Data analysis methods

Detailed structural data, in conjunction with timing information (e.g., when a fault ruptures or a volcano erupts) may reflect changes on magma pressure and stress fields. Pyroclastic deposits are the most common evidence of volcanic activity in the TgVC, and fault ruptures evidence the earthquakes. Interpretations of the timing of faulting are constrained by the ages of tephras exposed in the outcrops and displaced (or non-displaced) by faults. Well dated tephras are very useful stratigraphic markers to analyse the temporal variation of fault ruptures. Most faults have experienced multiple ruptures, showing more displacement on older tephras than on younger ones. In order to understand these temporal variations the geometry that existed before each rupture on a fault has to be restored. Ideally fault displacement restorations can be easily

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undertaken when the geomorphic surface pre-fault movement is sub-horizontal. However, in volcanic environments dominated by fall deposits the original surface is rarely sub-horizontal, fall deposits mantle the existing scarp and the fault deposit boundaries cannot be easily restored to a horizontal line. Therefore, the understanding of how paleosols, debris flows, debris avalanches and pyroclastic deposits form and what architectural shapes they form are important to understand the original shape of the scarp prior to each surface rupture.

The earthquake history was assessed by analyzing progressive displacement of tephra layers of increasing age. The age of stratigraphic markers and geomorphic surfaces constrain the age of a fault movement [e.g., Villamor et al., 2007]. Multiple ruptures on fault strands are identified by progressively larger displacement in older units. Identifying horizons where the total displacement suddenly changes can be used to identify a new faulting event, including its age and offset [McCalpin, 1996; Villamor et al., 2007]. Relative timing was obtained for most of the andesitic tephras by the identification of rhyolitic tephra with tephrostratigraphy. Ages of displaced strata were taken from the literature, where ages of the tephras have been estimated by their geochemical correlation to dated units [Cronin et al., 1996a; Moebis et al., 2011], radiocarbon dating [Topping, 1973; Froggatt and Lowe, 1990; Lowe et al., 2013], combined with isotopic dating methods like 238_U/230_{Th isotopes and (U-Th)/He zircon}

[e.g., Topping, 1973; Danišík et al., 2012], isotopic K/Ar and 40_Ar/39_{Ar dating for lava}

flows [e.g., Gamble et al., 2003; Conway et al., 2015], and cosmogenic nuclide dating for glacial sediments and lava flows [Eaves, 2015].

Geomorphic displacements have an uncertainty of 1 m, plus 10% of the scarp height, which represents the uncertainty due to irregularities in the ground surface. For the error propagation, the theory of errors was used [Taylor, 1982], as described by Villamor and Berryman [2006b]. Anomalous values were avoided, i.e., those that were not consistent with the geomorphic surface age.

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To identify the temporal associations between fault rupture and deposition of tephra on the field outcrops, the temporal relationship criterion described by Villamor et al. [2011] was applied:

a) Co-seismic tephra deposition: The tephra was deposited on the fault scarp at the same time as the rupture occurred, and the fault termination is within the tephra. In this case, early deposits of the tephra have larger displacement than those emplaced later. It can be identified when the early tephra deposits of an eruption show displacement after the deformation of the late tephra of the same eruption have been restored, or where scarp-derived colluvial wedge material (derived from the newly formed free-face scarp) is preserved within tephra deposits of the same eruption.

b) Fault rupture immediately pre-tephra deposition: the free face of the surface rupture is preserved intact without erosion, because it was immediately sealed by tephra deposits.

c) Fault rupture immediately post-tephra deposition: The fault exposure shows a colluvial wedge derived from the fault scarp footwall (free face of the scarp erodes). The colluvial wedge deposits overlie the tephra. The absence of a paleosol is a crucial criterion to assign a short time interval between the tephra deposition and the fault rupture.

d) Fault rupture without association to tephra deposition: the colluvial wedge overlies a paleosol, indicating a large time span between fault rupture and the eruption.

To be confident of the absence of volcano-tectonic interaction requires complete preservation of the tephra on both sides of the fault, sufficient layer thickness, and the presence of distinctive beds within the tephra. In sites of thin or distal tephra deposits, deposition may be naturally incomplete, making these methods challenging. Also,

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stratigraphic units on the footwall (upthrown side) of normal faults are often eroded from the free face of the scarp as the footwall is uplifted in successive ruptures, and the requisite relationships are not preserved.

To assess the effect of stress changes due to fault rupture or dike intrusion, the Coulomb 3.1 model [Lin and Stein, 2004; Toda et al., 2005] was used. This is a Matlab application that quantifies the stress changes on a receiver fault or volcano in the surrounding of the fault that experienced the earthquake. A positive stress change implies that the earthquake brought the receiver fault closer to failure, while a negative value indicates a delay of the next earthquake, or the closure of the magmatic conduit. Coulomb 3.1 calculates the strain field components and the total seismic moment of the sources in the input file, using the fault location, area, slip, dip, Young’s modulus, and Poisson’s ratio. Details of the parameters used and the method are further described in Chapter 7.

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CHAPTER 4. Earthquake history at the southeastern termination of the