(A grad school class project
to learn about the non-uniqueness in solutions to this
problem,
UW Geophys 503, Spring 2002)
Analysis of
Gravity Measurements
and Gravity Gradient Differences on the Seattle
Fault
Andrew A. Ganse
Applied Physics Laboratory, Seattle, Washington
15 June 2002
Abstract. Gravity data were measured
across the Seattle fault zone, on the east and west sides
of Lake Sammamish, near Seattle, WA. Large gradients
are seen in the data, about 50 mgal on the west side of the
lake (“Bellevue” data) and about 30 mgal on the east side
of the lake (“Issaquah” data). The data are compared
to a mathematical horizontal slab model for a vertical
fault, and while fault modeling of gravity data offers no
unique solution, the measured data and its differing
gradients between the two tracks are roughly consistent
with a model that uses the change in depth of the Seattle
basin seen in other data sources.
1. Introduction
The Seattle fault zone consists of
several parallel east-west reverse faults through the
greater Seattle area. It forms the steep southern
edge of the Seattle basin, a bowl-shaped vertical boundary
between less-dense sedimentary rock layers nearer the
surface and the denser volcanic rock below (Figure
1). At the fault zone this volcanic rock layer,
called the Crescent Formation, is suddenly uplifted,
creating a large, lateral density contrast between the
uplifted Crescent Formation to the south of the fault zone,
and the sedimentary layers to the north (Johnson et al,
1994). The particular interest in the Seattle basin
and the fault zone lies in the possibility of its being a
seismic hazard, in which the basin acts as a resonator for
seismic energy radiating from the fault zone.
Measuring gravity anomalies at the ground surface at
various points over the Seattle basin is one way these
underground structures are seen; seismic tomography and
boreholes also yield significant information about the
area. However, even with much analysis and synthesis
of the data from these different methods, the exact nature
of the fault zone remains somewhat elusive (Johnson et al,
1994). The analysis presented here of new gravity
data taken by students of the University of Washington’s
Earth and Space Sciences Department is just one piece that
lends support to other parts of the puzzle.
2. Measuring the Gravity Data
Gravity data were measured using a
Lacoste and Romberg geodetic gravity meter (L&R #G213,
UWser. #167654) along two north-south tracks across the
Seattle fault zone, on the east and west sides of Lake
Sammamish. The west track (“Bellevue” track) follows
the path of a geological slice seen in a USGS geologic map
of the area, between 148th Ave SE and 164th Ave SE to the
north of I-90, and through the Hilltop area to the south of
I-90. The east track (“Issaquah” track) follows
perpendicular to I-90 along 228th Ave NE to the north and
Front Street to the south. Measurements were also
taken at the reference station in the basement of Johnson
Hall (“JHN”) at the University of Washington for
calibration and as a common base station for
comparisons. Two measurements were taken at each
location and averaged together for the data used in the
analysis, and position and elevation were recorded via
handheld GPS (except for the JHN basement station position
and elevation, where there was no GPS reception but
position and elevation were previously known). The
data were measured on four different dates by three
different collection teams, with two different GPS
receivers. The GPS receivers have an accuracy in both
position and elevation of 15 meters, and in some locations
elevations were not recorded via GPS and instead were
inferred from a topography map, also with an accuracy of
approximately 15 meters. Uncertainty in elevation is
the strongest factor in the uncertainty of the reduced
gravity data values. The above elevation accuracies
make the reduced data accurate to only approximately 4.5
mgal, so data comparisons and conclusions must be drawn on
a somewhat broad scale, such as that of the Seattle basin’s
change in depth.
3. Data Reduction
The measured gravity meter units were
converted to milligals and then corrected with latitude,
free air, and Bouguer plate corrections and referenced to
the Johnson Hall reference station at the University of
Washington. For more precise surveys one would also
correct for tides, terrain changes, and instrument drift,
but these corrections are found to be insignificant at the
several-milligal accuracy considered. Tidal
corrections are generally on the order of hundredths of
milligals, the instrument drift is seen in the data to be
on the order of tenths of milligals, and the terrain
correction can also be neglected if terrain changes near
the measurement locations are within 5% (Milsom 1989), as
was purposely made the case for our data.
For the latitude correction, the
standard formula for relative measurements of 0.814 sin(2l)
mgal/km is used, which at Seattle’s latitude (l) gives a
correction of 0.812 mgal/km northward in the measurement
locations. The free air correction is 0.3086 mgal/m
above sea level. The Bouguer plate correction is
0.0419 r x 10-3 mgal/m -- since the Bouguer
plate correction is for additional surface rock above sea
level, and in this area that surface rock is less-dense
Quaternary deposits with an estimated density of 2200
kg/m3 (Danes et al, 1965), the Bouguer plate
correction is then 0.092 mgal/m elevation. The
gravity data for both tracks with all three of these
corrections applied are shown in Figure 2. Note the
approximately 50-mgal gradient in the Bellevue track and
the approximately 30-mgal gradient in the Issaquah track,
and compare with the differing basin depth gradients in
Figure 1 along those tracks (on either side of Lake
Sammamish on the right side of the figure).
4. Mathematical Modeling of the Data
The data are compared to a mathematical
horizontal slab model for a vertical fault (Lowrie
1997). While fault-modeling of gravity data offers no
unique solution, the measured data are roughly consistent
with this simple mathematical model which uses the change
in depth of the Seattle basin inferred from seismic and
borehole surveys. This model assumes a step function
in the rock density to represent the uplift of the fault;
the dip of the fault is neglected and assumed vertical, so
the Seattle basin becomes a rectangle (Figure 3).
While this model is certainly simplistic, it yields results
that roughly compare with the measured data. The
formula used is that for the gravitational anomaly of a
horizontal slab (Lowrie 1997):
(1)
Δgz is the change in
gravity seen over this fault, G is the gravitational
constant, Δρ is the difference between the two
densities used in the model, h is the thickness of the slab
in the horizontal slab model, z0 is depth to the center of
the horizontal slab, and x is the horizontal range across
the surface. To turn this slab model into our
rectangular basin one, we choose h=2z so that h becomes the
depth of the basin and z0 is its half-depth.
As seen in Figures 2 and 3, this
rectangular basin model roughly matches the measured
Bellevue data given a density difference of Δρ = -350
kg/m3 and a basin depth of 6 km, and roughly
matches the measured Issaquah data given a Δρ of -300
kg/m3 and a basin depth of 3 km. The basin
depths for these areas are taken from Blakely et al, 2000,
to try to constrain them to reality. The general
scale of the density differences is inferred from rock
layer profiles suggested by Johnson et al (1994) and Yount
et al (1991) and layer densities from Danes (1965).
Note that the Bellevue track required a greater density
difference to match the data than the Issaquah track.
While a roughly one-kilometer layer of less-dense
Quaternary sediments is shown to be on the surface of
moderately-dense sediments in the basin (Yount et al 1991),
and could bring down the average basin density, this model
is extremely simplistic and it is cautioned to draw too
many conclusions from it. However, this model does
lend support to the size of the uplift of the Crescent
Formation shown in Johnson et al 1994 and Blakely et al
2000, and the tapering of the basin to the east.
Acknowledgments. My thanks to my
classmates in Geophysics 503 at the University of
Washington for our working together to collect, reduce, and
discuss the gravity data, and to Adrienne Sherhart and Dirk
Bush for additional assistance in data collection on the
Bellevue track.
References.
Blakely, R., Brocher, T., and Wells, R., How the
jello-shakes depends on the shape of the bowl: a
three-dimensional view of the Seattle Basin, poster at the
Great Cascadia Earthquake Tricentennial Open House, January
26, 2000, Burke Museum, University of Washington, Seattle
WA.
Danes, Z., and nine others, Geophysical investigations of
the southern Puget Sound area, Washington, J. Geophys.
Res., 70, 5573-5579, 1965.
Johnson, S., Potter, C., Armentrout, J., Origin and
Evolution of the Seattle Fault and Seattle Basin,
Washington, Geology, 22, 71-74, 1994.
Lowrie, W., Fundamentals of Geophysics, pp. 46-81,
Cambridge University Press, Cambridge, 1997.
Milsom, J., Field Geophysics, pp. 26-38, Halsted Press, New
York, 1989.
Yount, J., Gower, H., Bedrock Geologic Map of the Seattle
30’ by 60’ Quadrangle, Washington, Open-File Report 91-147,
USGS, 1991.
Tables
Table 1. Gravity Data Along Issaquah and Bellevue
Track
ISSAQUAH:
date time easting northing elev mgalsraw anomaly
05May2002 0730 0551892 5278179 29 4502.74 0.00
10May2002 1235 0572499 5266021 23 4526.81 29.61
10May2002 1251 0572506 5265576 31 4529.09 33.98
10May2002 1307 0572510 5264982 40 4530.22 37.55
10May2002 1320 0572455 5264679 29 4531.61 36.80
10May2002 1332 0572492 5264194 34 4533.75 40.41
10May2002 1347 0572592 5263600 52 4534.23 45.27
10May2002 1403 0572576 5265753 36 4527.90 33.73
10May2002 1538 0572512 5267409 123 4500.97 24.29
10May2002 1630 0572499 5266021 23 4526.93 29.74
10May2002 1703 0572492 5270345 141 4497.75 22.59
10May2002 1720 0572640 5270941 120 4499.24 19.05
10May2002 1733 0572546 5271795 181 4487.34 19.66
10May2002 1753 0572500 5273460 120 4500.75 18.52
10May2002 1806 0572418 5274211 113 4498.91 14.56
10May2002 1823 0572301 5268651 127 4497.14 20.32
10May2002 1834 0572456 5269474 122 4502.29 23.72
10May2002 1843 0572489 5270346 133 4497.85 20.96
BELLEVUE:
date time easting northing elev mgalsraw anomaly
18May2002 1330 0551892 5278179 29 4505.75 0.00
18May2002 1425 0564174 5265546 195* 4498.57 38.98
18May2002 1520 0564165 5266131 175* 4498.81 34.41
18May2002 1540 0565195 5267082 360* 4443.42 18.30
18May2002 1600 0564865 5268057 220* 4471.76 15.55
18May2002 1618 0564955 5268944 135* 4487.15 11.82
18May2002 1632 0565191 5269530 117* 4491.32 11.62
18May2002 1655 0563971 5264437 229 4499.47 48.13
18May2002 1750 0551892 5278179 29 4505.75 0.00
19May2002 1620 0565198 5269523 119 4491.27 12.01
19May2002 1628 0565330 5270319 111 4493.42 11.78
19May2002 1645 0565445 5271310 94 4495.57 9.46
19May2002 1703 0565857 5272143 84 4492.37 3.41
19May2002 1717 0566019 5272787 99 4489.91 3.68
19May2002 1734 0566314 5274106 125 4484.25 2.58
19May2002 1752 0565194 5269528 108 4491.34 9.70
*GPS elevations were not recorded at some locations and elevations
there were taken from USGS topography map.
Position in UTMreWGS84 easting & northing (meters), elevs in meters.
2 GPS units used, Garmin Etrex and geophys dept's Garmin unit.
Both GPS meter manuals say accuracy is 15m.
Figures
Figure 1. Depths to the basement interface of the Seattle basin, with map and Seattle fault zone lines superimposed. Lake Sammamish is the rightmost body of water shown in the diagram, and the two tracks of data were taken on the west and east sides of it, across both fault lines shown. (Reproduced from Blakely et al, 2000.)
Figure 2. Plots of the measured data and matching model results for the Bellevue and Issaquah tracks.
Figure 3. Diagrams to explain the model parameters for the Bellevue and Issaquah tracks. The gray area represents the denser Crescent Formation that is uplifted at the Seattle fault zone.