Appendix (to Strain accumulation controls failure of a plate boundary zone - linking
deformation of the Central Andes and lithosphere mechanics, by
Oncken, O., Boutelier, D., Dresen, G., Schemmann, K.)
1. Potential errors and uncertainties in estimates of spatio-temporal deformation pattern
Uncertainty in the procedure of mapping spatial evolution of deformation
accumulation may originate from several aspects. Smaller grid distances theoretically
increases spatial resolution. However, increased spatial resolution will not greatly affect total
area fraction because grid spacing is already at the lower limit of map-scale structures. A gridspacing smaller than the typical map-scale structures (folds and faults) is meaningless, as
statements from field analysis typically relate to the geometry and kinematics of such
individual structures, preventing added spatial resolution. With larger grid spacing we expect
an increase of bulk deforming area fraction/Ma for the entire plateau because smaller
quiescent domains will not be resolved. The general results discussed here remain robust with
an across-strike grid spacing that is smaller than the E-W width of the first-order
morphotectonic units described above and shown in Fig. 1a, 1b - i.e. smaller than c. 100 km
(cf. grid chosen in Fig. 3).
Time binning has a larger influence because the degree of localization observed per
time increment obviously depends on the time length sampled. Reducing the time bin length
to the theoretical minimum of the duration of an earthquake would yield maximum
localization of deformation with no trend over time for the entire plateau. Longer time bins
beyond the value of 1 Ma significantly smooth the details shown in Figure 4b without
obliterating the trend. Beyond a 10-15 Ma sampling interval the trends are lost due to
temporal aliasing thus indicating the minimum temporal resolution required.
Another source of error is undetected deformation – due e.g. to cover of older
structures by younger deposits, poor age control, etc.. This expected effect probably increases
in magnitude with some function towards the past. Hence, the number of actively deforming
‘points’ defining the total deforming area fraction for the early stages of deformation history
presumably forms a minimum estimate of this area. While this may lead to an underestimate
of total area fraction, it should not, however, be able to produce or affect significant changes
of total area fraction. Hence, we conclude that the statistical properties of the procedure and
the values chosen yield robust results allowing to semi-quantitatively characterize changes of
deformation distribution at the orogen-scale.
2. Quantification of shortening rates and uncertainties
The procedure involves the identification of structurally linked units and the
assessment of the amount of shortening accumulated as well as of the time period (or periods)
of their activity (table 1). For shortening values, preference was given to results from well
documented balanced sections. Linear distribution of the incremental shortening measured
over the periods of fault activity provides averaged shortening rates. Summed for all units
across the orogen, these yield the evolution of the latitudinal shortening rate [see Elger et al.,
2005, for more detailed description of technique).
Uncertainty mainly results from three sources [see Elger et al., 2005, for details]: 1)
quantifying local tectonic deformation and its increments, 2) the error of isotopic dating, and
3) correctly identifying the onset and termination of a deformation increment. Along with the
assumption of linear distribution of shortening over a deformation increment, the joint effect
of the above limitations does not allow identifying and interpreting deformation signals of
apparent short duration (shorter than 5 Ma) with exception of the highly resolved section at
21°S. Accordingly, our description and analysis only focuses on these longer-lived features in
the resulting time series data.
We additionally assessed the magnitude of uncertainty of rates in an earlier attempt by
combining maximum shortening value with minimum shortening period for an individual
thrust system (yielding maximum rates) and vice versa (yielding minimum rates; see Elger et
al., 2005]. For very short time spans (< c. 3 Ma), resulting uncertainty in the rates may be as
large as 50%. Because latitudinal integration of rates must yield finite shortening, overall
uncertainty reduces to the error of evaluating tectonic shortening in sections. Developing a
sophisticated approach for the analysis of uncertainty in balanced sections, Judge and
Allmendinger [2011] have explored several published sections for the Subandean belt and
find that uncertainty for sections may be as large as 20-30% of the shortening reconstructed,
depending on the quality of the data.
Additionally, uncertainty in shortening has been estimated from correlating crustal
shortening and the observed cross-sectional crustal area as derived from geophysical
observations and from average elevation [see Kley and Monaldi, 1998]. We note that there is
fairly good agreement for the shortening estimate from cross sectional crustal area and from
section balancing based on upper crustal observations with exception of the Puna latitude [see
table 1). Moreover, for the Central Andes, Hindle et al. [2005] have shown that mismatch
between cross sectional crustal area and shortening is easily explained by lower crustal mass
redistribution along the orogen providing a consistent total volume balance for the crust
building the Central Andean orocline. Hence, sections covered only by few data most
probably underestimate shortening by an estimated maximum of possibly more than 20%, but
will rarely, if ever, exceed true shortening. This does not leave much room for additional
hidden deformation (see above). We expect, however, that new data will help to improve the
resolution of temporal distribution of deformation particularly for the early stages of
deformation.
We additionally use GPS shortening rates to assess the reliability of the geological
estimate for the present [data from Bevis et al., 2001; Klotz et al., 2006] and to check on the
short-term variability of rates that will be overlooked by linearly distributing observed
shortening over the time period of fault activity. In all cases, the GPS velocities roughly
match the geological velocities calculated for the present from the above strategy, lending
support to the robustness of the assumptions underlying the here chosen strategy.
2. Quantification of initial crustal thickness and uncertainties
The starting choice of 35 km for initial crustal thickness is based on several aspects.
Tassara et al. [2006, and references therein] summarize present day thickness of the
underthrusting Brazilian shield based on geophysical observations. Its thickness in the
foreland after stripping the foreland basin fill is around 35 to 40 km. Sempéré et al. [1997, and
references therein] summarize findings that nearly the entire Altiplano/Puna domain was
covered by shallow marine deposits of the Upper Cretaceous-Paleocene El Molino Formation
(73-60 Ma). This environment limits crustal thickness variations at this time to within a
probably rather narrow bracket. We additionally test the initial value for the thickness of the
crust at 50 Ma and its influence on the calculated final crustal thickness and on the buoyancy
force evolutions. Increasing the initial crustal thickness to 40-45 km leads to very important
thickening of the crust (80-90 km) and lithospheric mantle required to match the recent high
elevation (Fig. S1). This high initial value would most presumably preclude marine
sedimentation unless some thickening had occurred between 60 and 45 Ma. In addition, a
higher crustal thickness at 50 Ma (40-45 km) can produce the modest elevation (500-1000 m)
without the need of significant thinning of the mantle lithosphere, which is known to occur in
continental arcs (Fig. S1). Nonetheless small variations from the initial crustal thickness are
possible but their impact on the presented results is minor.
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