Many continental shelves tend to steepen landward. Existing models attribute this curvature to a progressive attenuation of the effect of postglacial sea‐level rise or sediment redistribution by modern coastal‐marine processes. Here, we present an alternative framework in which shelf curvature arises from an inherent self‐organizing mechanism. During sea‐level rise, if the critical length of the downstream alluvial river is exceeded, deltaic sedimentation cannot be sustained. In this non‐deltaic transgressive regime, the alluvial aggradation rate autogenically increases as the river shrinks, enhancing alluvial sediment accumulation and producing a steeper local shelf slope closer to the shoreline. Two‐dimensional geometric modeling reveals a simple governing equation for the self‐organized curvature of the shelf profile, with support from flume‐tank experiments and applications to modern systems, providing a mechanistic basis for interpreting existing shelf profiles.

Conventional sequence stratigraphy is based, explicitly or implicitly, on the hypothesis that steady external forcing results in a steady stratigraphic configuration (equilibrium response), so that an unsteady stratigraphic configuration is believed to result from unsteady external forcing. Recent advances in autostratigraphy, on the other hand, have led to a significantly different notion that steady external forcing generally results in an unsteady stratigraphic configuration (non-equilibrium response). To advance this debate, it is necessary to clarify what exactly is meant by a steady stratigraphic configuration. Here, we propose a quantitative criterion for defining the latter concept in terms of the straightness of the shoreline trajectory, and specifically a straight shoreline trajectory or the shoreline being held still as a sign to express steady stratigraphic configurations. In such a definition, a steady stratigraphic configuration means that the ratio of the rate of aggradation and the rate of progradation is constant, or one of these two rates is zero. Based on this criterion, a total of 7 types of steady stratigraphic configurations can be clarified, most of which require unsteady external forcing and are thus realized by non-equilibrium response, although special cases exist. The reason that non-equilibrium responses dominate the stacking of strata is that it is common for a growing basin-margin depositional system to change its surface area. The size-changing system will easily change the stacking pattern (unsteady stratigraphic configuration) if the external forcing is steady, or, if the steady stratigraphic configuration is maintained, the rate of external forcing must change in a particular pattern (unsteady external forcing). Equilibrium responses can occur, but in very special cases. Conventional sequence stratigraphy should aware the importance the importance of non-equilibrium response.

The dynamics of downstream alluvial systems undergoing relative sea level (RSL) rise exhibit significant variations depending on spatial size. According to autostratigraphy theory, such systems cannot sustain deltaic sedimentation under a steady RSL rise (rate Rslr), and are prone to non-deltaic transgression once their plain area A exceeds the critical limit Acrt. During this transgression, A decreases asymptotically toward Acrt, while the overall alluvial aggradation rate Ragg_overall increases toward Rslr. In this study, we investigated the behavior and morphodynamics of an overexpanded system through physical modeling, with a focus on the inherent area scale of the depositional system. In the early stages of non-deltaic transgression (A >> Acrt, Ragg_overall << Rslr), the alluvial channels experience minimal aggradation rate Ragg_channel (< Rslr), leading to stabilization and inundation. As the transgression progresses, the channels aggrade more rapidly, increasing the likelihood of lateral migration and avulsion. Eventually, a state of morphodynamic equilibrium is reached, characterized by A ∼ Acrt, Ragg_overall ∼ Rslr, and Ragg_channel ∼ constant > Rslr despite sustained non-deltaic transgression. During this equilibrium stage, the channels undergo rapid aggradation, resulting in complete destabilization with continuous lateral migration and frequent avulsion, forming system-wide subaqueous steps. The implications of overexpansion and autogenic shrinkage in response to RSL rise extend to stratigraphic convergence during RSL cycles and provide insights into Holocene non-deltaic transgression. Moreover, when combined with decelerating RSL rise, this process could have facilitated marine delta development. However, projected accelerated RSL may lead many modern marine deltas to transition into non-deltaic transgressive systems. Additionally, natural alluvial channels may exhibit varying behavior depending on the spatial size of the non-deltaic transgressive system. Furthermore, the autogenic shrinkage model may offer an explanation for the stepped surfaces observed on alluvial fans and deltas on Mars.

Autostratigraphic length scale Λ2D, given as qs/|Rslr| (qs: upstream sediment supply rate in unit width, Rslr: rate of relative sea level rise), provides a criterion for discriminating between deltaic and non-deltaic transgressions in geologic sections. Estimation of a Λ2D value makes it easy to identify transgressive surfaces. We here examine this quantitative but easy method in use of GPM, a simulator for diffusion-based forward stratigraphic modeling. This model has a peculiarity that qs changes with time, thus Λ2D does so. qs can be estimated from the cross-section area of the sediment accumulated for each time step. Another method of estimating Λ2D is to measure the length of the alluvial plain at the attainment of autobreak, when the deltaic system becomes a non-deltaic transgressive system. The results of the examination with GPM support the validity and usefulness of Λ2D in detecting transgressive surfaces, implying that the autostratigraphic analysis compensates for the conceptual thoughts in conventional sequence stratigraphy.

Autostratigraphy is the stratigraphy generated by large‐scale autogenesis, developed based on the full recognition of the non‐equilibrium behaviour of depositional systems in response to steady external forcing. The existing autostratigraphic concepts were derived mostly from studies of river deltas growing during a single rise or fall of base level (or relative sea level). The present study challenges to extend the autostratigraphic framework to the alluvial‐shelf system growing through steady base‐level cycles by two‐dimensional tank experiments. During each experimental run, the base level was changed symmetrically, wherein through cycles, the rise and fall had the same constant rate (|Rbl|) and period (Tbl), and thus the same constant amplitude (Abl), but with no basin tectonism. In total, nine runs with different combinations of |Rbl| and Abl were performed. The experimental results brought the following implications. (i) The shelf‐transiting active depositional system takes non‐equilibrium responses in earlier base‐level cycles, during each of which the system experiences episodes of degradation with base‐level fall. (ii) After the system has sufficiently grown through cycles, non‐equilibrium responses change into equilibrium responses, whereby the shelf‐transiting alluvial system, whether retrogradational or progradational, is free from degradation and continues to aggrade but with a gradually decreasing rate of aggradation. (iii) The alluvial topset river tentatively but autogenically attains a graded state during the falling limb of an intermediate cycle, which separates the earlier degradation‐inclusive and later aggradation‐sustainable cycles. (iv) The number (or duration) of cycles elapsed prior to this phase‐transition is linearly proportional to the amplitude (or the square of the period) of base‐level cycles, with a coefficient defined by the rates of base‐level change and sediment supply. Such a growth pattern does not necessarily hold when considering long‐term tectonic subsidence or uplift. These notions help to understand the stratigraphic architectures of natural alluvial‐shelf systems evolved through base level cycles.

国内と国外を問わず,遠隔地で開催される研究集会に参 加するときの楽しみの一つは,論文原稿の執筆に集中でき るいくばくかのまとまった時間が得られることである.若 き日のムッチー(Mucchie)も旅先から論文投稿することを 好み,自分だけの密かなルーチンにしていた.2005年 12 月,AGU秋季大会に参加するためにサンフランシスコを 訪れていたムッチーは,市内のヴァンネスアベニュー(Van Ness Avenue)に面したホテルの高層階の部屋にこもって論 文書きに勤 いそ しみ,離米前日の夕刻にオンライン投稿にまで 漕ぎ着けたのだった.その論文こそ,成因論的層序学 (genetic stratigraphy)のノルム的枠組みたらんとするオー ト層序学(autostratigraphy)を提唱したものであった.2回 の査読ラウンドを経て JSR誌 2007年 1月号の巻頭を飾っ たこの論文(Muto et al., 2007)の最後のページに印字され ている “Received 11 December 2005” を目にするたび,ムッ チーはあの日のホテルの窓から見た初冬のシスコの夕暮れ と,ただ何かしら ─それが何なのかは自分でもよく分から なかったが─ を突き抜けていくことにひたむきだった当 時の自分を想い起こすのである.渾身の力を込めて書けた 感のある自著論文はムッチーにはさほど多くはないが,そ れはまさしくそのような類の論文であった.論文は,どこ の誰にどう評価されようと,ディスられようと,ネグられ ようと,著者自身がその時点で良い論文を書けたと思える ならそれだけで 100%満足してよいのだ.共同研究者・共 著者となってムッチーをサポートし,進むべき方向へとも に歩んでくれたわが師 Ron Steel(テキサス大学オースチン 校)と盟友 John Swenson(ミネソタ大学ダルース校)には 今も感謝の言葉しかない. 出版から十数年が経過した今日,ムッチーの主観ではあ るが,オート層序学への関心と理解は研究者の間で着実に 浸透してきており,しかもその感触は年々強まっている. Facies Models 4(James and Dalrymple, 2010)の中で,Robert Darlympleはオート層序学に鑑みれば堆積相モデリングも シークウェンス層序学も依然として数多くの課題を残して いると述べている.また,Phillip Allen(2017)の著作 Sediment Routing Systemsでは数ページに渡るオート層序学の セクションがわざわざ設けられ,オート層序学の基本的な 考え方に加えてシークウェンス層序学との相補的関係を独 自の視点から小綺麗に解説してくれている.その前年の 2016年には,Steelが SEPM最高の栄誉とされるWilliam F. Twenhofel Medalを受賞した.Steel門下にとって素晴らし い慶事であったが,SEPM主催の Awards Ceremonyで読み 上げられた受賞理由の一つにオート層序学の最前線でその 発展に関わったことが挙げられていたことはムッチーを一 層感激させた.オート層序学は学界の中での市民権をすで に獲得したと言えるのだろう. その一方で,学界にはいまだに根深い葛藤があるように も思える.というのも,成因論的層序学といえば,それは 今も昔もシークウェンス層序学(sequence stratigraphy)の 代名詞であるのに,成因論的層序学のノルムを標榜する オート層序学はシークウェンス層序学と原理的なところで 相容れないからだ.シークウェンス層序学が 1970年代以 受付 : 2020年 8月 25日 受理 : 2021年 1月 23日 1 長崎大学環境科学部 〒852-8521 長崎市文教町 1-14 Department of Environmental Science, Nagasaki University, 1-14 Bunkyomachi, Nagasaki, 852-8521 Japan * Corresponding author: tmuto@nagasaki-u.ac.jp 堆積学研究 第 79巻 第 2号 95-111(2021) Journal of the Sedimentological Society of Japan Vol. 79, No. 2, p. 95-111 (2021) 95

Lowland river systems (with channel slopes of 10−5 to 10−4) inevitably shift away (retreat upstream) from the receiving basin under a sustained rate of base-level rise, even if the system can maintain a period of advance at the onset of rise. This autogenic pattern of transition from progradation to retrogradation through steady base-level rise and sediment supply is termed “autoretreat.” Using a morphodynamic model of autoretreat, this study explored the varying channel hydrodynamics of lowland fluvial systems and associated stratigraphic record under sustained base-level rise and constant sediment supply. Results from the numerical simulations show that a fluvial system will reach a state of dynamic equilibrium during autoretreat where both the backwater length and the morphodynamic adjustment of the downdip channel profile become steady. Moreover, when this dynamic equilibrium state is realized, simulated systems display a persistent twofold downstream deepening of flow depth across the backwater zone, a pattern that is also present in many natural systems. In general, backwater effects play a key role in the morphodynamics of a lowland fluvial-deltaic system during autoretreat, and this hydrodynamic condition is therefore critical for predicting river responses to sea-level change.

Grade index ( G index ) is a dimensionless number given as the volume‐in‐unit‐time ratio of subaerial allocation to both subaerial and subaqueous allocations of sediment supplied to a delta from upstream. It was originally proposed for understanding the effect of basin water depth on the morphodynamics of delta distributary channels under stationary relative sea level. We here examine how rising relative sea level modulates the G index , using geometrical reasoning and numerical simulations. We find that the grade index model can account for autoretreat of the deltaic shoreline, autodrowning of the whole system, and autobreak of the deltaic sedimentation, all of which are the consequences of autogenic nonequilibrium responses to steadily rising relative sea level. The regressive‐to‐transgressive threshold (i.e. the onset of autoretreat) is crossed when the delta plain's dimensionless basal area ( A t* ) encounters a critical value that is expressed in terms of G index : regression and transgression are sustained when A t* is below and above the threshold, respectively. The mode of transgression depends on the slope conditions. If the hinterland slope (γ) is steeper than the foreset slope (β), both A t* and G index decrease as the relative sea‐level rises. Eventually, the depositional system experiences autodrowning when A t* = G index = 0. If γ < β; on the other hand, both A t* and G index increase. This latter slope condition eventually causes autobreak of the deltaic sedimentation, afterward of which A t* = G index = 1. The grade index model is useful for interpreting and predicting the stratigraphic responses of natural deltaic clinoforms in conditions of rising relative sea level.

Grade, a fundamental concept in river geology and geomorphology, refers to a long-term sediment balance that is accompanied by zero net deposition and erosion. Recent physical and theoretical modeling proposed the notion that downstream alluvial rivers can autogenically attain grade only in a particular set of environmental conditions that include a constant fall of relative sea level. We here make the first successful identification of an autogenic grade system in the geological record: the late Holocene Mekong River delta, Vietnam. From 3.5 ka to subrecent, the record of the delta exhibits peculiar features, including (1) no trace of significant sediment accumulation and erosion on the delta plain surface, (2) a delta plain surface with the same slope as the underlying shelf surface, (3) distributary channels that are stabilized in transverse directions but extend linearly basinward, and (4) a delta set thickness that matches a theoretical value. These features in combination are indicative of autogenic grade. Coastal dispersal of river-derived sediment by tides, waves, and ocean currents, as well as tectonic features and mangrove vegetation, may have contributed to the attainment and maintenance of grade. Ongoing drastic changes in sea level and human activities have caused the downstream Mekong River to become ungraded and unstable with a much higher risk of channel avulsion and shifting than in the past.

Basin water depth (h) governs the long‐term morphodynamics of river deltas, which are embodied in the grade index (Gindex). The Gindex, a volume‐in‐unit‐time ratio of subaerial sediment allocation to the entire supplied sediment, can be given as a function of the dimensionless basin water depth (h*). Tank experiments reported herein reveal that delta progradation and deltaplain aggradation are suppressed and distributary channel migration and avulsion take place less frequently when the Gindex value is lower (i.e., when the basin water is deeper; h* ≫ 1). If the Gindex~0 (i.e., extremely deep basin water; h*~+∞), the delta can neither prograde nor aggrade, and the distributary channels tend to stabilize. The grade index model helps explain the contrasting morphodynamics of the Liwu Delta (east Taiwan) and Yellow River Delta, as natural examples of deepwater and shallow‐water deltas, respectively.

River channel geometry is often controlled by upstream boundary conditions, including fluvial discharge and sediment properties. At the coast, downstream boundary conditions (e.g., tides, waves, water depth) also strongly influence channel formation and evolution. We conducted a set of experiments to determine the effects of basin water depth (i.e., a downstream boundary condition) on the evolution and geometry of fluviodeltaic channels and lobes. Internal dynamics (autogenic processes) in the fluviodeltaic system drive channel avulsion through cycles of sediment storage and release. Experimental results indicate an increase in the timescale of autogenic storage and release with increasing basin water depth. Deeper basin water requires a larger volume to be filled within the delta front, thus more time to complete one autogenic storage and release cycle for a given sediment discharge. While a relationship between delta-front volume and autogenic storage and release timescales is expected, we show that autogenically generated morphological changes in the delta topset and distributary channels also exert control on timescales of storage and release. Deltas building into deeper basins develop steeper topsets, and deeper distributary channels that cause high-magnitude topset slope fluctuations, which contribute to the long autogenic timescales. Deposits in shallow basins exhibit both shallower topset slopes and shallower channels. Channel bed slopes are similar (similar to 0.06) across all experiments, but lateral channel migration rates varied with basin depth. Deltas building into shallow basins had rapid lateral channel migration, such that channels quickly reworked the delta topset. For deep basins, channel migration rates were much slower, so the topset was reworked less often, allowing the topset to build to steeper slopes before being reworked. These experiments indicate an intimate relationship between lateral channel migration and topset aggradation. In addition, the deeper and more stable channels in deeper basins generally developed a wider range of channel widths, some of which produced elongate lobes. We conclude that the downstream boundary has a strong control on fluviodeltaic morphology, which can result in a striking difference in the autogenic timescale.

The sequence stratigraphic model, although no longer focused on eustasy and accommodation, has been until recently based largely on observation and interpretation of outcrop and subsurface data. This approach may be restrictive if the current model places limits on what is observed and how observations are interpreted. To make progress in our understanding of strata, the sequence stratigraphic model and method should be tested against and fully incorporate theoretical and experimental results that provide new knowledge of (1) autogenesis, (2) intrinsic stratigraphic responses, (3) alluvial grade, and (4) scales appropriate to single depositional systems evolving with relative sea-level changes. More extensive inclusion of analogue and numerical experimental results could lead to significant modification and refinement of existing sequence stratigraphic models.

The profile of a river that conveys sediment without net deposition and net erosion is referred to as ‘graded’ with respect to vertical aggradation of the river segment. Three experimental series, designed in terms of the autostratigraphic view of alluvial grade, were conducted to clarify the diagnostic spatial behaviour of graded alluvial–deltaic rivers: an ‘R series’, which utilized a moving boundary setting with a stationary base level; an ‘F series’ in a fixed boundary setting with a stationary base level to produce ‘forced grade’; and an ‘M series’ in a moving boundary setting with constant base‐level fall to produce ‘autogenic grade.’ The results of the three experimental series, combined with geometrical modelling of the effects of basin water depth and other experimental data, suggest the following: (i) in a graded alluvial–deltaic system, lateral shifting and avulsing of active distributary channels are suppressed regardless of whether the downstream boundary of the deltaic system is fixed; (ii) in a delta with a downstream‐fixed boundary, the graded streams are stabilized within a valley that is incised in the axial part of the delta plain, whereby the alluvial plain outside the valley is abandoned and terraced; (iii) in moving boundary settings, the graded river simply extends basinward as a linearly elongated channel and lobe system without cutting a valley; and (iv) a modern forced‐graded alluvial river is most likely to be found in a valley incised into a fan delta in front of very deep water, and the stratigraphic signal of fossil autogenic‐graded rivers will be found in deltaic successions that accumulated in the outer to marginal areas of deltaic continental shelves during sea‐level falls. This renewed autostratigraphic view of alluvial grade suggests a thorough reconsideration of the conventional understanding that an alluvial river feeding a progradational delta is graded with a stationary base level.