 200 m
N
Frequency, HzFrequency, Hz
A. 8-Hz Array Velocity Spectrum
0.0 2.5Spectral Ratio
0 32282420161284
200 m/s
250 m/s
300 m/s
400 m/s
700 m/s
1000 m/s
2000 m/s
5000 m/s
500 m/s
A. 8-Hz Array Velocity Spectrum
F
-
K
A
l
i
a
s
i
n
g
B. 4.5-Hz Array Velocity Spectrum
0.0 2.3Spectral Ratio
0 2420161284
200 m/s
250 m/s
300 m/s
400 m/s
700 m/s
1000 m/s
2000 m/s
5000 m/s
500 m/s
B. 4.5-Hz Array Velocity Spectrum
F
-
K
A
l
i
a
s
i
n
g
0.00 0.10 0.20 0.30 0.40 0.50 0.60
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
C. Reno/Tahoe Airport Noise Dispersion
Period, second
Rayleigh Phase Velocity, km/s
8-Hz 24-Chan. Array Records
8-Hz 24-Chan. Array Fit
4.5-Hz 15-Chan. Array Records
4.5-Hz 15-Chan. Array Fit
4.5-Hz Extremal Fits
0 20 40 60 80 100 120 140 160 180
0.0
1.0
2.0 D. Reno/Tahoe Airport Velocity Model
Depth, meters
Shear Velocity, km/s
8-Hz 24-Chan. Model
4.5-Hz 15-Chan. Model
4.5-Hz Extremal Models ?
?
VaVa
8-Hz 24-Chan. Refraction Array
Model and Constraints
4.5-Hz 15-Chan. Refraction Array
Model and Constraints
Model from 1-Hz Arrays
Constraints from 1-Hz Microtremor
Arrays of Iwata et al. (1998)
Model from Ni et al. (1997)
0.2
0.4
0.6
0.8
1.0
1.2
0 1 2 3 4 5 6 7 8
Frequency, Hz
Phase Velocity, km/s
0.1 0.2 0.3 0.4 0.5
0.2
0.4
0.6
0.8
1.0
1.2 C. Noise Array Rayleigh Dispersion
Period, sec
Rayleigh Phase Velocity, km/s
Modeled Dispersion Fit
Interpreted Dispersion w/ Uncertainty
0.0
0.01
Slowness, sec/meter
0.0 24.9
Frequency, Hz
B. Velocity-Spectral Analysis of Noise Array
0.0 2.0
Spectral Ratio over Average Power at All Slownesses
0.0
192.0
Distance, m
20.0 30.0
Time, sec
A. Section of 30 s Noise Record from 200 m Array at Newhall Fire Station
-2.865E-4 2.865E-4
Vertical Particle Velocity after 0.0-20.0 Hz BP Filter after Trace-Equalize Surface Wave
F
-
K
A
l
i
a
s
i
n
g
1.0 2.0
150
130
110
90
70
50
30
10
D. Rosrine vs. Noise Array at Newhall F.S.
Velocity, km/s
Depth, m
Logged S Velocity
Refraction P Velocity
Logged P Velocity
Noise Array S Model
Extremal S Models
?
?
0
5
10
15
20 0 200 400 600 800 1000
Parkway, Wellington, New Zealand
Velocity, m/s
Depth, m
SASW Model
Seismic-Cone
Penetrometer
Refraction P Velocity
1-Hz Microtremor
200 400 600 800 1000 1200 1400 1600
200
400
600
800
1000
1200
1400
1600
30-meter Velocity Comparison
Shear Velocity from Microtremor, m/s
Vs Estimated from Refraction Vp, m/s
Vp/Vs=1.73 s=0.25
PIB
ALC
LJB
ANB
NFS
MCS
GLR
STN
PKY
RNO
Vp/Vs=2.21 s=0.37
