Source‐to‐sink analysis in an active extensional setting: Holocene erosion and deposition in the Sperchios rift, central Greece

We present a source‐to‐sink analysis to explain sediment supply variations and depositional patterns over the Holocene within an active rift setting. We integrate a range of modelling approaches and data types with field observations from the Sperchios rift basin, Central Greece that allow us to analyse and quantify (1) the size and characteristics of sediment source areas, (2) the dynamics of the sediment routing system from upstream fluvial processes to downstream deposition at the coastline, and (3) the depositional architecture and volumes of the Holocene basin fill. We demonstrate that the Sperchios rift comprises a ‘closed’ system over the Holocene and that erosional and depositional volumes are thus balanced. Furthermore, we evaluate key controls in the development of this source‐to‐sink system, including the role of pre‐existing topography, bedrock erodibility and lateral variations in the rate of tectonic uplift/subsidence. We show that tectonic subsidence alone can explain the observed grain size fining along the rift axis resulting in the downstream transition from a braided channel to an extensive meander belt (>15 km long) that feeds the fine‐grained Sperchios delta. Additionally, we quantify the ratios of sediment storage to bypass for the two main footwall‐sourced alluvial fan systems and relate the fan characteristics to the pattern and rates of fault slip. Finally, we show that ≥40% of the sediment that builds the Sperchios delta is supplied by ≤22% of the entire source area and that this can be primarily attributed to a longer‐term (~106 years) transient landscape response to fault segment linkage. Our multidisciplinary approach allows us to quantify the relative importance of multiple factors that control a complex source‐to‐sink system and thus improve our understanding of landscape evolution and stratigraphic development in active extensional tectonic settings.


INTRODUCTION
Temporal and spatial variations in sediment supply are widely recognized as key controls on stratigraphic architecture in sedimentary basins (Jordan & Flemings, 1991;Orton & Reading, 1993;Eliet & Gawthorpe, 1995;Paola, 2000;Forzoni et al., 2014). Furthermore, the grain size of sediment released from mountain catchments is critical for facies development within basin-fills (Visher, 1969;Whittaker et al., 2011;Allen et al., 2015;Armitage et al., 2015). At the same time the characteristics of the supply delivered to the basin margin are modulated by both autogenic and allogenic forcing conditions, such as the mechanisms that govern sediment transport and the spatial distribution of tectonic subsidence Paola et al., 1992;Fedele & Paola, 2007;Allen et al., 2013).
During the last few decades, sediment delivery to depositional basins has increasingly been viewed within a source-to-sink framework, the aim being to dynamically link the surface processes within the different segments of an erosional -depositional system (e.g., Allen, 2008;Sømme et al., 2009). The challenge has been to find natural systems for which sufficient constraints exist on each of the different segments of the entire system such that the key controls can be identified and evaluated. Simple source-to-sink systems that consist of an upland catchment and an adjacent fan are relatively well understood (e.g., Allen & Densmore, 2000;Densmore et al., 2007;Armitage et al., 2011;Rohais et al., 2012) and numerical models have been used to shed light on the geomorphic response of these systems to changes in both tectonic and climatic boundary conditions (e.g., Allen & Densmore, 2000;D'Arcy et al., 2016). However, these models may not apply to larger and more complex erosional-depositional settings, such as that considered here, because they do not, for example, address multiple sites of sediment input and deposition within fault-controlled landscapes. On the other hand, workers such as Covault et al. (2010Covault et al. ( , 2011 and Sømme et al. (2011Sømme et al. ( , 2013 reconstructed onshore -offshore sediment budgets for larger and more complicated natural examples but did not explicitly describe the dynamics of the sediment routing system. Matenco & Andriessen (2013) combined a wide range of surface and subsurface data to quantify sediment delivery to the Danube River Basin but the characteristics of the sediment supplied to the depositional system were not studied in detail. Allen (2008) argued that to fully evaluate the surface processes from source to sink and to understand the system response to different forcing mechanisms it is important to consider how the characteristics of the sediment supply are transformed by the internal dynamics of the sediment routing system. Michael et al. (2013Michael et al. ( , 2014 and Hampson et al. (2014) have demonstrated this point explicitly by applying a mass-balance analysis to ancient sediment routing systems in the Spanish Pyrenees and Central US, respectively. These studies showed that the depositional extraction of gravel and sand was controlled by the spatial distribution of accommodation and, implicitly, by the characteristics of the sediment supply, even though the erosional source catchments are not preserved in these examples. In contrast, Whittaker et al. (2010) analysed Pleistocene to recent systems in the Central Apennines of Italy, providing quantitative data concerning sediment volumes and the down-system grain size fining for individual catchments that have experienced a transient response to tectonics. These data indicated that the volume, locus and grain size characteristics of sediment in the supply were clearly sensitive to the fault activity, but the authors had few constraints on the depositional sink. In summary, studies of well-constrained natural examples of complete source-to-sink systems that also consider the sediment routing system are rare.
In this study we seek to understand the controls on sediment delivery to a tectonically active setting in the Sperchios rift, Central Greece, during the Holocene (Fig. 1). We follow an integrated approach (Fig. 2) by analysing and quantifying (1) the size, spatial distribution and characteristics of sediment source areas, (2) the dynamics of the sediment routing system, and (3) the depositional architecture and volumes of the Holocene Sperchios basin fill. We implement a combination of methodologies that have only been seperately applied in previous source-tosink studies and range from theoretical modelling of grain size distributions, numerical modelling of deltaic deposition, to methodologies that allow us to estimate catchment-averaged erosion rates and to assess the dynamics of the drainage network. We evaluate our modelling results against independent field observations from the different segments of the Sperchios erosional-depositional system. Using this multidisciplinary approach we are able to identify, quantify, and assess the relative importance of factors controlling the source-to-sink system in this active extensional setting and thereby develop a broader understanding of sediment supply variations and depositional patterns in rift basins.

BACKGROUND -THE SPERCHIOS RIFT Tectonic setting
The Sperchios rift is the northernmost of the central Greece active rift basins that have formed due to crustal extension since the Early Pliocene (~5 Ma) (Leeder & Jackson, 1993;Kilias et al., 2008). According to Goldsworthy et al. (2002), extension in the Sperchios rift began in the Middle Pliocene, approximately 3.6 Ma. It is characterized by an asymmetric half-graben geometry, approximately 100 km long, bounded along the south side by several major NW-SE striking, high-angle normal fault segments that dip towards the north (Fig. 1a). From west to east the three main faults, mentioned in this study, are the Sperchias, Kobotades and Thermopylae fault segments; collectively they are referred to as the Sperchios fault zone. Individual segments are typically 15-20 km long (Eliet & Gawthorpe, 1995) and display evidence of linkage along strike Whittaker & Walker, 2015). Bedrock lithology is dominated by Paleogene flysch (sandstone and siltstone), outcropping mainly in the southwest and western parts of the study area, whereas Mesozoic ophiolite and limestone characterize the northern and southeastern margins of the rift respectively (Fig. 1a). Along the rift axis, alluvial and deltaic sediments have gradually filled the graben during the Plio-Quaternary.
Results from gravity modelling (Apostolopoulos, 2005) reveal several major rift depocenters that decrease in depth from east to west (Fig. 1b) and correspond to the major fault segments. Maximum basin depths reach 2 km in the Maliakos gulf, estimated from the combined interpretation of resistivity and gravity measurements (Apostolopoulos, 2005). As the depth decreases towards the west, the width of the half-graben also decreases from 15 km to < 5 km and as it narrows, basin asymmetry becomes more pronounced ( Fig. 1b; see also Goldsworthy et al., 2002). The Sperchias fault segment is the most westerly segment and its western end defines the rift tip. In contrast, moving in an easterly direction, the fault offsets gradually increase and the rift becomes less asymmetric as south-dipping (antithetic) faults develop along the northern margin of the graben (e.g., the Lamia fault, Fig. 3a).
Footwall relief is characterized by topographic highs (1500-2000 m) along the central portions of the major fault segments bounding the southern margin of the rift. In contrast, the hanging wall dip-slope, along the northern margin, is characterized by lower elevations (~600 m). Near the rift tip, to the west of the Kobotades fault segment in particular, pre-existing (i.e., pre-extension) topography dominates over the rift-related topography and the relief remains in excess of 2000 m well beyond the western tip of the Sperchias fault segment (e.g., Mt. Timfristos; Fig. 1a). Based on analysis of knick-point elevations along rivers draining across the Sperchias and Kobotades fault segments, Whittaker & Walker (2015) calculated that most of the rift-related relief in this area has formed since about 1.0-1.6 Ma when segment linkage occurred and fault slip rates increased so that currently, and thus during the Holocene, the rate of relative footwall uplift (i.e. relative to the hanging wall basin fill) along the centre of the Kobotades segment is in the range 0.75-1.25 mm year À1 . Their preferred interpretation is that the lower estimate (0.75 mm year À1 ) is more reasonable so that the total throw rate at the centre of the Kobotades segment is at least 2 9 0.75 = 1.5 mm year À1 (a minimum, based on uplift: subsidence ≤1). Both footwall relief and the hanging wall basin depths (Fig. 1b) decrease along the Sperchias segment, indicating a gradual reduction in extension rate in a westerly direction towards the rift tip (Goldsworthy et al., 2002). Our own modelling of the Sperchios delta (see Results below) places constraints on tectonic subsidence rates along the Thermopylae rift segment and confirms that the extension rate increases along strike towards the east.

Surface processes within the Sperchios rift basin
The Sperchios source-to-sink system is characterized by a major axial river, approximately 80 km long, which drains the upland catchments and flows from west to east, supplying sediment to the shallow marine gulf of Maliakos (~30 m water depth). The Maliakos Gulf is partially Map showing the basement relief (in meters) of the Sperchios rift derived from interpretation of resistivity and gravity measurements using a sediment density of 2200 kg m À3 (from Apostolopoulos, 2005). Basin volume (in m 3 ) of the four distinct depocenters is also shown. Black arrows indicate sediment input from the two large transverse alluvial fans, i.e., Inahos and Xerias (see Fig 6 b, c and 8).
[Colour figure can be viewed at wileyonlinelibrary.com] enclosed by two land spits (the Skarfia and Karavomilos spits, Fig. 1a) and little sediment is thought to by-pass into the north Evvoikos gulf further to the east (Eliet, 1995). Over the first~50 km of downstream distance, the axial river migrates across a~1 km wide braid plain (Fig. 1a). Subsequently, there is a transition to a meandering channel that continues to the shoreline and terminates in a bird's foot delta referred to as the Sperchios delta (Figs 1 and 3a). The transition from the braided to meandering fluvial domains occurs near the eastern end of the sub-basin bounded by the Kobotades fault segment. It coincides with the development of the south-dipping Lamia fault (Fig. 3a), thus a reduction in rift asymmetry, and an increasing extension rate towards the east (i.e., along the Thermopylae rift segment, Goldsworthy et al., 2002). The position of the axial river along the rift is strongly influenced by the combination of footwallsourced alluvial fans and tectonic subsidence along the Sperchios fault zone. For example, where the large, low angle (~0.7°) Inahos alluvial fan progrades into the basin, it clearly diverts the Sperchios River to the north (Fig. 1a). In contrast, along the Thermopylae fault segment the tectonic subsidence rate is sufficiently high that the location of the axial river was, until recently, close to the southern margin of the rift (i.e., prior to end of the 19th century when it became artificially controlled, see Sperchios 'old channel' in Fig. 1a). Along this segment, footwall-sourced alluvial fans have steep surface slopes (~2.5°) and do not prograde more than 1-2 km into the hanging wall.
Multi-proxy analysis and age constraints on deltaic sediments deposited along the Thermopylae segment of the rift (Fig. 1a) indicate that they developed as a transgressive to regressive succession during the Holocene ( Fig. 3b; Pechlivanidou et al., 2014) and consist mainly of fine-grained sediments (i.e.,~60% silt). These deposits are~50 m thick and overlie alluvial plain deposits of Late Pleistocene -Early Holocene age (Pechlivanidou et al., 2014). Within this succession 14 C determinations indicate a marine transgression rate of approximately 3.5 m year À1 for the Early Holocene. Maximum transgression pushed the shoreline 6-7 km to the west of its present location, inferred by the lateral extent of shallow marine deposits (i.e., FA3, see Fig. 3b). Progradation of the Sperchios delta since~8000 cal. year B.P. and the current shoreline position indicate an average regression rate of~1 m year À1 over this period.

METHODOLOGY
We begin our analysis with the deltaic depositional system, where we have particularly good constraints (c.f. Pechlivanidou et al., 2014), and work progressively upstream by analysing the onshore fluvial system and ultimately quantifying the upland sediment sources. These different components are then brought together in a mass balance calculation for the whole erosional-depositional system in the Sperchios basin. The methods outlined below are summarized in a work flow diagram (see Fig. 2).
A minimum estimate of the volume of sediment preserved in the delta is obtained from boreholes that penetrate the transgressive -regressive succession of Holocene sediments (Fig. 3). We use these data to delineate the transgressive surface over which sediment was deposited during the Holocene and, by subtracting this 3D surface from the present-day topography based on a 5 m resolution DEM, we obtain an estimate of the volume preserved beneath the delta plain (Fig. 3c,d). However, to place constraints on the total (onshore and offshore) volume of the delta we implement the basin-filling numerical model Sedflux2D (Syvitski & Hutton, 2001;Hutton & Syvitski, 2008) to model the Holocene development of the delta. This model works by specifying an input sediment flux (volume, grain size, density and porosity) and outputs the thickness and the grain size variations of basin stratigraphy that can be compared with observations. The modelled profile is indicated in Fig. 3a and the input parameters are given in Table 1. Approximating the Fig. 2. Work flow diagram showing the methodology followed in this study to analyze the Sperchios source to sink system. The upper part of the diagram refers to the erosional system and depicts the methods used to quantify the spatial distribution and the characteristics of sediment source areas. The lower part of the diagram refers to the depositional system and depicts the methods used to quantify the dynamics of the sediment routing system and the volume of the Holocene Sperchios basin fill.
[Colour figure can be viewed at wileyonlinelibrary.com] geometry of the delta using a 2D model is justified in this case by the fact that it is largely confined to build axially by the rift bounding faults (Fig. 3). We include Holocene sea level variations according to that proposed by Lambeck & Purcell (2005) for the Aegean Sea, which is dominated by a rapid marine transgression until~6000 years B.P. Due to low wave activity in the Maliakos Gulf (Poulos et al., 1997) we ignore erosion processes and sediment reworking by waves. The initial surface along which sediment is deposited in the model is our estimate of the shape of the bathymetry at~10 000 years B.P. Spatial adjustments were made to the initial bathymetry, consistent with known rates of tectonic subsidence (Eliet & Gawthorpe, 1995;Whittaker & Walker, 2015; see Table 1). We assume a mean valley width of 7 km to take into account the cross-sectional geometry of the rift. This allowed us to go from a two-dimensional line to a volume estimate. We validate the results by comparing the model output with the stratigraphic interpretation of Pechlivanidou et al. (2014) and thereby constrain the Holoceneaveraged sediment load supplied to the delta.
The Holocene sediment volume stored in axial depocentres along the onshore part of the Sperchios rift may be estimated from available geophysical data (Fig. 1b) and knowledge of the age of the rift. However, this approach assumes average sedimentation rates apply for the entire duration of rift basin development. Thus, to constrain better the Holocene depositional volumes, as well as to analyse the dynamics of the sediment routing system, we quantify the present-day grain size distributions for the axial river and two major transverse alluvial fans that supply sediment to the axial system (Inahos and Xerias fan, see Fig. 1 for location). We explore the relationships between sediment caliber, the amount of supplied sediment and accommodation creation along the Sperchios rift by implementing the grain size fining model of Fedele & Paola (2007), developed for stratigraphic use by Duller et al. (2010). This methodology is based on the concept that grain size distributions in gravel rivers are self-similar i.e., both the mean and standard deviation decay at a similar rate downstream, and explains reduction in grain sizes in fluvial systems as a function of sediment supply and tectonic subsidence via the processes of selective transport and deposition of sedimentary particles. The potential contribution to down-stream fining from abrasion is also considered. We estimate the coarse fraction (>1 mm) sediment caliber based on the Wolman point count technique using scaled grain size photos (Attal & Lav e, 2006;Whittaker et al., 2010Whittaker et al., , 2011 at 40 localities (see red dots on Fig. 1a). We measure the intermediate axis of~11500 clasts and we obtain cumulative frequency distributions from which estimates of the median grain size value D 50 were derived as well as the mean and the standard deviation values of the grain size distributions (following Whittaker et al., 2011).
Constraints on relative tectonic uplift rates where rivers cross active normal faults (e.g., Whittaker & Walker, 2015) enable us to make a first order estimate of the volume of sediment released from upland areas. We assume that the rate of relative tectonic uplift, U, is balanced by the rate of erosion E, at the point where the Inahos River crosses the Kobotades fault (see Fig. 1 for location). Based on our field measurements of local channel slope, S, and high flow channel width, W, we calibrate the erodibility coefficient K, in the stream-power erosion model: where m and n are positive, empirical coefficients (Whipple & Tucker, 1999), A is the upstream drainage area (as a proxy for water discharge Q) and K is a parameter that subsumes factors such as substrate erodibility and climate. We use our estimate of K to calculate the catchment-averaged erosion rates and thus the long-term sediment supply from catchments with the same bedrock lithology (in this case the Paleogene flysch; Fig. 1a). The advantage of this simple approach is that it does not require that the landscape is in steady state. The empirical channel width model (Finnegan et al., 2005) best describes our measurements of channel width so that: This relationship accounts for dynamic channel adjustment and allows variations both in channel width, W, and channel slope, S, to control incision rates in tectonically active areas (Whittaker et al., 2007;Attal et al., 2008Attal et al., , 2011. A and S were readily extracted from a high-resolution DEM (5 m) (copyright © 2012, Hellenic Cadastre). We applied Eqn (2) to every pixel along the stream network using all channels down to first order and interpolated the obtained erosion rates across the whole catchment area.
Finally, we use the statistical tool of Mudd et al. (2014), based on the integral method of channel profile analysis, to assess spatial variations in erosion rates. The integral of drainage area over flow distance produces the transformed coordinate known as v, which has dimensions of length . We map the slope of transformed channel profiles (Mv) across individual catchments. In addition, we compare values of v on opposite sites of the main Sperchios drainage divide for all catchments with a base-level at the coast, following the approach of Willett et al. (2014), in order to assess whether the size and extent of upland source areas may have changed as a result of drainage reorganization.

Volume of sediment preserved in the Sperchios delta
The relief of the present-day Sperchios delta plain, the meandering fluvial domain, and the 3D geometry of the transgressive surface (TS) over which sediment was deposited during the Holocene are shown in Fig. 3c,d. The maximum depth of the TS (~50 m below m.s.l.) occurs close to the Thermopylae fault segment, consistent with geophysical constraints (see dotted line in Fig. 3c) and the asymmetric graben geometry. The difference between the topographic surface and the TS surface ( Fig. 3c) indicates a minimum estimate of the Holocene delta volume of~0.5 9 10 10 m 3 as it only accounts for the volume preserved in the delta plain.
To account for the amount of sediment that lies in the subaqueous part of the delta, we use Sedflux2D to model the Holocene delta development (see Figs 4 and 5). The value of sediment load (q s ) that we use in the initial model run (i.e., 1.0 9 10 6 m 3 year À1 , Fig. 4) is greater than the estimate from the volume calculation for the delta plain only as this is an under-estimate. We then test this assumption below (see Fig. 5). The cross-section of predicted grain size variation (Fig. 4a) depicts the transgressive to regressive geometry of the modeled Sperchios deltaic succession in a NW to SE direction. Facies associations (FA) recognized from borehole data (Fig. 3b) are comparable with model predictions in terms of the overall geometry, grain size and thickness. Medium to very fine silt and clay sediments (5-8 phi, i.e., 31-3.9 lm) overlie the pre-transgressive terrestrial deposits (FA1, in Fig. 3b) and reflect the coastal and distal prodelta transgressive sediments observed in the stratigraphy of the Sperchios delta (FA2 and FA3 I , in Fig. 3b). The total transgressive succession has a maximum thickness of approximately 25 m, which also matches field observations. Fine sand to coarse silt deposits (3-5 phi, i.e., 125-31 lm) overlie the transgressive sediments (Fig. 4a). These deposits depict a maximum thickness of~30 m and comprise an overall upward shallowing lithological succession that reflects the highstand deposition (i.e., delta front and lagoonal deposits) observed in the published stratigraphic data (e.g., FA3 II and FA4, in Fig 3b). The Holocene delta plain development is characterized by coarse to medium sand (2 phi, i.e., 250 lm) in Sedflux2D simulation. The model output does not fully reproduce the geometry and thickness of the floodplain deposits (see FA5, in Fig. 3b), but this does not significantly affect our volume estimate.
The cross-section of sediment age (Fig. 4b) shows the modelled temporal evolution of the Sperchios deltaic succession and the predicted distribution of sediment age. Age constraints derived from dating of shallow marine fossils collected from borehole samples (Pechlivanidou et al., 2014) indicate a succession from early to late Holocene and match the model predictions within a range of AE 700 years. The position of the shoreline through time, shown by the chronostratigraphic plot (Fig. 4c), enables us to estimate shoreline migration rates and verify that they are also consistent with the rates indicated by the field data. In addition, the timing and position of the maximum flooding (i.e., 8000 years B.P. at a distance of~6-7 km further west) agrees with the observed stratigraphy of the Holocene deltaic succession (see Fig. 3b). Based on these model results, calibrated using grain size analysis of core samples (see Table 1), we estimate a volumetric supply of 1.0 9 10 6 m 3 year À1 of sediment has been delivered and stored in the Holocene delta plain and subaqueous realm. In addition, our Sedflux modelling of the delta enables us to place tighter constraints on tectonic subsidence rates in this portion of the rift and indicate that the rate increases across strike from~0.5 mm year À1 , close to the Lamia fault on the northern margin, tõ 1.5 mm year À1 in the proximal hanging wall to the Thermopylae fault (Table 1).
To assess this result we conduct sensitivity tests (Fig. 5) where we vary the initial value of sediment load (q s ) over a range of AE 50% (q s = 2 9 10 6 m 3 year À1 (Fig. 5a,b) and q s = 0.5 9 10 6 m 3 year À1 (Fig. 5c,d)). All other input parameters are kept constant. Neither scenario matches the observations. In the case where we increased the value of q s , the facies associations are shifted basin-wards and the position of the shoreline at the end of the simulation is located further east from its present location, thus implying a greater regression rate, inconsistent with the field data (Pechlivanidou et al., 2014). Moreover, regression commences almost 1000 years earlier than the field data suggest. In contrast, in the low sediment supply scenario ( Fig. 5c,d), the position of the shoreline is 8 km westwards from its present location and regression commences at a lower rate almost 1000 years later (i.e., from 7000 years B.P.) than in our initial model run and the field data suggest. We therefore conclude that our estimated volumetric supply rate of 1.0 9 10 6 m 3 year À1 of sediment to the delta is reasonable.
Volume of sediment stored in the alluvial plaingeophysical constraints Using geophysical constraints that indicate hanging wall stratigraphic fill thicknesses (see basement relief map, Fig. 1b) combined with information about the age of the rift (Goldsworthy et al., 2002) we can estimate approximate volumetric sedimentation rates along the rift where it is occupied by the Sperchios River. This calculation assumes that sediment rates have remained constant over time and thus provides only a first order constraint. For example, if the rift basins in this area formed~3.6 Ma (Goldsworthy et al., 2002) then the average volumetric sedimentation rate, for the hanging wall sub-basins adjacent to the Sperchias and Kobotades faults segments combined, is (9.5 9 10 10 )/(3.6 9 10 6 ) m 3 year À1 = 2.6 10 4 m 3 year À1 (for basin volumes see Fig. 1b). A maximum estimate of the rate is obtained if we assume that most of the offset on the basin bounding faults has accumulated since~1.6 Ma (Whittaker & Walker, 2015), i.e., (9.5 9 10 10 )/(1.6 9 10 6 ) m 3 year À1 = 5.9 9 10 4 m 3 year À1 . These rates imply that the volume of material deposited over the Holocene (10 kyrs) in this part of the rift is in the range 2.6-5.9 9 10 8 m 3 . Note that these volume estimates are nearly 2 orders of magnitude lower than those inferred for the Sperchios delta, consistent with the smaller size of the hanging wall basins and lower throw rates along the Sperchias and Kobotades fault segments (Fig. 1b).

Volume of sediment stored in the alluvial plain -rates of downstream fining
An alternative way to quantify Holocene depositional volumes, more relevant to the recent history of depositional processes operating within the rift is to use the grain size fining model of Fedele & Paola (2007) (see Methodology). We use this model to obtain an estimate of the initial volumes (Q so ) of the coarse sediment fraction supplied to the axial river and to the two largest transverse alluvial fans (Fig. 1a) using published constraints on rates of tectonic subsidence r(9) (e.g., Whittaker & Walker, 2015; see Figs 7b and 8c,d) plus our measurements of down-system grain size variations (Fig. 6). This approach not only provides an estimate of the total volume of gravel deposited along the rift axis but also provides additional constraints on the spatial distribution of deposition and thus the dynamics of the sediment routing system that supplies the Sperchios delta.
The grain size distributions of active gravel bars observed along the braided domain of the axial Sperchios River reveal fining downstream (Fig. 6a). The mean D 50 , at the western tip of the rift is 57 AE 4.75 mm. Over the first~30 km of downstream distance the mean grain size shows no systematic variation but at distances > 30 km downstream, in the hanging wall to the Kobotades fault, there is a pronounced decrease towards the east (Fig. 6a). The gravel front is located at a downstream distance of 53 km, approximately coinciding with where the channel changes from a braided to a meandering morphology. Both Inahos and Xerias alluvial fans also fine down-system from the fan apex (Fig. 6b,c, respectively) particularly over the first few kilometers of downstream distance.
According to the theory of Fedele & Paola (2007), grain size distributions in gravel rivers are self-similar with a constant value for the coefficient of variation, C v . The grain size distributions of all our samples approximately match the theoretical prediction, justifying the use of the selective deposition theory to model our grain size data. In the supplementary file, the data used to calculate C v as well as the similarity variable (ξ) are presented. Along the braided portion of the axial Sperchios River we find that C v = 0.64 AE 0.1, whereas the Inahos and Xerias alluvial fans are characterized by C v~0 .85-0.88.
Grain size modelling -Axial Sperchios river Figure 7 presents the grain size fining model results for the axial Sperchios River. For simplicity, we assume that tectonic subsidence r (v) increases linearly from west to east along the rift axis, from~0 to 1 mm year À1 (see Fig. 7b) based on published constraints on fault throw rates along the Sperchias and Kobotades fault segments (Whittaker & Walker, 2015) and the gradual increase in extension rate with distance along the rift from the tip (see Background -Tectonic setting; Goldsworthy et al., 2002). Using a non-linear increase (e.g., Cowie & Shipton, 1998) does not significantly change our results (see, for comparison, a stepped increase Fig. S2).
The grain size fining model is based on a 2D calculation and thus we multiply the result by the active fluvial valley width to obtain the volumetric sediment supply in m 3 year À1 . We use the initial median grain size value that we obtained from our grain size data (i.e., D 50 = 57 AE 4.75 mm; Fig. 6a). The dimensionless parameter F qs (Fig. 7) is the ratio of sediment supply (Q s ) to accommodation creation due to tectonic subsidence (r (v) ). When F qs = 1 the system is completely filled with coarse sediment (i.e., gravels) at the rate that accommodation is generated. Values of F qs >1 imply an overfilled system and values of F qs <1 imply that the system is underfilled (Duller et al., 2010). All of the model curves shown in Fig. 7 have a convex-up shape and the main difference between these curves is the predicted position of the gravel front. The measured grain size data (black dots) and the position of the gravel front are best described by F qs % 1 (see red line in Fig. 7a) although there is some scatter that can be attributed to transverse sediment input. Even if the initial grain size is lower (e.g., 45 mm), F qs % 1 describes well the downstream variation. Specifically, the linear increase in tectonic subsidence rate along strike assumed here (Fig. 7b) predicts that grain size varies little over the first~30 km of downstream distance and then decreases rapidly close to the gravel front, consistent with the overall pattern of measured grain sizes (Fig. 7a). In contrast, a spatially uniform subsidence rate of 0.5 mm year À1 would predict gradual  Fig. 6). Black dots represent measured grain sizes and solid lines represent predicted grain size distributions for different values of the dimensionless parameter F qs . The curve for F qs = 1 and with the gravel front set at 53 km downstream is shown with a red solid line. The initial volume of the gravel fraction (Q so ) supplied to the axial system is also shown. Note that the amount of gravel decreases downstream due to mass extracted from the system. Grey box indicates the area of lateral sediment input from the Inahos and Xerias fans. fining over the entire downstream distance and a less abrupt gravel front (Fig. S2).
We also considered abrasion as an alternative potential mechanism for the downstream variation in grain size, using the model of Attal & Lav e, 2006 (see Fig. S2). However, a mass loss per kilometer of 4-10% would be required to explain the observed amount of fining, which is high compared to laboratory estimates of abrasion rate (e.g. Attal & Lav e, 2009). Moreover, the abrasion model predicts a concave-up shape to the grain size trend and thus is inconsistent with what we observe (compare Figs 7 and S2). We cannot exclude abrasion as a contributing factor to grain size reduction but the independently-constrained west-to-east increase in subsidence rate (see Background) is able to account for the main features of the fining trend along the axial river. By ignoring abrasion we may be underestimating the amount of gravel supplied by upstream source areas so our results are minimum estimates (see Summary and Discussion).
The F qs = 1 curve implies that the basin is filled at exactly the rate accommodation is created and equates to a total gravel supply of Q so = 1.9 9 10 4 AE 0.2 9 10 4 m 3 year À1 . Here we assumed an active fluvial valley width of 2.0 AE 0.2 km and that the subsidence rate in the centre of the hanging wall basin is half the maximum rate along the southern margin of the rift. This gravel volume is slightly lower but of similar order of magnitude to the independently derived geophysical estimate (i.e., 2.6-5.9 9 10 4 m 3 year À1 ; see above), which increases our level of confidence in this result. In this interpretation, Fig. 8. Grain size fining model results for the Inahos fan (a) and Xerias fan (b) (BB' and CC', see Fig. 6). Preferred model predictions are shown with red solid lines. The initial gravel supply (Q so ) and the dimensionless parameter F qs that fit the measured grain size data on both fans are also shown. Model runs performed using an exponential decrease in subsidence rate from the apex to the toe of the Inahos and Xerias fans, which is shown in (c) and (d), respectively. Red arrow indicates the Kobotades fault. (e) and (f) show the percentage of gravel bypasss (%) down-fan Inahos and Xerias, respectively. Note the percentage of sediment bypass to the axial river by the end of each system length (i.e., at the fan toes). [Colour figure can be viewed at wileyonlinelibrary.com] gravel is progressively extracted into stratigraphy until the gravel in the system is exhausted and the transition to the meandering channel occurs (Fig. 3a). It explains both the shape of the fining trend in the down-stream direction and why only the finer material (sand, silt and clay) reaches the delta plain to form the fine-grained Sperchios deltaic succession.
The curve F qs = 1 (Fig. 7a) also predicts that, where the axial river is joined by the transverse system of Inahos, i.e., at~28 km downstream (Figs 1a and 7a), only 25-30% of the gravel (~5 9 10 3 m 3 year À1 ) derived from upstream has been extracted into the stratigraphy along the hanging wall to the Sperchias fault segment. The scatter in the grain size data makes it difficult to constrain the percentages precisely but most of the gravel (>70%; 1.4 9 10 4 m 3 year À1 ) is deposited along the basin bounded by the Kobotades fault segment. In order to investigate this conclusion further, and to test the sensitivity to valley width, we apply the grain size fining model from the point where the Inahos River joins the Sperchios River (Figs 1 and 7a,c). We use the mean measured grain size (i.e., 45 mm) observed near the toe of the Inahos fan and assume a linear increase in subsidence rate from 0.5 to 1 mm year À1 along this section of the rift axis. This model (Fig. 7c) again shows a good fit between measured and predicted grain size data for F qs = 1 with the observed location of the gravel front, and furthermore implies a volume of coarse sediment extracted into stratigraphy of 1.4 9 10 4 -3.4 9 10 4 m 3 year À1 . This reflects a range of estimates of the active fluvial valley width along this section of the rift (2.0-5.0 km); the higher value therefore represents an upper estimate of the gravel extracted along the Kobotades fault segment.

Grain size modelling -Transverse alluvial fans
In order to account for the gravel trapped in the transverse alluvial fans that feed into the axial river (see Fig. 1), we again apply the mass extraction modelling methodology. The down-system widening of the fans is taken into account in these calculations (D'Arcy et al., 2016). The results of the model are shown in Fig. 8a,b for the Inahos and Xerias fans, respectively. We assume that where the Inahos fan develops, in the zone of linkage between the Sperchias and Kobotades fault segments, the maximum subsidence rate along the fault is 1 mm year À1 , whereas the rate along the central part of the Kobotades fault segment where the Xerias fan develops is 1.25 mm year À1 (see Fig. 8c,d respectively). These rates are consistent with the upper estimates inferred by Whittaker & Walker (2015) and take into account the different structural positions of these two fans plus the fact that in general hanging wall subsidence along extensional faults is greater than footwall uplift (Armijo et al., 1996). We use an exponential decay function to describe the spatial distribution of proximal hanging wall subsidence with distance from a normal fault . The subsidence rate approaches zero at the toe of both fans to allow for the fact that accommodation at the fan toes is filled by the axial fluvial system. The median grain size value measured at the apex of the fans is used in the grain size fining model (i.e., D 50 = 52 mm for Inahos fan and D 50 = 81.5 mm for Xerias fan).
The exponential decay function successfully predicts the observed rapid fining over the first few km of downstream distance (Fig. 8a,b). The volumes of sediment supplied to these fans (Q so ), inferred from the fits shown in Fig. 8a,b, are~1.7 9 10 4 m 3 year À1 for Inahos fan and 0.8 9 10 4 m 3 year À1 for Xerias fan. The predicted grain size distribution for both fans matches the measured field data for values of F qs >1 (F qs = 3, for Inahos and F qs = 2, for Xerias), indicating that they are overfilled and that roughly 60% of the sediment released from the Inahos catchment bypasses the fan and enters the axial Sperchios River (Fig. 8e) and~50% of sediment flux bypasses Xerias fan (Fig. 8f).
The lateral sediment input to the axial river from these two sources is reflected in locally higher grain size values (e.g., at 27.5 km and 31 km downstream distances, Figs 6a and 7a) but the relatively high C v of this material means that the signal dies out rapidly downstream (Duller et al., 2010). These bypass percentages are consistent with laboratory experiments on the interaction between axial and transverse channel systems (Kim et al., 2011). Together the two fans therefore supply~1.4 9 10 4 m 3 year À1 of gravel to the axial river, which when combined with the supply coming from upstream (1.9 9 10 4 minus 5 9 10 3 = 1.4 9 10 4 m 3 year À1 ; see Grain size modelling -Axial Sperchios River) give a total of~2.8 9 10 4 m 3 year À1 , which is similar, within the uncertainty, to our estimate of gravel stored in the sub-basin to the Kobotades fault segment (i.e., 1.4 9 10 4 -3.4 9 10 4 m 3 year À1 ).
In summary, the grain size modelling indicates that 1.1 9 10 4 m 3 year À1 of coarse sediment is stored in the two large alluvial fans whereas 1.4 9 10 4 -3.4 9 10 4 m 3 year À1 , is stored in stratigraphy along the axial fluvial system. We therefore obtain an estimate of the total volumetric gravel accumulation rate of 2.5 9 10 4 -4.5 9 10 4 m 3 year À1 , or 2.5-4.5 9 10 8 m 3 for the Holocene (10 kyrs), for the transverse and axial fluvial systems combined, upstream of the delta plain. Note that this estimate is close to the lower estimate inferred from the geophysical data shown in Fig. 1b (i.e., 2.6 9 10 8 -5.9 9 10 8 m 3 ) based on assuming a constant sedimentation rate. The agreement between these independent methods increases our confidence in this result.

Onshore erosional volumes
Modelling studies suggest that fault propagation and linkage within an active rift basin affect the location of the main drainage divide and thus the volume of sediment supplied to a rift over time (Cowie et al., 2006). Although we focus on a short time interval, i.e. the Holocene, we investigated this possibility by comparing the values of the transformed coordinate v on opposite sides of the main Sperchios drainage divide for all the catchments that have a base-level at the coast, following the approach of Willett et al. (2014). Our analysis (see yellow arrows in Fig. 1 and Fig. S3) showed that >95% of the main drainage divide along the southern and western margins of the Sperchios rift appears to be stable as we did not observe any significant cross-divide contrasts in the v values. Along the northern, hanging wall margin of the half graben, v analysis could not be performed because the catchments lying to the north of the main drainage divide are internally drained and hence the base-level history is unconstrained. However, as this margin is tectonically relatively inactive the drainage divide is expected to be more stable. Thus, the total upland sediment source area has not changed significantly over the Holocene, i.e., the Sperchios River basin can be considered as a 'closed system'. Individual catchments along the tectonically active southern rift margin show evidence for local river diversion/capture (Eliet & Gawthorpe, 1995; see below) but sediment delivery remains directed towards the rift axis. Therefore, the overall mass balance for the source-to-sink system is unaffected (see Summary and Discussion).
A likely source material for the fine-grained Sperchios delta is the Paleogene flysch as it comprises interbedded layers of sandstones, friable siltstones and mudstone. It is one of the main lithologies particularly in the southwest and western parts of the study area, exposed over 54% of the total upstream drainage area (Figs 1 and 9). The similar overall relief of the largest flysch catchments, plus their location near the rift tip, suggests that they are to some extent relict features of the pre-rift topography (Figs 1 and 9).
To quantify the volume of sediment released by erosion of the flysch during the Holocene we estimate catchmentaverage erosion rates by applying the modified streampower erosion model (Eqn 2). We estimate the erodibility coefficient K using our field data of channel slope, S, and high flow channel width, W along the Inahos river (for location see Fig. 1a) and m = 0.6, n = 1.2 (see Eqns 1 and 2). We assume that river incision keeps pace with relative tectonic uplift where the river crosses the Kobotades fault and use a range of relative uplift rates of 0.5-0.75 mm year À1 (Whittaker & Walker, 2015). We thereby obtain values of K for the flysch that range between 1.5 9 10 À6 and 2 9 10 À6 m À1/2 kg À3/2 s 2 . Similar values of the order of 10 À5 -10 À6 m À1/2 kg À3/2 s 2 have been inferred for settings composed of similar lithologies (e.g., Attal et al., 2008).
Based on this calibration and applying Eqn (2) across the whole catchments area using every channel down to first order, we find that altogether the flysch catchments, which represent 54% of the total source area, account for 61% (~0.63 9 10 10 m 3 ; Fig. 9b), of the total Holocene sediment supply. However, the Inahos catchment alone produces most (~68%) of all the sediment derived from the flysch, i.e., approximately 0.43 9 10 10 AE 0.05 m 3 over the Holocene (Fig. 9b). Taking into account the volume of sediment stored in the onshore fluvial systems (2.5-4.5 9 10 8 m 3 , see Volume of sediment stored in the alluvial plain), we can argue therefore that ≥40% of the sediment that comprises the Sperchios delta (1 9 10 10 m 3 , see Volume of sediment preserved in the delta) is supplied by the Inahos catchment alone, even though it represents only 22% (Fig. 9a) of the source area of the entire Sperchios rift basin. Furthermore, these results imply an average erosion rate over this catchment (~1.5 mm year À1 ) that exceeds the relative uplift rate at the fault and indicates that the catchment is not in steady state. A hillslope and curvature analysis of this catchment (Fig. S4) reveals its incised morphology. Steep hillslopes coupled to incising channels occur not only in the footwall of the active faults but also in upstream areas of this catchment and provide supporting evidence for high erosion rates (see dashed lines in Fig. 10 and Fig. S4). In contrast, the flysch catchments located at the western end of the Sperchios rift, cover a similar proportion of the total source area (i.e.,~26%; Fig. 9a) but release a much smaller amount of sediment (~0.11 9 10 10 AE 0.012 m 3 ) and account for only~10% of the delta volume. The average erosion rate of this latter area is also lower, i.e., 0.3 mm year À1 . The contrast in implied erosion rates and sediment volumes for these two source areas within the flysch is revealed by maps of channel slope in v-elevation space (Mv) (Fig. 10). Mv is related to the ratio between erosion rate (E) and erodibility (K) (Mudd et al., 2014) if the stream power law applies. Since both areas consist of the same bedrock lithology (i.e., K % constant), higher Mv values imply higher erosion rates and vice versa. Differences in channel slope due to variations in bedload caliber can be excluded as the D 50 and D 84 are approximately the same for these two catchments (Riiser, 2016). The Inahos catchment is characterized by high erosion rates (warmer colours, Fig. 10), particularly in the eastern part, in a response to tectonic uplift in the proximal footwall of the Kobotades fault segment and in the zone of linkage with the Sperchias fault segment (Whittaker & Walker, 2015). Note that erosion rates >1.5 mm year À1 , estimated using Eqn (2) and our estimate of K (red dashed lines, Fig. 10), occur in less than half of the Inahos catchment, which represents an even smaller fraction of the total source area. In contrast, the western flysch catchment depicts lower Mv and thus lower erosion rates (cooler colours, Fig. 10), consistent with this catchment lying at the tip of the rift beyond the zone of active normal faulting, thus not experiencing fault-controlled uplift.
The calculations above provide a first order constraint on the magnitude of the eroded volumes where the bedrock is flysch and allow variations to be highlighted between catchments that differ in terms of relative tectonic uplift rate. However, to estimate the volume of sediment supplied to the rift during the Holocene from the remaining catchments across the Sperchios River basin, where the bedrock lithology is not flysch, we first note that the overall source-to-sink system has been a closed system at least over the Holocene (see Fig. S3). We then subtract the sediment volume supplied by all of the flysch catchments combined (~0.63 9 10 10 m 3 ; Fig. 9a) from the total depositional volume preserved in the onshore fluvial systems and the Sperchios delta (1.025 9 10 10 m 3 -1.045 9 10 10 m 3 ). This calculation indicates that 0.41 9 10 10 m 3 , or 39%, of the total Holocene sediment supply, comes from the remaining (non-flysch) catchments (Fig. 9b), which cover 46% of the total source area. The bedrock in these catchments is comprised mainly of limestone (along the southern margin of the basin) and ophiolite (along the northern margin), which have lower erodibilities compared to the flysch. These lithologies are seen preserved in coarse-grained alluvial fans along the rift margins but are only sparsely represented (by coarse sands and occasional pebbles within channel fills) in the Fig. 11. Schematic summary of the Sperchios source-to-sink system. River capture events (see A) lead to the development of a large catchment (see B) at the footwall of active faults. Thick red arrows indicate high sediment supply from this catchment. Axial supply from the rift tip due to high relief pre-existing topography is shown with a thick pink arrow. Grain size fines down the axial river that passes from a braided to a meandering channel. The entire amount of the coarse fraction is extracted into stratigraphy leaving a finegrained delta at the eastern part of the rift. The position of the gravel front is indicated with a red dashed line. Small red arrows show transverse gravel supply from fault segment-boundary and fault segment-center fans. [Colour figure can be viewed at wileyonlinelibrary.com] Holocene deltaic deposits (Pechlivanidou et al., 2014). Therefore, even though the Thermopylae segment is bounded along its south side by active normal faults, the limestones catchments in this area are not the dominant source of the axial fill within the rift because most of the eroded material is trapped along the basin margin (Fig. 3). This is confirmed by the borehole samples described in Pechlivanidou et al., 2014 (see Fig. 3a for location of boreholes).

SUMMARYAND DISCUSSION
A schematic summary of our results for the Sperchios source-to-sink system is presented in Fig. 11. The Sed-flux2D modelling indicated that a total sediment supply of 1 9 10 6 m 3 year À1 , of predominantly sand and silt, is needed to build the Sperchios bird's foot delta within a period of 10 000 years. We validated this estimate by comparing model output with the observed stratigraphic architecture of the delta and independent constraints on its total thickness. By using Sedflux2D we obtained better constraints on both sub-aerial and submarine sedimentation and were also able to take into account both eustatic and tectonic accommodation creation along the Thermopylae segment of the rift. The main limitation in the Sedflux2D modelling is our assumption of a constant rate in sediment supply throughout the simulation time (10 000 years). High-frequency climatic shifts during the Holocene (Zanchetta et al., 2011;Gogou et al., 2016) probably affected the rates of sediment delivery but in this study we are concerned with the Holocene-averaged supply and not the variability in supply due to climatic forcing.
Using 'v analysis' we demonstrated the stability of the main drainage divide at least along the most active, southern, rift margin and thus we are able to demonstrate that long term changes in the total sediment supply are unlikely to have significantly affected the Holocene depositional history, i.e., the Sperchios rift basin is a 'closed' system. The boundaries of individual catchments along the southern rift margin do show evidence for being unstable, consistent with the active tectonic setting (e.g., Cowie et al., 2006), and there is field evidence for local river capture (e.g., Eliet & Gawthorpe, 1995;Fig. 10). Although individual catchments probably have supplied a variable amount of sediment over time, the timescale of this variation is set by the landscape response to fault growth and particularly segment linkage, which is thought to have occurred~1.6 Ma (Whittaker & Walker, 2015) and therefore does not influence significantly the sediment supply during the Holocene. Furthermore, we are concerned here with the overall sediment budget for the entire source-to-sink system, not the fluctuations in the volume of sediment derived from specific catchments that might arise due to river capture. In summary, therefore, the overall source-to-sink system of the Sperchios rift has remained a 'closed system' over the timescale of the Holocene.
Our grain size modelling of the alluvial fans and braided axial river indicates that a linear increase in the rate of hanging wall accommodation creation from west to east along the rift axis and a total gravel supply of 2.5 9 10 4 -4.5 9 10 4 m 3 year À1 can explain the observed downstream grain size fining trend and the present-day position of the gravel front near the eastern tip of the Kobotades fault segment. Where the gravel is eventually exhausted there is an associated downstream change in the fluvial morphology from a braided to a meandering channel and mainly sand and silt only are ultimately transported to the delta. Changes in tectonic subsidence rate through time along the rift could lead to variations in the position of the gravel front, e.g., if more (or less) of the coarse material is extracted in to stratigraphy at the rift tip. Our grain size measurements only reflect characteristics of the modern river and there is uncertainty about the active fluvial valley width. However, our volume estimates compared well with those inferred from gravity data (Fig. 1b) and estimates of the age of the rift. In fact, Whittaker & Walker's (2015) preferred tectonic model for the evolution of the Sperchios rift (extension initiated~3.6 Ma and rates of fault slip increased by a factor of 93 at~1.6 Ma) would imply a volumetric sedimentation rate since~1.6 Ma of 4.2 9 10 4 m 3 year À1 for the Sperchias and Kobotades segments combined, which is very close to our upper estimate. This not only lends confidence to our results but also suggests that the pattern of tectonic subsidence, at least along this part of the rift, has remained relatively stable over long time periods.
Our grain size analysis of the two main footwallsourced alluvial fan systems suggests, in addition, that location of fluvial systems relative to fault segmentation, and the associated variations in relative tectonic uplift/ subsidence, influence gravel delivery to hanging wall depositional systems. We found that the catchment that feeds the Inahos fan, through the zone of linkage between the Kobotades and Sperchias fault segments, produces approximately double the amount of gravel compared to the Xerias catchment, located near the centre of the Kobotades fault segment, due to its much larger drainage area (i.e., Q so~1 .7 9 10 4 m 3 year À1 for Inahos and Q so~0 .8 9 10 4 m 3 year À1 for Xerias; see Fig. 8a,b). However, the Xerias catchment produces coarser material and a higher gravel fraction due to its location in an area of higher uplift rates near the central part of the fault segment, i.e., for Xerias D 50 = 81.5 mm and the gravel fraction is~16% whereas for Inahos, D 50 = 52 mm and gravel represents~4%. The overall gravel fraction of the entire Holocene depositional system is estimated to be 3-5% of the total sediment and (c) to illustrate the impact of sediment supply characteristics and rate of accommodation creation on depositional architectures within rift basins. Fault-controlled subsidence along rift margins increases from (a) to (c). Pre-existing topography increases from (c) to (a). Coarse-grained sources characterize (a) and (c) and finegrained sources characterize (b). Note the change of the location of the main drainage divide from distal in (a) to proximal in (c). In rift setting shown in (a), the sediment routing system is characterized by an axially flowing braided river that interacts with transverse fans emerging from the tips of fault segments and forms a coarse-grained delta. In rift setting shown in (b), the axial river forms meandering belts and a fine-grained delta. Alluvial fans and fan deltas prograde into the basin and interact with the axial river. In (c), the rift is characterized by a marine basin. Footwall-sourced fan deltas are building aggradational units close to the border fault zones at both rift margins. [Colour figure can be viewed at wileyonlinelibrary.com] supply. However, this is a minimum estimate because abrasion may have also contributed to reducing grain size and, furthermore, there are other alluvial fans in the Sperchios basin that do not feed the delta (Fig. 1a). This estimate of the gravel fraction is consistent with previous work (Syvitski, 2011) but our study demonstrates that there is a strong spatial variation in gravel inputs into the source-to-sink system.
Many source-to-sink studies use empirically-derived models such as the 'BQART' model of Syvitski & Milliman (2007) to predict sediment supply rates and thus calculate sediment budgets for depositional systems (e.g., Sømme et al., 2011). However, the 'BQART' model does not capture the potentially large variations in surface processes and rates that characterize landscapes in tectonically settings such as the Sperchios rift. For example, the 'BQART' model would predict similar sediment production from the Inahos and the western flysch catchments, as both are characterized by similar drainage areas, maximum relief, lithology and climatic conditions. In contrast, our analysis suggests that they differ in terms of sediment production by about a factor of 94 (Fig. 9b). Our calculations reveal that nearly 70% of the sediment supply derived from all the flysch catchments combined comes from the Inahos catchment, which represents less than half the area where flysch is exposed. This catchment, located in the mutual footwall of the Kobotades and Sperchias fault segments (see B on Fig. 11), exhibits the highest erosion rates in a relatively small part of this catchment located in the proximal footwall to the Kobotades fault. This catchment experienced a doubling of its drainage area when the main channel captured the upper reaches of the catchments draining the footwall of the Sperchias fault segment (see star on Fig. 11). The capture event is well-documented by an abandoned alluvial fan (Fig. 11), emerging from the footwall along Sperchias fault segment, for which the source area is no longer evident (Eliet & Gawthorpe, 1995). The cause of the capture is most likely related to fault segment linkage that occurred~1.6 Ma (Whittaker & Walker, 2015) and led to a change in the pattern of footwall uplift. Thus, we can attribute the high sediment flux from Inahos catchment to a transient landscape response, over a timescale of 1-2 million years, in response to an increase in relative tectonic uplift in the linkage area as well as an increase in drainage area. In contrast, the sediment supply from the western catchments is a consequence of the pre-existing (i.e., pre-extension) topography beyond the rift tip as tectonic uplift rates in this area are low.
Finally, by combining the evidence that the Sperchios rift has been a 'closed' source-to-sink system over the Holocene, with our estimates for the sediment supply from all of the flysch catchments, and the total depositional volume in the fluvial-deltaic system, we are able to show that ≥ 40% of the sediment that builds the Sperchios delta is supplied by the Inahos catchment alone even though it represents ≤22% of the entire source area. The fine grained character of the delta is thus due to the combination of (1) the dominant source area being in the flysch plus (2) the trapping of coarse material within transverse alluvial fans and (3) deposition of gravel bars and other channel sediments along the axial river within the Sperchias and Kobotades segments of the rift.

Implications
This study allows us to identify and assess the relative importance of key controls in the development of the Sperchios rift source-to-sink system: (1) the role of preexisting topography in influencing the location of the main drainage divide in the area of the rift tip, (2) bedrock lithology and its influence on the grain size of source material delivered to the rift, and (3) lateral variations in the rate of tectonic uplift/subsidence that control patterns of erosion and deposition. By generalizing these results, we can predict the response of the shoreline and the gravel front to the volume and characteristics of supplied sediment and to accommodation creation, thus improving our broader understanding of sequence evolution in extensional settings. Figure 12 shows three schematic block diagrams of rift settings, based on generalizations of the Sperchios rift itself, where tectonic accommodation creation increases (left-hand axis; from top to bottom). We also allow for a variation from the case of an asymmetric half-graben to the case of a symmetric graben. At the same time, the relief of the pre-rift topography increases (right-hand axis; from bottom to top), which has the effect of shifting the main drainage divide from a location in the proximal footwall of the rift-bounding faults to a more distal position as a result of a relatively mountainous landscape that existed prior to the initiation of extension. Furthermore, we allow for variations in source lithology (e.g., limestone, ophiolite, Fig. 12a,c vs. flysch, Fig. 12b) that determine the relative amounts of coarser vs. finer sediment supply to the rift.
In the case where the rift is characterized by low rates of accommodation creation and high palaeotopography (Fig. 12a), so that the main drainage divide is at a distal location, large volumes of sediment are supplied to the rift tip. In this scenario, and assuming that the source area supplies relatively coarse grained material, extensive alluvial fans and a braided channel domain will be developed and a coarse-grain delta will form at the shoreline. In the second case scenario (Fig. 12b), the main drainage divide is at a more proximal position, controlled by footwall uplift along the rift-bounding normal faults, and hence less sediment is supplied to the rift tip. In this scenario, if we further assume that the source area is dominated by flysch and that the coarse sediment fraction is trapped entirely in hanging wall alluvial fans close to the rift margins (Fig. 12b), then a more extensive meandering axial fluvial channel forms and a finegrained delta develops where it debouches into the sea. However, the reduced volume of the sediment supply means that the delta forms closer to the rift tip compared to the present-day position of the Sperchios delta. In the third case scenario (Fig. 12c), subsidence occurs along both rift margins (i.e., a symmetric rift) as well as the total sediment supply being limited by the proximal position of the main drainage divide. Coarse sediment, derived from steep catchments draining the scarps of the basin bounding faults is mainly trapped along the rift margins in transverse fan-deltas and subsidence exceeds sediment supply overall. These conditions favour the development of an underfilled open marine or lacustrine basin.

CONCLUSIONS
The aim of this study has been to understand controls on sediment supply, transport and deposition within an active rift setting from a source-to-sink perspective. Via our analysis of the Sperchios rift basin, in central Greece, we demonstrate explicitly how characteristics of the sediment supply, the rate of accommodation creation and pre-rift topography, control depositional patterns and facies development. We show the importance of integrating different data types and modelling approaches with field observations in order to understand how complex source-to-sink systems function. Specifically, we use a numerical model to quantify sedimentation rates in an area where accommodation creation is controlled by both sea-level variations and tectonics, grain size analysis to quantify spatial variations in gravel production and storage along the transport system, the stream power model to estimate average erosion rates, and 'v analysis' to reveal spatial variations in erosion rates as well as to investigate the stability of drainage divides. Combining all of this information allows us to calculate the sediment budget for the offshore and onshore depositional system and to perform a mass-balance analysis for the Sperchios rift over the Holocene.
We demonstrate that the Sperchios rift comprises a 'closed' system at least over the Holocene, so that the sum of the sediment volumes deposited at the delta (~1 9 10 10 m 3 ) and along the routing system (~4 9 10 8 m 3 ) during the Holocene balances the sediment volumes released from the upland source areas. Tectonic subsidence modulates the characteristics of the sediment supply leading to a significant grain size fining along the axial system. All the coarse material is extracted into the stratigraphy due to selective deposition, resulting in the formation of an extensive meandering belt (>15 km) that feeds the fine-grained Sperchios delta. Approximately half of the coarse supply is produced from transverse catchments that cross the border fault zone, controlling the south margin of the Sperchios rift. Abrasion is not required to explain the grain size fining trends. Moreover, we show that one catchment in particular (Inahos) covers only 22% of the Sperchios upland drainage area but releases >40% of the total sediment that builds the Holocene delta. High erodibility of the bedrock lithology (Paleogene flysch), active normal faulting and a long-term transient landscape response to fault segment linkage, together can explain the higher sediment supply from this catchment. The flysch is the source of the relatively large volume of silt and sand that produces the characteristic bird's foot geometry of the Sperchios delta.
Finally, the quantitative process based models used in this study provide a greater understanding of the sourceto-sink system because they not only allow quantitative characterization of source areas but also link accommodation creation and depositional volumes with grain size variation and facies development.
the axial system (black dots). Figure S3. Map view of chi (v) values calculated on the opposite sides of the main Sperchios drainage divide for all catchments with a base-level at the coast, following the approach of Willett et al. (2014) and using m/n = 0.5. Figure S4. Slope map of the Inahos flysch catchment with all slopes <25°shown with grey colour and slopes >25°shown with orange to red colours.