Predicting river mouth location from delta front dip and clinoform dip in modern and ancient wave‐dominated deltas

Wave‐dominated deltas and strandplains make up the majority of the world’s depositional coastlines, provide an important record of sea‐level change and serve as hydrocarbon reservoirs worldwide. Satellite imagery forms a great source of data on the recent depositional history of modern deltaic systems. In the subsurface, three‐dimensional seismic and well data make the three‐dimensional assessment of large‐scale deltaic reservoir bodies possible but struggle to resolve internal heterogeneities away from wells. To bridge this gap in characterizing deltaic sedimentation, this study combines measurements from both the shallow, high‐resolution section of three‐dimensional seismic data of the Eocene Halibut Delta in the Outer Moray Firth, offshore Scotland, with information from Google Earth’s satellite imagery and digital elevation model on south‐east Brazilian river deltas (São Francisco, Jequitinhonha, Doce and Paraíba do Sul) to present a means of predicting the location of fluvial sediment input points with respect to clinoform geometry. The key measurement for this study is the delta front and clinoform dip which has been measured at multiple locations along strike of the coastline of the examined deltas. Dip decreases away from the inferred river mouth for all deltas by 50% within 7.2 km. The river mouth location was inferred from the position of palaeo‐channels visible on the delta top and coarse sediment recorded in grab samples offshore for the south‐east Brazilian deltas, and from imprints of palaeo‐channels on attribute maps for the Eocene Halibut Delta. In summary, this study found that delta front dip is steepest at the location of the river mouth and decreases, along with grain size, away from it. This suggests that high dip values correlate with the proximity to the channel mouth and can be used to predict fluvial channel facies in modern deltaic systems and subsurface reservoirs.


INTRODUCTION
Wave-dominated deltas and strandplains comprise 62% of the world's depositional coastlines (Nyberg & Howell, 2016). They provide an important record of sea-level change in the recent past (Dominguez et al., 1987;Bhattacharya & Giosan, 2003;Anthony, 2015) and they serve as arable living space for a large part of the world's population (Small & Nicholls, 2003;Nicholls et al., 2007). Such systems are also important hydrocarbon reservoirs in the subsurface (Kantorowicz et al., 1987;Løseth & Ryseth, 2003;Howell et al., 2008;Hampson et al., 2015). The modern and geologically recent depositional systems provide valuable data for analogue studies to understand the facies distribution and the depositional history of these more deeply buried intervals.
Characterization of modern delta front systems starts with maps and bathymetric data. It is augmented with near-surface geophysical data such as ground-penetrating radar (Rocha et al., 2013;Hein et al., 2013) or shallow seismic data (Schwamborn et al., 2002). These studies are costly to carry out and the number of acquired lines is often quite low. The recent availability of free global remote sensing data and elevation data made available through Google Earth© in 2005 has added considerably to current study of modern depositional systems (Hartley et al., 2010;Nyberg & Howell, 2016;Evenstar et al., 2018;Hartley et al., 2018;Santos et al., 2019).
In the subsurface, data availability has progressively improved over the last 40 years. Twodimensional seismic lines available in the 1960s and 1970s provided the first insight lines, typically spaced a kilometre apart (Cartwright & Huuse, 2005). The advent of three-dimensional seismic data in the 1980s and 1990s made it possible to view features in the subsurface in 3D with tens of metres to metres accuracy (Cartwright & Huuse, 2005). Three-dimensional seismic data undergoes continued improvement with typical bin spacings of 12.5 m and long offsets providing very high-resolution data. These surveys are typically aimed at imaging reservoir depths and the upper portion of the data is largely ignored. However, the shallow, high frequency section of conventional 3D seismic data is an often-overlooked resource that offers high resolution insights into sedimentary and stratigraphic architecture.
This paper combines data from modern systems with data from the shallow portion of conventional seismic to examine wave-dominated deltas. Specifically, variability in clinoform dip angles along a series of wave-dominated delta fronts and their relationship to fluvial input points is analysed. Using data from both modern and ancient systems allows for combining the different strengths of these types of data. Satellite imagery and elevation data from the modern systems examined along the south-eastern coast of Brazil offer good control on the present-day facies distribution on the delta top, as well as some insight into the recent past. Within the modern systems, delta front dip is inferred from bathymetry and there is no insight into the internal architecture of the delta front deposits. Geometric data based on 3D seismic data from the Eocene Halibut Delta in the Outer Moray Firth of the North Sea Basin (Zimmer et al., 2019) provides information on the delta front development through time, although imaging the facies distribution on the delta top in these systems can be problematic. Combining both types of data enables the relationship between clinoform dip development in multiple sections along strike, the location of fluvial input points, and the facies distribution on the delta top to be uncovered. This relationship can inform reservoir modelling as well as sampling of modern systems to investigate their recent past.

CLINOFORMS
Clinoforms are basinward dipping surfaces which record the palaeo-depositional surface. They occur at a variety of discrete scales from the very large (continental margin scale) to the much smaller systems that are characteristic of shallow-marine deltaic and shelf-edge deposits which are the focus of the current study (Rich, 1951;Johannessen & Steel, 2005;Patruno et al., 2015a). Clinothems are packages of sediment bound above and below by a clinoform (Rich, 1951). The stacking pattern of clinoforms as well as the onlap, toplap and downlap that define their terminations have been studied along 2D seismic lines applying the concept of seismic stratigraphy ever since the technique's advent in the 1970s (Vail et al., 1977). The height and dip of clinoforms has been used as a means of distinguishing between the different scales with deltaic systems typically tens of metres high and dipping at <15°, and shelf edge clinoforms typically hundreds of metres high with clinoform dips <6° (Johannessen & Steel, 2005;Patruno et al., 2015a). An offspring of seismic stratigraphy and the usage of 2D seismic cross-sections is the development of the shoreline trajectory concept by which the upper rollover point of successive clinoforms is connected by a trajectory (Helland-Hansen & Martinsen, 1996). The shoreline trajectory represents the migration path of a shoreline or shelf edge and can be used in its most simple form to classify whether the system is regressive (migrating seaward) or transgressive (migrating landward) (Helland-Hansen & Martinsen, 1996;Henriksen et al., 2009;Henriksen et al., 2011). The concept has been extended to give information on sediment accumulation as well as sea-level change , uncovering the depositional system of successive clinoforms (wave-dominated or river-dominated) and their potential to deliver sediment offshore (Henriksen et al., 2009;Cosgrove et al., 2018). The two datasets used in this study are presented in the following sections, starting with the modern, Brazilian study, and then compared and discussed.

Study area
The south-eastern coast of Brazil between Recife in the north and Rio de Janeiro in the south is characterized by numerous wave-dominated deltas and shorefaces along a passive margin (Fig. 1). For this study, measurements of the delta front of four deltas along this stretch of coastline have been taken. The deltas were chosen due to their similarity with the Halibut Delta in terms of depositional process classification, grain-size distribution and delta plain area (especially São Francisco and Para ıba do Sul). Additionally, all of these deltas have been studied in the past, with data available on their offshore sediment deposits and dating of palaeochannels. From north to south the examined deltas are the São Francisco, Jequitinhonha, Doce and Para ıba do Sul river deltas. These four deltas are fine sand-dominated systems, with grain sizes ranging from fine to coarse sand, displaying a cuspate shape characteristic for wavedominated deltas (Orton & Reading, 1993). The tidal regime is microtidal to mesotidal (Table 1; Martin et al., 1993;Dominguez, 1996;Oliveira et al., 2012), with the tidal range increasing from south to north (Dominguez, 2009). The shelf width along the south-east Brazilian coast increases from 24 km in front of the São Francisco delta to 82 km in front of the Para ıba do Sul delta (Table 1). The south-east Brazilian coastline is situated within the Southern Hemisphere trade wind zone with prevalent winds coming from the north-east and south-east. The river plumes of the deltas studied here are affected by the orientation of the coast, the direction of the prevailing winds, and the resulting Ekman transport (Oliveira et al., 2012). The river plumes of the north-east/south-west oriented São Francisco and Doce deltas are perpendicular to the coast whereas the river plumes of the north-south oriented Jequitinhonha and Para ıba do Sul deltas are deflected towards a more coast-parallel direction (Oliveira et al., 2012). Longshore sediment transport influences the symmetry of wave-dominated deltas and their sediment and facies distribution. Stronger longshore drift will enhance delta asymmetry and additionally deflect the river mouth downdrift (Bhattacharya & Giosan, 2003). Sediments deposited updrift are usually more mature through higher wave influence, as opposed to the more riverine influenced sediments downdrift (Martin & Suguio, 1992;Bhattacharya & Giosan, 2003). The modern systems studied here are mostly of symmetrical plan view shape with only the Doce and Para ıba do Sul deltas exhibiting slight asymmetry (Bhattacharya & Giosan, 2003). However, a facies asymmetry through differences in the influence of waves and riverine sediment deposition is displayed by all four deltas. The São Francisco River forms the boundary between the states of Sergipe and Alagoas with the São Francisco Delta located roughly 320 km SSE of Recife. With 634 000 km 2 the São Francisco has a larger drainage basin than all other East Brazilian rivers combined (622 600 km 2 , Table 1, Souza & Knoppers, 2011). The São Francisco River delivers sediment offshore to the Sergipe-Alagoas Basin. 320 km south of Salvador, the Jequitinhonha River forms a delta in the state of Bahia and discharges into the Jequitinhonha Basin offshore. The Doce River flows through the state of Esp ırito Santo with its delta roughly 500 km ENE of Rio de Janeiro, prograding into the Esp ırito Santo Basin offshore. The delta plain of the Doce River covers an area larger than the other three delta plains combined ( Table 1). The Para ıba do Sul delta is the southernmost delta examined in this study. It is situated 260 km ENE of Rio de Janeiro and discharges into the Campos Basin offshore.

Geological history and delta development
During the breakup of the supercontinent Gondwana in the Cretaceous, South America and Africa separated following lithospheric extension and rifting Chang et al., 1992;Macdonald et al., 2003;Mohriak et al., 2008). Fully marine conditions were established at the transition from Lower to Upper Cretaceous (Albian-Cenomanian, Chang et al., 1992;Mohriak et al., 2008). While rifting along the Atlantic Mid-Ocean Ridge continues to this day, the influence of active rifting on the south-east Brazilian coastal basins investigated here ceased during the Upper Cretaceous and subsequent subsidence was due to sediment loading and thermal relaxation rather than rifting (Chang et al., 1992;Lawver et al., 1992). In the offshore section of the south-east Brazilian basins, a succession of fluvial, lacustrine and marine sediments, including a thick succession of evaporites, was deposited during the Late Jurassic to Cretaceous (Milani et al., 2007). Onshore of the south-east Brazilian basins, Cenozoic sediments directly  Table 1. Selected characteristics of the south-east Brazilian deltas. Delta plain area and shelf width in front of the river mouth were measured in Google Earth© as part of this study. The other data are derived from Oliveira et al. (2012), Souza & Knoppers (2011), Patchineelam & Smoak (1999 and Martin et al. (1993).  Andrade et al., 2003), regressive wavedominated deltas formed along the Brazilian south-east coast. These deltas were made up of 'regressive sandsheets' (Martin & Dominguez, 1994) and resembled the deltas developing at the present day, with beach ridges prograding basinward. This phase of regression lasted for most of the Upper Pleistocene until a transgression submerged the deltaic deposits from the end of the Upper Pleistocene (18 ka) onward into the Holocene (5.1 ka) (Andrade et al., 2003). Lagoons and intralagoonal deltas developed during the 5.1 ka highstand (sea level 5 m higher than present day), submerging the Pleistocene prograding deltas and beach ridges (Martin & Dominguez, 1994). After this highstand, sea level dropped along the south-east Brazilian coast, causing the lagoons to develop into mangrove swamps. The subsequent deposition of regressive sandy beach ridges continues to the present day (Martin & Dominguez, 1994).

Methodology
The key measurement for this study is the dip angle of the delta front ('delta front dip') which is measured on the dip-parallel bathymetric profile of the delta front. The delta front dip is considered to be a proxy for clinoform dip on the delta front and thus comparable to clinoform dip measured in subsurface data. Delta front dip was measured at multiple locations along strike of the coastline of the studied deltas. To determine delta front dip, a path perpendicular to the present-day coastline is created in Google Earth© and the elevation profile along this path is displayed (Data: SIO, NOAA, U.S. Navy, NGA, GEBCO). From the change in bathymetry between the upper and the lower rollover point and the distance between them, the delta front dip can be inferred (Fig. 2). Measurements derived from remote sensing data carry a horizontal and vertical error. The vertical resolution of Google Earth's bathymetric digital elevation model is dependent on the accuracy of the underlying depth data, the cell size, and the interpolation technique used (Weatherall et al., 2015;Amante & Eakins, 2016). Because data for this study are measured in the coastal zone immediately adjacent to the coastline, it can be assumed that the depth data quality was high. South-east Brazil being close to the equator also means that data derived from satellite altimetry is of good quality due to the almost vertical path between satellite and measuring point (Weatherall et al., 2015). In water depths below 200 m a data resolution below 1 m is possible (Mayer et al., 2018). The horizontal resolution of satellite imagery data can be highly variable but is in this case assumed to be in an equal range to a recent study of the Doce River delta (between 0.5 m and 10 m, Polizel & Rossetti, 2014). Since the changes in distance and elevation measured here lie above 10 m and 1 m, respectively, horizontal and vertical accuracy is deemed sufficient to support the study's outcomes. To capture along strike variations in delta front dip, multiple measurements were taken along strike of the modern-day coastline of each of the examined deltas. Measurements were taken at an average spacing of 1.5 km along the coast for the São Francisco, Jequitinhonha and Para ıba do Sul rivers and at an average spacing of 2 km for the Doce River. This spacing was sufficiently small to identify changes in delta front dip and large enough to keep all datasets manageable and convenient to display. Clinoform dip was measured along 32 transects for the Jequitinhonha delta front, along 38 transects for the Para ıba do Sul delta front, and along 44 transects for both the São Francisco and the Doce delta fronts.

Facies and sediment distribution on delta plain and delta front
Satellite imagery allows approximate interpretation of the delta plain sediments of all four analysed modern systems. This visual evaluation was augmented with published studies to gain a better understanding of the delta's evolution.
Radiocarbon dating has been carried out on the Doce and Jequitinhonha delta plain (Dominguez et al., 1987;Rossetti et al., 2015) but is lacking for the São Francisco and Para ıba do Sul delta plains. The distribution of sediments at the delta front and further offshore has been deduced from sediment grab samples for the Doce and the Para ıba do Sul delta (Murillo et al., 2009;Quaresma et al., 2015) but is absent for the São Francisco and Jequitinhonha.

São Francisco
The active river channel of the São Francisco River has an S-shape on the delta plain and lies within a channel belt characterized by meander scrollbars. The channel sits in a central position within the delta (Fig. 3). The São Francisco River has been occupying this position for the last 5 ka (Dominguez, 1996). Longshore drift is directed towards the south-west and the beach ridges developed on the southern side of the channel are interspersed with more fine-grained riverine sediments than the beach ridges on the northern delta flank (Dominguez, 1996;Bittencourt et al., 2005). Towards the north-east and south-west two canyons are visible, although the rivers occupying them are small and do not reach the sea at present. In the location of the northern canyon, the beach ridges are cut suggesting that there was a distributary (in the location of the current Piau ı River) reaching the sea in the past just south of the headland of Pontal de Peba. Between Pontal de Peba and the river mouth of the São Francisco River, an aeolian dune belt masks the most recent beach ridge development. A similar dune belt is active to the south of the delta although the dunes here show more vegetation. Palaeo-dune fields are visible further inland of both active dune fields.

Jequitinhonha
Similar to the São Francisco River, the active channel of the Jequitinhonha River and its channel belt occupy a central position on the Jequitinhonha delta plain (Fig. 4). However, longshore drift along the Jequitinhonha delta is directed towards the north (Bittencourt et al., 2005). Beach ridges are visible in the north and in the south of the delta plain, but the beach ridges north of the Jequitinhonha River are disrupted by two meandering rivers (Pardo and Salsa rivers). Carbon-14 dating of the fluvial sediments deposited in the palaeo-channel belt yielded an age of 5.57 (AE0.15) ka (Dominguez et al., 1987). It is thought that both of these northern rivers were active during most of the Holocene and contributed to beach ridge formation (Dominguez et al., 1987;Martin et al., 1993;Dominguez, 1996). The youngest beach ridge system has been dated to 2.57 (AE0.1) ka in its most landward position and the continuity of these beach ridges towards the north suggests that both northern rivers did not supply significant amounts of sediment to the delta from 2.5 ka to the present day (Dominguez et al., 1987). South of the river the beach ridges are very uniform with only a few small channels in the far south of the delta. Measurements of delta front dip and clinoform dip are taken on the slope between the upper and lower inflection point of the delta front/clinoform. Delta front dip is measured on a bathymetric profile and clinoform dip is measured on a seismic cross-section, both are oriented perpendicular to the (palaeo-) shoreline. This orientation has been observed to capture maximum dip in the data used but does not account for local variations such as spits.

Doce
The Doce delta plain is characterized by at least four distinct palaeo-channels cross-cutting most of the delta plain (Fig. 5). Close to the escarpment enclosing the Doce River delta, the eroded remains of two older generations of beach ridges are visible. These beach ridges are truncated in a seaward direction by uniform deposits lacking distinct depositional features on satellite imagery but which have previously been characterized as interdistributary bay deposits (Rossetti et al., 2015). Areas of tropical forest surround the palaeo-channels and the active river channel. The most recent advance of beach ridges is developed along the coast in a belt which is up to 10 km wide and thins significantly towards the north (<1 km). Longshore drift along the Doce delta is not uniform and may change direction during storm events (Quaresma et al., 2015). A coast-parallel meandering river and associated lagoonal belt is developed in the north, immediately landward of the most recent beach ridge. Carbon-14 dating of the palaeo-channels yields ages of 10.8 (AE0.460) ka and 5.4 (AE0.401) ka for the southernmost channel visible on the delta plain and ages between 6.3 (AE0.541) ka and 5.7 (AE0.566) ka for the northernmost palaeo-channel (Rossetti et al., 2015). The beach ridges visible on satellite imagery are either older (>7 ka, Cohen et al., 2013) or younger than these palaeochannels, although the most landward section of the youngest beach ridge belt is speculated to be associated with the northernmost palaeo-channel (Rossetti et al., 2015). Sediment grab samples from the seabed at the delta front and offshore transition zone document coarse grain sizes (granules, coarse and medium sand) approximately 25 km north of the Doce River mouth in water depths between 10 m and 67 m (Quaresma et al., 2015). Due to the additional high carbonate content and the high density of the deposits, this sediment has been classified as relict sands belonging to a past river mouth location (Quaresma et al., 2015). Due to the high carbonate content, these sediments might be a remnant of Holocene lagoonal deposition. South of the river mouth, mud content is reported to be greater than 75% and is attributed to southward drift of a mud plume coming from the river mouth (Quaresma et al., 2015).

Para ıba do Sul
The Para ıba do Sul River is situated in a northern-central position on the delta plain. Beach ridges are developed either side of the river in continuous bands with the beach ridges south of the river crossed by several smaller streams (Fig. 6). The channel belt of the Para ıba do Sul River is relatively narrow measuring 6.5 km at its widest point. The northern edge of the delta plain is directly bordered by an escarpment cut by multiple incised canyons. In the south, the delta plain is not bounded by an escarpment but the beach ridges of the current delta pass landward (westward) into palaeo-channel deposits which are not clearly visible on satellite imagery due to the city of Campos and agricultural use of the land just south of the city. However, close to the southern coast, palaeomeander bends are preserved and further west along the coast a second set of beach ridges unconnected to the current Para ıba do Sul delta plain is visible, with the Lake Feia lying inland of these beach ridges. During the Pleistocene, the Para ıba do Sul occupied an approximately 35 km long channel trending NNW-SSE from the present site of the city Campos towards the SSE facing coastline where it contributed to beach ridge formation (Martin et al., 1985;Martin et al., 1993). Longshore transport is not uniform along the Para ıba do Sul delta, with southward longshore drift around the river mouth and northward drift along the southern and northern delta flanks (Bastos & Silva, 2003). Sediment distribution in front of the current river mouth shows predominantly coarse sand within the first kilometre offshore, extending 4 km to the north and 2 km to the south of the river mouth along the coast (Murillo et al., 2009). This coarse sand is followed by a 2 to 3 km wide mud belt in a seaward direction which stretches for at least 15 km north and southward (Murillo et al., 2009). Four kilometres offshore from the current river mouth, very coarse and coarse sand is recorded at the delta front with a tongue of fine to medium sand extending ca 10 km in a coast-parallel direction from the river mouth to the south where the surficial sediment transitions to biogenic mud (boundary corresponding to transect 21 in this study, Murillo et al., 2009).

Results on delta front dip at multiple sections along strike
Delta front dip along the south-east Brazilian deltas is not uniform but shows systematic variation. The São Francisco River has delta front dips of up to 0.32°towards the northern and the southern edge of the delta front and  shallower dips of 0.12°in the central part (Fig. 3). However, there are two outliers from this trend in the central part where the dips reach up to 0.38° (Fig. 7). Delta front dip along strike of the Jequitinhonha River delta shows three high points (Fig. 4): one in the south with 0.25°; one in the centre reaching 0.32°; and one in the north going up to 0.36°. In between those high points, dips are between 0.13°and 0.22°. The two northernmost points measured along strike also show higher dips of 0.29°and 0.37°. The Doce River has the steepest delta front dip of all deltas and the overall dip distribution has two very distinct areas of steep dip in the centre reaching up to 3.91°in the centre-north and 1.39°centresouth position (Figs 5 and 7). The rest of the along strike profile of the Doce delta shows values between 0.03°and 0.71°. In a similar manner to the Doce River delta, the Para ıba do Sul delta has two areas of high delta front dip in its centre and lower dip along the rest of the delta front (between 0.12°and 0.25°, Figs 6 and 7). The steeper dips are found in the centre-south position reaching 0.74°with the steepest dip in the centre-north position only reaching 0.32°. Both areas of steep dip of the Para ıba do Sul delta appear two-pronged with the bathymetry profile showing two shoulders of high delta front dip values with a small decrease in dip in between them.
HALIBUT DELTA, OUTER MORAY FIRTH, NORTH SEA

Study area and geological history
The Eocene Halibut Delta lies in the Outer Moray Firth east of the Scottish mainland (Fig. 8). It was documented and described in detail by Zimmer et al. (2019). The delta was deposited north of the Halibut Horst on the North Halibut Shelf. The North Sea Basin is a tripartite system with the Viking Graben to the north, the Central Graben to the south and the Moray Firth to the west. The North Sea Basin underwent multiple phases of rifting starting with the establishment of a north-south trending graben system following the collapse of the Middle Jurassic thermal dome (Ziegler, 1990;Underhill & Partington, 1993;Quirie et al., 2019). A later change in tectonic regime formed the WNW-ESE oriented horst and graben structures of the Moray Firth (Boldy & Brealey, 1990). Rifting lasted until the Lower Cretaceous and was followed by thermal subsidence of the North Sea Basin. During the Palaeocene, magmatic under-plating resulted in uplift in the area of the East Shetland Platform and the Scottish mainland in conjunction with the opening of the Atlantic Ocean (Stucky de   Mudge, 2015). During the following regression, the deltaic succession studied here was deposited. Sedimentation during the start of the Eocene was more localized than during deposition of the Dornoch Formation (Underhill, 2001). The deltaic succession is characterized by fine to coarse-grained glauconitic sand which passes basinward into marine shales of the Horda Formation (Knox & Holloway, 1992). The Oligocene to Pliocene marine shale and clay deposits of the Westray and Nordland groups overlie the delta (Deegan & Scull, 1977;Knox & Holloway, 1992). These deposits are crosscut by tunnel valleys which developed at the ice-sheet margins during Pleistocene glaciations (Wingfield, 1990;Rea et al., 2018).

Measuring clinoform dip in 3D seismic
The 3D seismic dataset utilized in this study is the PGS CNS/NNS MegaSurvey, which covers large parts of the North Sea Basin including the British, Dutch, German, Danish and Norwegian continental shelf areas from 62°29'8''N to 54°08'18''N and from 4°35'29''W to 7°52'10''E (>148 000 km 2 ). This regional 3D seismic dataset is made up of a merge of numerous datasets acquired throughout the North Sea Basin exploration history. The zero-phase normal polarity survey was available to a depth of 1 second twoway-time (TWT). The bin size is 50 m and the survey has a vertical sample interval of 4 ms. A vertical resolution of 13 m has been calculated based on a borehole-derived mean sediment velocity of 2050 m/s and a dominant frequency of 40 Hz at the examined depth. While for the south-east Brazilian deltas delta front dip has been measured along the current coastline, clinoform dip for the Halibut Delta was measured with reference to palaeo-shoreline strike interpreted for eight successive clinoform surfaces throughout the delta's development history (Figs 2 and 9). Clinoform dip was measured along multiple transects perpendicular to the palaeo-shoreline with a spacing of 405 m.

Time depth conversion, decompaction and attribute analysis
In the Halibut Delta study area checkshot data from eight wells were used for time depth conversion of the interpreted horizons upon which the clinoform dip measurements were based. Additionally, the pre-burial thickness of the deposits was determined to correct for the influence of compaction on the clinoform dip values (decompaction calculation after Allen & Allen, 2013). For decompaction purposes, the overlying sediment was treated as one layer of shaley sand using a surface porosity of 0.56 and a porosity coefficient of 0.39 (Sclater & Christie, 1980). Root mean square (RMS) amplitude was computed to image lithology on the clinoform surfaces of the individual clinothems. The RMS amplitude attribute highlights horizontal changes in amplitude which are caused by the change in acoustic impedance between neighbouring lithologies. The RMS amplitude is frequently used to image lithology in shallow and deep marine settings (Posamentier & Kolla, 2003;Posamentier, 2004;Jackson et al., 2010).

Halibut Delta clinoform dip along strike
Clinoform dip for the Halibut Delta varies along strike for each clinothem interpreted in this study, showing up to three peaks in clinoform dip angle. Clinothems 1 to 4 show three peaks along strike (Fig. 9). All four clinothems have peaks in their clinoform dip in a similar centralsouthern and central-northern position, although each clinothem has one peak that deviates from this pattern. While high clinoform dips in clinothems 1 to 4 are generally more abundant towards the south, only clinothems 2 and 4 show a peak in clinoform dip angle in the far south of the study area. Clinothem 1 has a small peak of 1.5°in the north and a two-pronged peak further towards the south reaching 2.1°. The baseline in between those peaks for clinothem 1 remains at around 1.0°. In clinothem 2 two of the peaks are more centrally located (2.7°a nd 2.5°) with one smaller peak (1.8°) located further south. Clinothem 3 has two peaks in a central southern position which both measure a maximum of 4.7°and a slightly smaller peak further north reaching 4.6°. Clinothem 4 again shows three peaks which are more spread out than in clinothem 3. The highest clinoform dip (6.5°) for this clinothem is in a central northern position whereas the peaks in the south reach maximum clinoform dips of 5.6°and 5.3°. In clinothems 5 and 7 the number of peaks in clinoform dip reduces to two whereas clinothems 6 and 8 only show one peak. Overall, highest clinoform dips for these clinothems are present towards the north. In clinothem 5 the peaks are in a central position and reach 7.5°in the north and 5.6°in the south. The highest peak along strike of clinothem 6 lies in the north and reaches up to 6.2°. Clinothem 7 has a peak reaching 7.2°in a northern position and a smaller peak towards the centre (6.8°). Clinothem 8 only shows one significant peak in clinoform dip along strike towards the north which reaches 3.1°.

Attribute analysis of the Halibut Delta
With the seismic data it is possible to examine RMS amplitudes and other attributes. In Fig. 9 low RMS amplitudes (dark blue) mark the sandy main body of the clinothems. Palaeo-channel incisions on the clinothem surfaces are relatively faint on RMS amplitude maps (Figs 9 and  10). Faint incisions are visible as low RMS amplitude bands at the delta front (Fig. 10) which could be associated with mass transport deposits originating at the location of the fluvial input points and transporting sediment down the delta front towards the offshore transition zone. The RMS maps also show two broad, lobate tongues of low amplitudes in front of the delta which extend eastward replacing the otherwise high amplitudes there. In the south, the low amplitude tongue begins with clinothem 2 whereas in the northern part, the low amplitude tongue is only present from clinothem 6 onward. These low amplitude areas extend a short distance beyond the Balder Formation palaeo-coastline and are in line with the location of highest clinoform dips along strike for most of the clinothems.
Palaeo-channel incisions on the delta plain of the Halibut Delta are faint at best. There are multiple reasons for this to be the case. Firstly, from clinothem 1 to 6 normal regression followed by forced regression took place during which sediment was scavenged from each preceding clinothem. Clinothems 7 and 8 are transgressive deposits which in turn eroded and redeposited sediment from the underlying regressive systems tract. Secondly, the sediments infilling the closely overlying glacial tunnel valleys typically have very strong reflections. This influences the spectral decomposition maps through their broad frequency content and results in a bright response, masking subtle variations on the delta top itself. In addition to that, the change in lithology between channel deposit and clinothem might not be pronounced enough to produce a sufficient change in amplitude or frequency to be visible on an attribute map.

SYNTHESIS OF RESULTS
Delta front dip is a modern proxy for clinoform dip and provides an opportunity to compare modern and ancient systems. According to Ainsworth et al. (2019), a delta body is classified as an element-complex assemblage which is made up of multiple element-complex sets representing individual delta lobes. The delta front dip measurements presented here for the south-east Brazilian deltas are taken at the delta front of the element-complex assemblage. The variations measured in delta front dip are therefore a composite expression of multiple delta lobe and mouth bar deposits (element-complex sets). In contrast to that, the clinothems in the Halibut Delta represent beach-ridge sets which are classified as element-set pairs, a constituent of an element-complex set (Ainsworth et al., 2019). Although clinoform dip and delta front dip are not measured on deposits of the same hierarchy in this classification scheme the results of both study areas are compared here. The discrepancy in scale must be considered as a measure of uncertainty that is a feature inherent to the data types used in this study. It is apparent from both datasets that dip angles are highest near fluvial input points. In order to allow a more systematic comparison, the results for each system were normalized such that the dip value at the inferred fluvial input point (marked by an arrow in Fig. 9 and by grey bars in Figs 3 to 6) was set to '1' and the clinoform dip values away from it were calculated as fractions of the maximum dip. The data were plotted with normalized clinoform dip against distance from fluvial input point for two distance brackets (Figs 11 and 12). From the location of the fluvial input point to a distance of 10 km away, clinoform dip decreases. A trendline was added to the data which shows a reasonable coefficient of determination (R 2 of 0.5). At 7.2 km away from the fluvial input point, clinoform dip halves on this trend line (marked by blue 'X' in Figs 11 and 12). The trendlines for the individual deltas vary between a high coefficient of determination of 0.7 for the Para ıba do Sul delta and Halibut Delta clinothems 7 and 8 and a low coefficient of determination of 0.3 for the São Francisco Delta and Halibut Delta clinothem 5 ( Table 2). The coefficient of determination for individual trendlines is generally higher for the Halibut Delta clinothems. From 10 to 20 km away from the fluvial input point clinoform dip does not show a trend but most points lie close to or below half the maximum clinoform dip (normalized dip of 0.5). It should be noted that the deflection of the river mouth and its associated sediment accumulation by longshore currents is challenging to reconstruct for systems in the subsurface and introduces a measure of uncertainty into the inferred location of palaeo-river mouths, especially in the examined Halibut Delta dataset.

DISCUSSION
High delta front dip and coarser sediment correlate with proximity to fluvial input points (Fig. 11). These include both modern and recent channels in the south-east Brazilian examples, suggesting that dip angles may persist after avulsion of delta channels. Palaeo-channels of the Doce delta are visible on the delta top and a palaeo-channel north of the modern Doce River course has been dated to between 6.3 (AE0.541) ka and 5.7 (AE0.566) ka (Rossetti et al., 2015, Fig. 11. Normalized delta front dip shown against distance from fluvial input point for the clinothems of the south-east Brazilian deltas (A: São Francisco, B: Jequitinhonha, C: Doce, D: Para ıba do Sul). The trendlines are computed for the distance bands of 0 to 10 km and 10 to 20 km separately. Please refer to Figs 3 to 6 for error bars based on the horizontal and vertical resolution of the data. marker 'c' in Fig. 5). The location of this channel's palaeo-river mouth aligns with high delta front dips at transects 33 to 36 measured in this study. Sediment grab samples from this area record coarse sediment which is partly cemented and has been interpreted to have been deposited by an ancient riverine input point (Quaresma et al., 2015). A second palaeo-channel which skirts the current Doce River channel and has its palaeo-river mouth just north of the current river mouth (marker 'e' in Fig. 5) also lines up with a peak in delta front dip, albeit a smaller one. The current river mouth does not coincide with a significant change in delta front dip which suggests that the systems take time to adjust and develop a steeper delta front. Sediment grab samples from the delta front of the Doce River record 75% mud south of the river mouth (Quaresma et al., 2015) which is in accordance with the low delta front dips recorded in this study. It is worth noting that the delta front dips measured for the Doce River delta are an order of magnitude higher than the delta front dips of the other deltas examined here. Drainage area and shelf width are unlikely to be the source of this difference since these are comparable with the other examined deltas (Table 1). The lower inflection point of the steepest delta front dip profile of the Doce delta is recorded at close to 90 m below sea level (Fig. 7). For the other three deltas, the lower inflection point of the steepest delta front dip profile lies in much shallower water depth (between 10 m and 25 m, Fig. 7). This difference in water depth provides increased accommodation for the Doce delta and could cause the higher delta front dips.
Sediment samples seaward of the current mouth of the Para ıba do Sul River record coarse sediment at the immediate coastline as well as a tongue of coarse-grained and fine to mediumgrained sand deposited 2.5 km offshore of the river mouth (Murillo et al., 2009). Coarsegrained sand in two locations in front of the current river mouth along with high delta front dips at the corresponding transects measured in this study suggests that the Para ıba do Sul has occupied its current channel position long enough to have deposited substantial amounts of sediment. However, 15 km south of the current river mouth delta front dip reaches its highest values along strike for the Para ıba do Sul delta. No palaeo-channels are apparent on the delta top in this location and there are no sediment grab samples documented far enough south to identify the lithology offshore. It is likely that the Para ıba do Sul occupied a channel halfway between the SSE directed palaeo-channel active during the Pleistocene (Martin et al., 1985;Martin et al., 1993) and the currently active channel position for a substantial amount of time to leave such a significant impact on delta front dip. The small streams traversing the beach ridges in the southern half of the delta plain could be exploiting a palaeo-channel course underlying the most recently deposited beach ridges. Although longshore currents are not uniform along the Para ıba do Sul delta front, higher delta front dips in the south could be due to northward directed longshore currents in this area, favouring deposition of coarser material.
Neither the São Francisco River nor the Jequitinhonha have been as extensively studied and the data on sediment distribution for these deltas are sparse. The São Francisco River has its highest delta front dip along strike at the position of the current river mouth (transects 21 and 22, Fig. 3). North, at Pontal de Peba, and in the south at the location of a small river (Papagaio River) delta front dip is higher again suggesting that rivers have been contributing sediment to the delta front at these locations in the past. Additionally, with longshore currents directed towards the south-west, the northern part of the São Francisco delta is subjected to greater wave influence, depositing coarser material than is found on the southern flank. This is reflected in the generally higher delta front dips in the north. The rivers to the north of the Jequitinhonha, the Pardo and Salsa rivers, correspond to a peak in delta front dip (transects 27 and 28, n.a. = not available due to missing data in the 10 to 20 km distance bands. Fig. 4) and given that they are said to have been larger rivers contributing to beach ridge formation during the Holocene (Dominguez et al., 1987;Martin et al., 1993) it is likely that this peak in delta front dip records the palaeo-river mouth location for one of these rivers. Overall, the correlation between high delta front dip along strike, coarse sediment either at the delta front or in the offshore transition zone and the location of palaeochannels on the delta top support the interpretation that high delta front dips are found where the river mouth is located at present or has been located in the past. The influence of storm or flood events on grain-size distribution around the river mouth has not been investigated in this study but has been shown to result in significant changes in sediment distribution observable on short timescales (Z ainescu et al, 2019). Remobilization of finer sediment during storm and flood events and redistribution along the delta front, through wave action and longshore currents, may lead to a higher concentration of coarse grain sizes at the river mouth. The coarse sediment allows for higher clinoform dips which are in turn an indicator for the current river mouth or a palaeo-river mouth (Fig. 12).

Dip development with regard to the location of fluvial input points
To identify whether dip development along strike could be used for the prediction of the palaeoriver mouth location, dip measurements have been normalized and plotted in relation to their distance from the fluvial input point (Figs 11 and 12). Plotting this normalized dip data against the distance from the (inferred) fluvial input point shows that there is a steady decrease in delta front/clinoform dip in the first 10 km either side of the fluvial input point with an average reduction in dip of 50% of its maximum value. This is the area where coarse and immature sediment from riverine input plays a significant role in the sediment budget of the delta front, causing high delta front/clinoform dips. Lateral sediment dispersal does not seem to carry significant amounts of the coarser sediment further than 10 km away from the fluvial input point. It has been suggested that transport offshore is significant in river-dominated clinothems which are found to be associated with deposition of coarse-grained sediment at the shoreface and with transport of the sediment to the offshore transition zone (Cosgrove et al., 2018). Ten to 20 km away from the input point values are generally below 50% of the maximum clinoform dip but the data distribution is more chaotic and does not show a further decreasing trend. Sediment is reworked by longshore currents and wave action and overall clinoform dips are lower in this area. The riverdominated character of the clinothem is not prevalent any more at this distance from the fluvial input point, grain sizes are finer and shoreparallel sediment transport prevails over downdip transport (Cosgrove et al., 2018). The significant changes in clinoform dip along strike illustrate that the processes which lead to sediment transport at the front of a wave-dominated delta are not uniform, and that close to the river mouth transport processes are river-dominated rather than wave-dominated. Given enough data points, dip variation along strike can thus be used as an indicator for the location of fluvial input points and it can be assumed that ca 10 km away from the fluvial input point wave-dominated processes are more influential than riverine input and sediment transport.
A larger drainage area does not seem to have a significant effect on delta front dip, with the São Francisco displaying similar dips to the Para ıba do Sul and Jequitinhonha delta fronts, despite its much larger drainage area. The south-east Brazilian deltas were also deposited in a passive margin, whereas deposition of the Halibut Delta took place towards the end of active rifting. Still, this difference in tectonic regime does not impede the comparison. However, the deltas examined here were chosen for their similarity and comparability. Marked differences in factors such as overall grain-size distribution, sediment supply and wave regime might prove to influence delta front dip distribution.
The results presented here have significant implications for predicting reservoir properties in more deeply buried, less well imaged delta systems, in the subsurface. Jackson et al. (2010) illustrated that, with amplitude analysis, distributary channels and beach ridge complexes could be imaged from the Brent Group reservoirs of the Oseberg Ost area of the Norwegian North Sea. Recent advances in seismic geomorphology and seismic attribute analysis (Posamentier et al., 2007;Reijenstein et al., 2011;Patruno et al., 2015b;Klausen et al., 2016;He et al., 2017) could improve on such mapping. Given the known position of input points and the relationships to grain size and clinoform dip, this information could be used to condition the property modelling workflow when building reservoir models Howell et al., 2014).

CONCLUSION
The locations of deltaic river mouths can be inferred from the along strike development of clinoform dip. Clinoform dip is highest at the river mouth. Within the first 7.2 km away from it, maximum clinoform dip decreases by half. This has important implications for the facies and grain-size distribution of the associated clinothem. Coarse grain sizes are more abundant close to the river mouth, and fine sand, silt and clay are found further away from the fluvial input point. Further work should be carried out to verify the findings of this study by collecting and dating samples on the delta top and the delta front of the Jequitinhonha and São Francisco deltas which suffer from sparse data coverage. Additional targeted sampling of the better studied Doce and Para ıba do Sul deltas could be carried out guided by the findings from this work.

ACKNOWLEDGEMENTS
This work was undertaken as part of the SAFARI project in a collaboration between the University of Aberdeen, United Kingdom and NORCE in Bergen, Norway. SAFARI is sponsored by a consortium of oil companies, the Norwegian Petroleum Directorate, and the Norwegian Research Council. Details at www.safaridb.com. PGS generously provided the seismic data for this case study. Software used for seismic interpretation and satellite imagery analysis was Petrel 2016 by Schlumberger and Google Earth Pro 7.3.2.5491. We would like to thank the associate editor C. Fielding as well as the reviewers G. Hampson and E. Anthony for critically reviewing the manuscript and offering constructive advice leading to significant improvement of both text and figures.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.