Geophysical Research Letters
Supporting Information for
The origin of Mauna Loa’s Nīnole Hills – Evidence of rift zone reorganization
Jeffrey Zurek1, Glyn Williams-Jones1, Frank Trusdell2, Simon Martin3
1 Department of Earth Sciences, Simon Fraser University, Burnaby, BC, Canada;
jmz3@sfu.ca
2 Hawaiian Volcano Observatory, U.S. Geological Survey, Hawai‘i National Park,
Hawaii, USA; trusdell@usgs.gov
3 School of Environmental Sciences, University of Liverpool, Liverpool, UK;
smartin@liverpool.ac.uk
Contents of this file
Text S1
Figures S1 to S4
Introduction
The supplementary text accomplishes three different points. First it elaborates on
how and why different inversion software were used. Secondly it explains how
the regional gravity field was removed and thirdly presents end member
inversions that provide a range to the anomalies detected beneath the Nīnole
Hills.
Text S1.
Residual gravity data from this study was inverted with both GROWTH2.0
(Camacho et al., 2011) and GRAV3D (GRAV3D, 2007) to investigate the inherent non
uniqueness of gravity inversions. Each software suite has strengths and weaknesses when
dealing with different datasets. For instance, GRAV3D inversions attempt to create
density contrasts that are smooth in three directions and match observations consistent
with data error levels and degree of misfit (GRAV3D, 2007). For datasets with irregular
station spacing, 3D anomalies will appear smeared to maintain smoothness across the
model; however, for datasets with a regular grid, GRAV3D balances smoothness, data
misfit and resolution well. GROWTH2.0 treats inversion problems differently, using a
1
least squares inversion approach (Tarantola, 1988) that “grows” positive and negative
density contrasts with predetermined density values. This method will produce relatively
sharp contrast boundaries as model smoothness is less of a priority then in GRAV3D.
This process works well with irregular station spacing as imaged density structures are
not excessively smoothed.
To remove the effect of density contrasts outside of the survey area, the regional
gravitational field must be removed. There are several techniques using filters and
derivatives to accomplish this, however, they often leave edge effects unless the dataset is
resampled to a smaller area. If a much larger and wider dataset exists, a two-step
inversion process can be performed to remove the regional field reducing edge effects
and allowing the use of the full dataset. This is done by taking the density model created
by inverting the large dataset and setting the area corresponding to the survey to a zero
density contrast. Setting the survey area to 0 kgm-3 effectively removes all effects of
anomalous mass in the survey area. Therefore forward modeling the modified inversion
will result in the regional field, which can then be removed; the Kauahikaua et al. [2000]
island wide dataset was used for this purpose. GRAV3D was used to complete this step
due to its flexibility and ease of use when manipulating large density models. GRAV3D
inversion models can be directly imported into MeshTools, an associated software which
can display, edit and forward model gravity and magnetic models. At this time,
GROWTH2.0 inversion models are not easily modified and forward modeled.
Both inversion suites can reproduce the residual gravitational field with
approximately the same amount of model misfit and the same amount of required
additional mass (within 1 to 2 %). However, GRAV3D inversions show an intrusive
volume of 1.5 km3 to 6.5 km3 beneath the Nīnole Hills; much less than the 500 km3 to
3200 km3 obtained from GROWTH2.0. The large discrepancy in intrusive volumes is
indicative of how GRAV3D smears density contrasts due to poor station coverage. While
the intrusive volumes calculated by GROWTH2.0 are likely too high and those calculated
by GRAV3D are likely too low, the value range obtained by GROWTH2.0 is likely more
accurate based on its effectiveness in solving inversions with irregular station spacing.
Even though GRAV3D and GROWTH2.0 solve inversion problems differently, leading
to different concentrations of dense material, the resulting shapes of the density contrasts
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are similar. The anomaly imaged beneath the Nīnole Hills by GROWTH2.0 is linear and
elongated in a NE/SW direction and the GRAV3D (Aux -2) inversions show a more oval
body elongated in the same direction. Even though the inversion method is inherently
non-unique, two different inversion suites, using different approaches to inversion
problems, show a concentration of dense material beneath the Nīnole Hills elongated in a
SW/NE direction.
To further investigate the sensitivity of the growth inversion method, a test was
conducted using synthetic data. First a stepwise body consisting of three blocks (3 x 3 x 2
km, 3 x 3 x 3 km and 3 x 3 x 4 km) beside each other but at different depths (-2 to -4 km
a.s.l, -4 to -7 km and -7 to -11 km a.s.l.) was forward modeled using the same coordinates
and area as the survey. This geometry was chosen because the bodies imaged by the
Growth2.0 inversions (Figure 3, S 2 and S 3) are this size or bigger in regions where we
have poor resolution. Furthermore, it allows for the investigation how sensitive the
inversion is to horizontal and vertical changes. The resulting gravitational potential field
from the forward model was sampled at each gravity station to obtain the same resolution
as the survey. The sampled data where then inverted using Growth2.0 (S 4). The resulting
inversion mimics the original body even where resolution is poor. This increases the
confidence that the two different gravity anomalies do in fact merge at depth as the size
of the imaged connection is equal to or bigger than the synthetic shape.
Supplementary References
Gottsmann J., A.G. Camacho, J. Martí, L. Wooller, J. Fernández, A. García, and H.
Rymer (2008), Shallow structure beneath the Central Volcanic Complex of Tenerife from
new gravity data: Implications for its evolution and recent reactivation, Phys. Earth
Planet. In., 168(3–4), 212-230.
Kauahikaua, J., T. Hildenbrand, and M. Webring (2000), Deep magmatic structures of
Hawaiian volcanoes, imaged by three-dimensional gravity models, Geology, 28(10), 883886.
Keller, G. V., L. T. Grose, J. C. Murray, and C. K. Skokan (1979), Results of an
experimental drill hole at the summit of Kïlauea volcano, Hawaii, J. Volcanol. Geotherm.
Res., 5(3), 345-385.
3
Moore, J. G. (2001), Density of basalt core from Hilo drill hole, Hawaii, J. Volcanol.
Geotherm. Res., 112(1–4), 221-230.
Tarantola, A. (1987), Inverse Problem Theory, Elsevier, Amsterdam, 613 pp.
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S 1. Smoothed density contrast depth slices from the optimized GRAV3D inversion with density bound of
+/- 400 kg m-3 and the residuals for each station. Black dots in the -2190 m a.s.l. depth slice represent
gravity measurement locations. Contours at 100 m.
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S 2. Smoothed density contrast depth slices from the optimized GROWTH2.0 inversion with density bound
of +/- 185 kg m-3 and the residuals for each station. Positive density variations shown in red approximately
correspond with interpreted intrusive material based on a zero density contrast obtained from drill holes
[e.g., Keller et al., 1979; Moore, 2001]. Contours at 100 m.
6
S 3. Smoothed density contrast depth slices from the optimized GROWTH2.0 inversion with density bound
of +/- 900 kg m-3 and the residuals for each station. Positive density variations shown in red approximately
correspond with interpreted intrusive material based on a zero density contrast obtained from drill holes
[e.g., Keller et al., 1979; Moore, 2001]. Contours at 100 m.
7
S 4. Sensitivity tests modeled after Gottsmann et al., 2008. Frames 1 and 2 show two sensitivity test
where a step wise body (shown in 3) was forward modeled with the resulting field (far right) sampled
at station locations (black triangles). The new generated data was inverted by Growth2.0 to see if the
limited station spacing can resolve the size of bodies we are seeing with our data.
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