2. Inversion Modelling
Camacho et al. [2000; 2002; 2011] proposed a method of 3-D gravity inversion
inspired by the method of René [1986], which is based on a ‘growth’ process and the
mathematical exploration of the model space, in the sense of Tarantola [1988], for
pre-defined positive and negative density contrasts. The intrinsic non-uniqueness of
the solution is addressed by a mixed minimization condition based on model ‘fitness’
(least-squares fit) and ‘smoothness’ (total anomalous mass) optimised for a minimum
distance-normalised autocorrelation between resulting inversion residuals. This
condition is balanced through parameter λ, which we keep constant in all models in
order to compare model outputs (however, we acknowledge that changes to lambda
do not affect the bulk of the large bodies imaged, including the one beneath
Uturuncu). The inversion routine optionally removes a first-degree polynomial
surface, as a proxy to long-wavelength “regional” signal-overprint, and
simultaneously models the residual short-wavelength “local” density anomalies. The
preferred solution is therefore a robust oversimplification of the density distribution in
the upper crust.
2.1. Inversion set-up
The inversion uses a pre-designed 3D grid of cells, which are initially distributed
following the spatial distribution of gravity benchmarks. After each inversion run the
grid is recomputed to minimise its size and optimise cell size and distribution around
identified anomalous bodies. The inversion is then performed again using the new
grid. This process is repeated five to six times until the extent and geometry of the
anomalous bodies is fully captured, inversion results are constant and re-computed
grids are almost identical. Initial grid cell sizes are of 2 to 4 km whereas in the final
re-computed grid cell lengths are ~1km.
In our models we invert for the initial Bouguer anomaly at the benchmarks (supfig2a)
and set an a priori density contrast between anomalous bodies and a background
“neutral” crust. We consider the density contrasts within the felsic mid-upper crust to
be <800 kg m-3, and thus invert for a prescribed contrast range ±30 to ±400 kg m-3 to
represent all plausible anomalous bodies. The lowest contrast applies for a
homogeneous crust subject to thermal expansion whereas the largest contrast applies
to a heterogeneous crust where melt may be present. In addition, we include the
presence of a regional gravity component. We consider five different scenarios, which
we term: Minimum, Free, Flat, Bottom Free and Bottom Flat (see below).
2.2. Inversion results
All models provide similar quality results with ~1 mGal standard deviation in the
residuals and a <0.03 distance-normalised autocorrelation between resulting residual
values (supfig1). Our initial models (Minimum) calculate an average mathematically
optimal regional polynomial (-336484 µGal plus a NE trend of 202 µGal km-1) that
minimises the local anomaly to approx. ±24 mGal (similar in magnitude to the
isostatic residual anomalies [Gotze and Kirchner, 1997; Prezzi et al., 2009]) and
“grow” negative and positive anomalous bodies (supfig1). However, since most of
our survey is over the inferred extent of the APMB (supfig1a), an optimally
minimised local anomaly determines a combined value of host rock and APMB as the
background density, and hence introduces artificial positive anomalous bodies where
the APMB is absent, whereas low-density anomalies represent mass deficiencies
overprinted on the signal of the APMB (see profiles in Figure 1c).
In subsequent models, and following the gravity residual values of Prezzi et al. [2009]
we force the local anomaly to be mostly negative, and hence control the density
contrast between the host and the anomalous bodies (i.e. we use APMB-free crust as
background density). In this case (Free), the average mathematically optimal regional
surface is -319908 µGal plus a NE trend of 230 µGal km-1) and ~95% of the
anomalous mass is negative (supfig1). The resultant local anomaly is between -40 to
12 mGal, similar in magnitude to the Minimum models The inversion results show
how the main negative bodies observed in the first set of models remain and large
deep negative bodies appear beneath the arc and the SE part of the survey, indicative
of the presence of the APMB. At the same time the positive anomalous bodies are
reduced and some even disappear. The optimum regional component corresponds to a
gradient of 230 µGal km-1 N25E which is significantly steeper than the ~N-S ~100
µGal km-1 slope inferred from the cross-sections (Figure 1c). This discrepancy may
be caused by the limited extent of our survey to the south, which does not allow
identifying the southern limit of the APMB. As a consequence the regional gradient
may be overestimated causing the inversion to underestimate the mass deficiency in
the southern part of the surveyed area. In order to test the significance of this we
introduce a third set of models, which we name Flat, were we keep most of the local
anomaly negative (similar to Free) but invert only for an optimal regional constant.
The average value is -316143 µGal and the resultant local anomaly, -45 to 14 mGal,
is only slightly larger than in the Free case. As expected, the inversion results of Flat
are very similar to those of Free (supfig1) with the exception that now the modelled
negative anomalous bodies in the southern part of the survey area are larger.
The two latter cases, Free and Flat, show large, negative anomalous bodies in the
south-eastern sector, coinciding with the strongest Bouguer anomaly, that extend
down to the lower crust. We interpret these bodies as indicative of the presence of the
APMB. Other geophysical interpretations approximate the geometry of the APMB by
a horizontal slab [Yuan et al., 2000; Zandt et al., 2003], and place it at mid-upper
crustal depths. Herein, in the final set of models (Bottom Free and Bottom Flat) we
assume the anomaly is generated within the mid-upper crust by limiting the extent of
the inversion model to the top 30 km. We use the same regional polynomials
calculated for Free and Flat respectively. The results show a slab-like APMB with a
top at 16 to 20 km from where ridges and necks of anomalous bodies root-up
(supfig1). Note that the geometry of the anomalies is identical to Free and Flat
solutions for the top 15 km and is only modified at depths where the APMB is
present.
In conclusion, the different inversion configurations produce variations in the size and
distribution of anomalous bodies around the periphery of the model domain but, in
every case, the presence and characteristics of the negative anomalous bodies near the
centre of the survey remain unchanged.
2.3. Preferred models
We prefer the Bottom Free and Free configurations as best-fit scenarios, as they
produce a mostly negative anomaly but still contemplate the presence of denser
material. In the Free case inversion the optimum regional signal is -320079 µGal and
a N26E trend of 232 µGal km-1 (supfig2b). The corresponding “local” anomaly of -40
to +12 mGal is shown in supfig2c. This local anomaly is inverted for using a depthunlimited (Free) and a depth-limited (Bottom Free) domain that produce the residuals
and distance-normalised autocorrelations shown in supfig5. We assume that most of
the gravity signal is produced within the mid-upper crust and hence favour the result
of the Bottom Free model and a melt fraction similar to that inferred for the APMB,
given by a density contrast of -150 kg m-3 (Figure 2).
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