Shoal water delta is developed in water basin with shallow water, stable structure and gentle slope^[1,2,3,4]. Presently, the large scale reservoirs of shoal water delta have been found in Mesozoic and Cenozoic of Bohai Bay Basin, Ordos Basin and Songliao Basin, China.

The depositional characteristics of shoal water delta are affected by both the basin and source river. Different depositional conditions would result in widely different geomorphology and architecture of shoal water deltas^[5,6,7,8,9]. Researchers divided shoal water delta into lobate, branched (or bird-foot) and sheet delta^{[2, 10-15]}. The lobate shoal water delta consists of continuous sand bodies with low suspended load and high sand-mud ratio. The branched shoal water delta consists of one or more elongate sand bodies separated by interdistributary bays with high suspended load and low sand-mud ratio. The sheet shoal water delta consists of sheet sand bodies in seaward semicircle shape which are reworked seriously by water basin. Most researches thought that sand bodies of shoal water delta front were formed by distributary channel, whereas mouth bars were largely reworked by distributary channel or existed as residual bars^{[16,17,18,19,20,21]}. By analyzing modern deposits of Poyang Lake shoal water delta in China, some researchers concluded that the sand body of lobate shoal water delta front was distributary channel type, mainly made up of distributary channel and levee, and that of branched shoal water delta was distributary bar type made up of distributary channel and mouth bar^{[14, 22]}. But by examining reservoirs of shoal water delta in Lower Member of Minghuazhen Formation, Neogene, Bohai BZ25 Oilfield, Bohai Bay Basin, we found that the elongate branched sand bodies within shoal water delta front were bar fingers consisting of distributary channels and mouth bars. In this paper, by using core, well logging and seismic data, sedimentary microfacies, distribution and architecture of the bar fingers within shoal water delta front were analyzed. The research findings have significant impact on formulation and adjustment of fine exploration and development plans for oil and gas reservoirs of bar finger, and are important for deepening the study of deltaic sedimentology.

Bohai BZ25 oil field is located in southern Bohai Bay, and at the junction of Bozhong Sag and Huanghekou Sag in western Bonan low uplift tectonically^[23,24] (Fig. 1a). With an area of 116.9 km², the oilfield has 205 wells drilled in total (Fig. 1b). The main oil-bearing interval is the Lower Member of Minghuazhen Formation, Neogene, about 750 m thick at buried depths from 1 300 to 1 900 m. It is divided into 6 oil layer groups, Ⅰ-Ⅵ oil layer groups. In this work, Ⅳ and Ⅴ oil layers are the main intervals of interest, which are divided into 20 sublayers. The interval of interest was formed during four whole medium-term base level cycles within a long-term base level rising cycle^[25-26] (Fig. 1c).

Researchers have systematically studied the regional sedimentary facies in the study area before^[27]. They concluded that Bohai Oil Province had warm and humid subtropical climate during Neogence, and developed a shoal depression lake basin in the depocenter composed of Huanghekou sag and Bozhong sag. Because fourteen surrounding palaeodrainages fed into this lake basin, a shoal water delta-lake depositional system is developed consisting of fourteen constructive shoal water deltas of various sizes during the depositional period of Lower Member of Minghuazhen Formation, Neogene (Fig. 1a). The main evidences that there developed shoal water deltas are: (1) Abundant dark mudstones in cores contain many shallow aquatic fossils (e.g. coelleporites, alga and gastropods, etc.), indicating shallow underwater sedimentary environment in low- energy shallow lake basin. (2) The grains size of sandstone is fine and presents two-stage on cumulative probability curve, illustrating the sand deposit is mainly made up of jumping and suspended load developed in the sedimentary environment with strong tractive current. (3) Progradational reflection configuration on seismic profiles along the provenance is the typical feature of delta, and the local larger progradational angle and smaller aspect ratio imply strong hydrodynamic environment. A relatively large shallow delta developed in the southwest margin of the lake basin (the delta within the red dash line in Fig. 1a). The source river of it was Zhangweixin ancient river system. The deltaic sand bodies extended into lake basin along NEE direction in several branched fingers (Fig. 1a). The study area is located in the front of the southeastern deltaic branch where the deposit must be shoal water delta front deposit.

The interval of interest in the study area is composed of medium sandstone, fine sandstone, siltstone and mudstone. The sandstone is dominated by fine sandstone of fine lithology. Four main sedimentary microfacies are identified by core observation and description in interval of interest of the study area, including distributary channel, mouth bar, overbank (joint name of levee, crevasse channel and fan) and interdistributary bay (Fig. 2). The characteristics of sedimentary microfacies have been identified.

Distributary channel mainly consists of well-sorted medium-fine sandstone and fine sandstone, with parallel bedding, tabular cross-bedding, wedge cross-bedding and trough cross-bedding, and so on. Scoured base is often seen at bottom of the distributary channel. The sand bodies are generally 4 to 10 m thick and fining upwards.

The mouth bar also mainly consists of well sorted medium-fine sandstone and fine sandstone with parallel bedding and trough cross-bedding, and so on. The sand bodies are 2 to 10 m thick in general and coarsening upwards.

The overbank deposit mainly consists of siltstone with horizontal bedding and wavy bedding. The sand bodies are mostly less than 2 m thick.

The interdistributary bay mainly consists of dark mudstone or silty mudstone.

Core characteristics were figured out and logging interpretation standard was set up for each type of sedimentary microfacies by core-electricity calibration (Table 1), then sedimentary microfacies in wells were interpreted. In interval of interest of study area, the sand body is sandstone coarser than silt. Sedimentary microfacies of the sand bodies include distributary channel, mouth bar and overbank. Statistical results show that the distributary channel and mouth bar sands account for 55% and 35%, respectively, while the overbank sand only accounts for 10%. Accordingly, the distributary channel and mouth bar are main sedimentary microfacies of the sand bodies in shoal water delta front of the study area.

On the basis of sedimentary microfacies identified in wells, the spatial distribution and architectural characteristics of sand bodies in shoal water delta front were analyzed by using the data of dense well area (boundary of the dense well area is shown in Fig. 1, where the well spacing is about 200 m).

Taking Ⅴ3.2 sublayer as an example, the plan view of the sand body thickness was described by using well data (Figs. 1c and 3), which illustrates that a wider finger-shape sand body is developed in the dense well area. Aimed at this finger sand body, two architectural cross profiles and one architectural provenance-oriented profile were selected (locations of the profiles are shown in Fig. 3). Based on sedimentary microfacies interpreted from individual wells, the architecture profiles of the 3 finger-shaped sands were built (Fig. 4). Figs. 3 and 4 show that the sand bodies of V3.2 sublayer appear in finger shape on the plane, extend long distance along the direction of provenance, and have flat bottom and convex top on the cross profiles. They are about 10 m thick and 1 000 m wide, and their width and thickness decrease gradually toward the basin. The finger sand bodies are separated by stable mud deposits. They all consist of mouth bar, distributary channel over bar and levee. The mouth bar is the main sand body with flat bottom and convex top on the cross profiles. The distributary channel is at the center of the mouth bar with convex bottom and flat top. It is only 1/4-1/3 times the width of the finger sand body and could incise mouth bar deeply or shallowly, making the mouth bar separate at both sides of the distributary channel like wings, forming the architecture pattern of channel walking on or in the mouth bar. The levee is thin (mostly 1-2 m), draping on the mouth bar at both sides of the distributary channel. Basinward, the width and thickness of the distributary channel decrease gradually, the thickness could decrease from more than 1 to 1/2 times of the finger sand body, and the incision depth of the mouth bar turns from deep to shallow. The levee is also thinner and smaller (Fig. 4). Multi-period finger sand bodies are mostly separated by muddy interlayers, and some distributary channel deep incising into the bar could cut through the interlayer, leading to connection of finger sand bodies of two stages vertically (Fig. 4). The mouth bar is the main microfacies in the finger sand bar, accounting for 50%-80% of the finger sand body, the distributary channel takes the second place, and the levee only accounts for 10% of the finger sand body.

In this study, we name the finger sand body “bar finger” based on morphology and architectural characteristics of the sand body. It is the compound sand body (equivalent to 3-level architectural unit in Miall^[28] architectural classification) consisting of mouth bar, distributary channel above bar and levee (equivalent to 4-level architectural unit in Miall architectural classification).

On the basis of architectural analysis of bar fingers in the study area, the horizontal distribution and scale of bar fingers were defined by using logging and seismic data.

Although the study area has abundant drilling data and small average well spacing, the well pattern there is uneven (Fig. 1b). Luckily, the area is fully covered by 3D-seismic with dominant frequency of up to 45 Hz. Therefore, the distribution of sand body can be predicted by combining well data with and seismic data. In this work, the seismic attribute and seismic inversion analysis were combined to predict the distribution of sand thickness. Firstly, the results of well-seismic calibration (Fig. 5a) show that the maximum trough amplitude value has good correlation with lithology (sand/shale) (Fig. 6a). Taking maximum trough amplitude value of 8 000 as a threshold value, the distribution of high trough value can reflect the distribution area of bar finger over 3 m thick (Fig. 5b, 5c). Then, the shale-content inversion data volume was obtained by spectral-decomposition inversion, which has a good probability correlation with lithology (sand/shale) (Fig. 6b). Taking shale-content value of 0.6 as the threshold value, the thickness distribution of bar finger over 3 m thick could be delineated by distribution range of low shale-content (Fig. 5d). Therefore, under the constrain of sand body distribution range, taking interpreted sand body in single well as conditional data and seismic inversion volume as collaborative data, the horizontal thickness of bar finger in sublayer was predicted effectively (Fig. 7). Fig. 7 shows that there are several bar fingers developed in shoal water delta front of the study area. The bar fingers are separated by muddy interdistributary bay deposits and converge locally.

Guided by the architectural analysis results of bar fingers, the distribution of dominant microfacies in the study area has been mapped based on horizontal distribution of sand body and microfacies interpretation of individual wells (Fig. 8). The levee draping on mouth bar is thin and has similar horizontal location with underlying mouth bar. Fig. 8 shows that bar fingers in the study area appear in sinuous long finger shape, and extend a long distance basinward. The bar fingers, separated by interdistributary bay, mainly consist of mouth bar and distributary channel over bar. On the plane, the distributary channel comes in narrow band in the middle of the bar finger. The mouth bar reworked by distributary channel and overlying thin levee are waistband-like. The bar fingers could appear as discrete branches or interlaced branches. The discrete branched bar fingers mean that the bar fingers don’t have obvious convergence and are separated by continuous interdistributary bay basinward. In contrast, the interlaced branched bar fingers mean that bar fingers converge locally and the interdistributary bays separating the bar fingers are discontinuous lenticular shape basinward. The discrete branched bar finger becomes more sinuous basinward (Fig. 8a), but the interlaced branched bar finger has higher sinuosity overall, especially at intersection, and its sinuosity doesn’t increase obviously basinward (Fig. 8b).

According to the thickness and architectural distribution map, the dimensions of bar fingers and their internal channels and mouth bars in 15 sublayers (from IV1.1 to V3.2) are collected. The results show that the width and thickness of bar fingers ranges from 100 to 1 000 m and from 3 to10 m, respectively, and the aspect ratio of bar fingers ranges from 25 to 110 (Fig. 9). The dimensions of bar fingers reduce basinward (Fig. 7).

In general, there is a double logarithmic positive linear correlation between the width and thickness of the bar fingers, but the dimensions and aspect ratio of bar fingers in different sublayers are different (Fig. 9). In terms of dimensions, the bar fingers could be divided into 3 types (Fig. 9a). Bar fingers in Ⅳ1.1-Ⅳ4.1 sublayers are the smallest, with width of less than 200 m and thickness of less than 5.5 m. Bar fingers in Ⅳ4.2-Ⅴ2 sublayers are larger, with a width from 200 to 300 m and thickness from 5.5 to 10 m. Bar fingers in Ⅴ3.1-Ⅴ3.2 sublayers have the largest width of more than 300m and thickness from 4 to 9 m. In terms of width-thickness relationship and the aspect ratio, the bar fingers could be divided into 4 types (Fig. 9). For each type of bar fingers, there is a good double logarithmic positive linear correlation between the width and thickness. The bar fingers in Ⅳ1.1-Ⅳ7 sublayers have an aspect ratio from 25 to 35. The bar fingers in V1&V2 sublayers have a higher aspect ratio from 30 to 40. The bar fingers in IV8.1&IV8.2 have an even higher aspect ratio from 40 to 55. Bar fingers in V3.1&V3.2 sublayers have the highest aspect ratio from 60 to 110 (Fig. 9).

The dimension and aspect ratio of the bar fingers have good correspondence with the base level changes (Figs. 1c and 9). The width of the bar fingers is controlled by changes of the long-term base level, and decreases as long-term base-level rises. The aspect ratio of the bar fingers is controlled by both long-term and medium-term base level, and increases as long-term base-level rises, while it is the largest during the deposition of the bottom of the rising hemicycle in a medium-term base-level.

The bar finger mainly consists of distributary channel and mouth bar. The distributary channel is 1/3-1/2 times the width of the bar finger. It is 1/2 times the width of the wider banded bar fingers in V3.1 and V3.2 sublayers (Fig. 8a), while it is 1/3 times the width of the narrower banded bar fingers in Ⅳ8.1-Ⅳ8.2 sublayers (Fig. 8b). Basinward, the width of distributary channels and mouth bars decrease gradually as the hydrodynamic force of distributary channel decreased. The thickness of distributary channel may be reduced from 1.5 times to less than 1/2 times of the mouth bar thickness (Fig. 4).

Architectural pattern of bar finger in shoal water delta front was worked out by analyzing reservoir in Lower Member of Minghuazhen Formation, Neogene, Bohai BZ25 Oilfield, Bohai Bay Basin (Fig. 10). The architectural pattern shows that the bar finger in shoal water delta front appears as sinuously elongate branch and could extend long distance basinward. There is stable muddy interdistributary bay deposit between bar fingers. The bar finger has flat bottom and convex top on the profile perpendicular to provenance. There is a good positive double logarithmic linear correlation between the width and thickness of bar finger. The aspect ratio of the bar finger ranges from 25-110. The bar finger consists of mouth bar, distributary channel above bar and levee, among which, mouth bar takes dominance, whereas the levee is low in development degree. The distributary channel is of band shape in the middle of the mouth bar, and only 1/4-/3 times the width of the bar finger. It could incise mouth bar deeply or shallowly, forming the architecture pattern of channel walking over or in the mouth bar. The thin (1-2 m) levee occurs on both sides of distributary channel draping on the mouth bar. Basinward, the distributary channel in bar finger decreases in scale and increases in sinuosity gradually, and turns from incising mouth bar deeply to shallowly; the levee decreases in development degree and hardly occurs at the front of bar finger. The bar fingers in shoal delta often appear as discrete branches on the plane, whereas they could interlace under the conditions of sufficient source material supply and limited accommodating space. Compared with the discrete branched bar finger, the interlaced branched bar finger and inner distributary channel are more sinuous. In terms of seismic response, the strong reflection of bar finger in shoal water delta is discontinuous on the profile perpendicular to provenance (Fig. 5a), and it is banded on the plane (Fig. 5c).

The formation of bar finger in shoal water delta front is controlled by many depositional factors, including discharge of source river and sediment properties, water basin depth and energy, lake level fluctuation and climate, and so on. High discharge river and weak basin energy are beneficial to the formation of fluvial-dominated shoal water delta, and make mouth bar prograde long distance basinward^[29,30]. It is conducive to the generation of bar finger in shoal water delta front. Property of sediments carried by source river influences the morphology of delta^[10,11,12]. High-cohesive fine sediments, existing as suspended load, has lower settling velocity and is likely to deposit on both sides of distributary channel as levee. The levee confines bifurcation and avulsion of distributary channel, making it possible to form bar finger in shoal water delta^[31]. Seasonal variation of source river could also influence the formation of bar finger in shoal water delta front^[32,33]. During flood season, the mouth bar would prograde and distributary channel would extend basinward as the distributary channel had strong supply capacity. And the suspended load in channel could deposit as levee and avulsion channel, leading to generation of avulsing distributary channel. However, during dry season, as the distributary channel had weaker supply capacity, the bar finger would prograde slowly. The lake level fluctuation also affects the development of bar finger in shoal water delta front. The bar finger is easy to prograde basinward during fall or stabilization of lake level, whereas during rise of lake level, the shoal water delta degrades and the bar finger may be reworked by water basin. In addition, the warm, humid climate could promote growth of vegetation. The flourishing vegetation could enhance the levee on both sides of distributary channel, which is conducive to the generation of bar finger^[34,35]. During the deposition of lower Minghuazhen Formation, the study area had humid subtropical climate, the rivers had stronger discharge and carried fine sediments, and the basin water was shallow and low in energy, providing good depositional conditions for the development of bar finger in shoal water delta front.

The bar finger in delta front could form in both shallow water and deep water. Architecture features of bird-foot deep water delta represented by modern Mississippi delta were analyzed before, which showed the finger sand bodies within delta front had large thick, and consisted of distributary channel and mouth bar too, so they were named “bar finger”. But the bar finger in deep water delta straightly extends into basin and incises only the top of mouth bar^[1].

The bar fingers in shoal and deep water deltas all consist of distributary channel, mouth bar and overlying levee. But they have two obvious architectural differences: (1) The bar finger in shoal water delta is sinuous, whereas the bar finger in deep water delta is straight. (2) The distributary channel in shoal water delta usually incises mouth bar deeply, whereas the distributary channel in deep water delta only incises the top of mouth bar.

Water depth of basin is the critical factor causing the architectural differences of bar fingers in shoal and deep water delta fronts. On the one hand, sufficient accommodation space in deep water basin leads to the formation of thick mouth bar which is hard to be incised through by distributary channel, while in shallow water, the accommodation space is limited, so thin mouth bar is likely to be formed, which can be cut through by distributary channel easily. Moreover, although the bar finger is formed by inertia-dominated delta, the bed friction affects water flow. The effect of friction is less in deep-water basin, so the water current would flow straight forward drived by inertia, giving rise to formation of straight bar finger. By contrast, the effect of friction is enough to diffuse water flow in shallow-water basin, giving rise to formation of sinuous bar finger.

The effect of architectural distribution of narrow banded channel sand body on development of oil and gas was analyzed before. The results showed that in the case of development with vertical wells and waterflooding, the well pattern with water injection wells at the channel edges and production wells in the middle of the channel is the best. And the remaining oil is distributed at top of the sand body^[36,37]. However, the effect of architectural distribution of narrow banded bar fingers on development of oil and gas is still not clear. The results of this study show the architectural pattern of bar fingers in shoal water delta has two aspects of development geological significances.

(1) It’s crucial for well pattern arrangement in oil and gas development. The bar finger mainly consists of distributary channel and mouth bar. These two types of sand bodies are similar and good in physical properties. Taking the interval of interest in the study area as example, the statistical results of analysis test data of 600 samples from 9 wells show that the mouth bar and distributary channel have an average permeability of 2 640×10^-3 μm² and 2 620×10^-3 μm², respectively, with little difference. However, channeling-path of bottom flooding is still easy to be formed between injection and production wells within the same distributary channel, influencing the development effect of oil and gas in mouth bar sand. Taking Ⅳ8.2 sublayer as an example, tracer testing was conducted in several well groups of the study area. In the testing well groups, the injection wells are all at distributary channel, and the production wells are at high-permeability part of distributary channel or mouth bar (with similar permeability). The testing results show that seepage velocity of tracer in distributary channel is faster than that from distributary channel to mouth bar (Fig. 11a). Therefore, for the bar finger, injection and production in the same distributary channel should be avoided during water flooding development, and undrilled mouth bar is the key target to tap remaining oil.

(2) It has guiding significance for tapping remaining oil in bar finger of shoal water delta during the late stage of oil and gas field development. In the study area, the bottom of distributary channel has suffered severe water-flooding and the remaining oil accumulates in middle-upper part of distributary channel. In contrast, in mouth bar, the sand water flooded is thicker and oil only left in the upper part. Based on interpretation of water flooding in wells, water flooding largely appears in bottom flooding (Fig. 11b). The thickness of sand water flooded in normal rhythm distributary channel is smaller than 50%, while that in reverse rhythm mouth bar is more than 50% (Fig. 11b). Therefore, middle-upper part of distributary channel in bar finger is the key part for tapping remaining oil.

The finger sand in the front of shoal water delta is the bar finger deposit. It appears in sinuously elongate branch-shaped on the plane and has flat bottom and convex top on the cross profile. It consists of mouth bar, distributary channel over bar and levee. The mouth bar is the main sand facies and levee is less developed. Warm and humid climate, strong discharging river with fine sediments, shoal water basin with low energy are advantage conditions for the formation of bar finger in shoal water delta.

The distributary channel in bar finger of shoal water delta could incise mouth bar deeply or shallowly, forming architecture patterns of going over or in the mouth bar. The thin levee deposited on both sides of the distributary channel and above the mouth bar. Basinward, the distributary channel decreases in scale gradually and turns from incising the mouth bar deeply to shallowly, and the levee also gets smaller.

The bar fingers in shoal water delta front of Lower Member of Minghuazhen Formation, Neogene, Bohai BZ25 Oilfield come in two combination patterns, discrete branch pattern and interlaced branch pattern. The discrete branched bar finger becomes more sinuous basinward, while the interlaced branched bar finger has higher sinuosity, especially at intersection, but its sinuosity doesn’t increase significantly basinward.

The bar fingers in shoal water delta front of Lower Member of Minghuazhen Formation in the study area are about 100- 1000 m wide, 3-10 m thick, and 25-110 in aspect ratio. There is a double logarithmic linear relationship between the width and thickness of the bar finger. As long-term base-level rises, the width of bar finger decreases and the aspect ratio of bar finger increases gradually in general. While in a medium-term base-level cycle, the bar finger depositing at the bottom of the rising hemicycle has the largest aspect ratio.

Architectural pattern of bar finger in shoal water delta is not only crucial for well pattern arrangement, but also of guiding significance for tapping remaining oil during late stage of oil and gas field development. For the bar finger, injection and production in the same distributary channel should be avoided during water flooding development, and middle-upper part of distributary channel and undrilled mouth bar are key parts for tapping remaining oil.