Page 174 - Carbonate Sedimentology and Sequence Stratigraphy

APPENDIX B

Introduction to modeling programs STRATA

and CARBONATE 3D

In the past three decades, numerical modeling of depo- in a beach-to-shelf transect (Fig. 4.1). In addition, the pro-
sitional systems has steadily gained momentum. It has be- gram models a number of processes and parameters not
come a versatile tool that forms a bridge between direct ob- used here, e.g. lithospheric flexure under sediment load,
servation of natural systems and their theoretical analysis sediment compaction during burial, physical properties and
based on principles of physics, chemistry and mathematics. synthetic seismic traces.
A particularly important role in geology is that numerical
models offer a quantitative framework for our free-wheeling Diffusion equation for sediment dispersal
thoughts.
In this book, modeling runs have been shown to illustrate STRATA assumes that sedimentation and erosion at the
the effect of a principle or to compare natural examples with Earth’s surface are governed by the diffusion equation, one
predictions from first principles. All model runs were made of the fundamental equations in geophysics (e.g. Turcotte,
with two programs whose structure and theoretical under- 1997, p.202). Its application to sedimentation and erosion is
pinnings are described below. Only the most essential ele- intuitively plausible and can be justified as follows. If one
ments of the programs are discussed. Complete descriptions watches how sediment is transported in rivers or, during
can be found in the quoted publications. sheet floods, over the land surface, one gets the distinct im-
The philosophy of STRATA, CARBONATE 3D and most pression that transport is faster on steeper slopes. Measure-
other sedimentologic modeling programs is to capture long- ments confirm this qualitative insight. In first approxima-
term trends. Large sediment accumulations were formed tion, sediment flux is proportional to slope. In mathematical
by many individual events of sedimentation and erosion. terms
Rather than attempting to model individual events, most
programs rely on statistical laws for sediment input and dis- q = −∂h/∂x
persal that provide good approximations of the cumulative where q is the sediment flux (expressed as sediment vol-
effect of the individual events. ume per unit time), h is the elevation, x the horizontal dis-
tance along the x axis, and k is a coefficient of proportion-
PROGRAM STRATA ality, called diffusion constant in STRATA. The coefficient is
given a negative sign because material moves from high to
Overview
low values of h. The dimension of the diffusion coefficient
2
in STRATA is m /y because the program models in two di-
STRATA is a 2D modelling program for siliciclastics and
mensions. In real-world experiments the coefficient would
carbonates, developed for large-scale basin studies (Flem- 3
ings and Grotzinger, 1996). Elegant simplicity and concen- be m /y. The partial derivative of height with respect to
tration on few fundamental principles is a hallmark of the horizontal distance, ∂h/∂x, is the tangent of the slope an-
program. gle, or simply “the slope”. If one assumes that no material
The program produces cross sections. Siliciclastic mate- is dissolved or precipitated during transport, then our sys-
tem also satisfies the condition that sediment volume is con-
rial is supplied to the system from external sources on the
served during erosion and deposition. In quantitative terms
side, carbonate material is produced within the system in
designated areas. Distribution of siliciclastics and carbon-
∂h/∂t = −(∂q/∂x).
ates in the system, i.e. deposition and erosion, are governed
by the diffusion equation discussed below. Subsidence and This equation states that the rate of change of elevation at a
sea-level changes can be prescribed and the output can be given position is equal to the rate at which material is added
viewed in spatial cross sections as well as time-distance to or removed from this position. Combining the two equa-
plots (“Wheeler diagrams”) with time on the vertical axis. tions yields the diffusion equation
The program can calculate first-order grain-size distribu-
2
2
tions based in the decrease of grain size with water depth ∂h/∂t = −k · ∂ h/∂x .
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