The autostratigraphic view of responses of river deltas to external forcing: a review of the concepts - From Depositional Systems to Sedimentary Successions on the Norwegian Continental Margin - page 144

Decelerating
sea-level fall

Shoreline positions

Alluvial-basement
transition remained
stationary

Entirely foreset deposit

20 cm

Fig. 5. Allogenic alluvial grade attained and sustained with decelerating sea-level fall, illustrating an allogenic
non-equilibrium response. The timeline interval is approximately 11 minutes. Note that the feeder alluvial river simply
extended basinward without significant topset aggradation and degradation, representing the graded state of the river. See
Muto & Swenson (2005) for details of the experimental runs.

CONTROL OF MANIFESTATION
OF NONEQUILBIRUM RESPONSE

where υ is linear diffusivity in alluvial sedimen-
tation and α is averaged alluvial slope (Muto &
Swenson, 2005). Λ reflects, for example, the
horizontal distance between shelf basement and
shoreline position at the attainment of autobreak
(Muto, 2001; Fig. 3).
The stratigraphic meaning of τ is as follows. Let
T be the time interval for external dynamic forc-
ing of relative sea-level rise. If τ < < T, prominent
signals of the non-equilibrium response are
expected. The river delta cannot avoid experienc-
ing autoretreat and autobreak within the period of
the sea-level rise. The non-equilibrium response
of such a case is referred to as 'large-scale' in auto-
stratigraphy. However, if τ > > T, only a very small
window of time is available for the non-equilib-
rium response and the river delta can behave
steadily, as if making an equilibrium response. In
the case of the experimental run shown in Fig. 3
for example, T (= run time) was 1470s, whereas
the calculated magnitude of τ is a much shorter
179s. This is the reason why autoretreat and auto-
break were attained during the run of the experi-
ment. If the experiment had been stopped one
minute after the beginning of the run, only the
initial regressive part would have been seen. In
that case, it would be hard to recognise any non-
equilibrium response.

If one is unaware of non-equilibrium response
(and thus deterministic autogenesis), the conven-
tional explanation of regression and transgression
simply follows the hypothesis of equilibrium
response, i.e. in terms of balance or imbalance
between the effect of sea-level rise and the effect
of sediment supply. Full recognition of non-
equilibrium response, on the other hand, provides
a totally different explanation. Regression, aggrada-
tion (with stationary shoreline) and transgression
are simply the non-equilibrium response of the
deltaic system to a constant rise of relative sea-
level. As long as relative sea-level continues to
rise, none of these represent an equilibrium con-
figuration but rather transient states of the deposi-
tional system evolving toward a non-deltaic
transgressive system, the final state.
Magnitudes of R slr and Q s themselves do not
determine which one of regression, aggradation
and transgression occurs. The primary function of
the two factors is to control length and time scales
of the depositional system. Any river delta grow-
ing during sea-level change has a particular time
and length scale that is specified with R slr and Q s
(Muto et al ., 2007). Autostratigraphic length scale
Λ and time scale τ are usually defined as:

APPLICATION TO STRATIGRAPHIC
RECORDS

Λ= Q
R

S

(1)

slr

A primary aim of autostratigraphy is to explore
deterministic autogenic processes and their strati-
graphic responses, thereafter to identify allogenic

Λ 2

Q
R

τ == α

S

(2)

υ

2

slr