FISCHERPLOTS: An Excel spreadsheet for computing Fischer plots of accommodation change in cyclic carbonate successions in both the time and depth domains

doi:10.1016/j.cageo.2007.02.004

Computers & Geosciences

Volume 34, Issue 3, March 2008, Pages 269-277

https://doi.org/10.1016/j.cageo.2007.02.004 Get rights and content

Abstract

Fischer plots are plots of accommodation (derived by calculating cumulative departure from mean cycle thickness) versus cycle number or stratigraphic distance (proxies for time), for cyclic carbonate platforms. Although many workers have derived programs to do this, there are currently no published, easily accessible programs that utilize Excel. In this paper, we present an Excel-based spreadsheet program for Fischer plots, illustrate how the data are input, and how the resulting plots may be interpreted. The plots can be used to derive periods of increased accommodation, shown on the plots as a rising limb (which commonly matches times of more open marine, subtidal parasequence development). Times of decreased accommodation, shown on the plots as a falling limb, generally are coincident with thin, shallow, peritidal parasequences.

Introduction

Fischer plots are a graphical method to define accommodation changes (sea level plus tectonic subsidence), and hence depositional sequences, on “cyclic” carbonate platforms, by graphing cumulative departure from mean cycle thickness as a function of time (Fig. 1; Goldhammer, 1987; Read and Goldhammer, 1988; Sadler et al., 1993). Sadler et al. (1993) reviewed the use of Fisher plots and suggested that, instead of a time scale as originally used, the horizontal axis of the plots should be labeled by cycle number, to avoid the problem of the poor absolute time control on the stratigraphic record. They also recommended the use of a minimum of 50 cycles, in order to separate non-random from random fluctuations. Day (1997) transposed Fischer plots into the depth domain by plotting cumulative stratigraphic thickness rather than cycle number. This allows the Fischer plots to be drawn directly alongside stratigraphic columns to plot accommodation change.

Read and Sriram (1990) developed a computer program for the construction of Fischer plots. It was written in VS FORTRAN version 2.0, and it plotted relative sea-level curves, subsidence vectors and cycle thicknesses against time, using calculated average cycle period. The input data included locality name, horizontal scale (years per inch) and vertical scale (meters per inch), total duration of plot (millions of years), subsidence rate (meters per thousand years), average cycle period (years), starting elevation, and time increment (years).

Besides computer language, the fundamental difference between FISCHERPLOTS described here and the earlier programs is in the input, as well as the output data. Namely, instead of inputting the data on cycle thicknesses, time, and subsidence, the FISCHERPLOTS require no information on age or subsidence, only data on cycle thickness and number of covered intervals in the section. Sadler et al. (1993) and others used Excel to generate such plots but these workers did not publish the code. This paper presents an easy to use Microsoft Excel spreadsheet program for Fischer plots.

Section snippets

Fischer plots and cyclic carbonate platforms

Cyclic carbonate platforms consist of many repeated shallowing upward, meter-scale cycles (or more correctly, parasequences) bounded by marine flooding surfaces; each parasequence results from repeated marine submergence of the platform, followed by shallowing to sea level. Parasequences may form by Milankovitch-driven, high-frequency changes in sea level related to orbital eccentricity, and tilt and wobble of the earth's axis (Fischer, 1964; Imbrie, 1985). This is supported by the apparent

Program description

Use of the Fischer plot program is given below, with detailed instructions on data input, and reading output. These are plots of cumulative departure from mean cycle thickness (accommodation) versus cycle number (a proxy for time). It will also generate plots of cumulative departure from mean cycle thickness versus cumulative thickness (stratigraphic position), that is, Fischer plots in the depth domain.

Assumptions: All thicknesses are measured in meters (although any other unit can be used,

Example

The cyclic carbonate section used here as an example is from Lastovo Island, Croatia. The section is Late Jurassic (Tithonian), 750 m thick and composed of many shallowing upward parasequences. A total of 333 cycles were picked, and the section contains a 70 m covered interval. The facies composing the parasequences (Husinec and Read, 2007) include dasyclad-oncoid mudstone-wackestone-floatstone (“deeper” lagoon), skeletal-oncoid wackestone-packstone (moderately shallow lagoon),

Conclusions

We present a simple method of generating Fischer plots of cumulative departure from mean cycle thickness plotted against either cycle number or stratigraphic distance, using an Excel spreadsheet program. The only data that need to be input are number and thickness of covered intervals (or uncored intervals in core), and cycle thickness data. An example is given and the mode of interpretation provided.

Acknowledgments

Support for this work was provided by Fulbright Grant no. 68428172 to A. Husinec, NSF Grant EAR-0341753 to J.F. Read, and NSF Grant EAR-0639523 to J.F. Read and A. Husinec.

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The sixfold ichnofabric index (i.i.) established by Droser and Bottjer (1986) was adopted to distinguish degrees of bioturbation. Thickness patterns of metre-scale cycles were visualised by the Fischer plot method, using the “FISCHER PLOT” program of Husinec et al. (2008). These graphical data represent the cumulative departure from mean cycle thickness plotted against cycle number as a qualitative measure of time, assuming that each sedimentary cycle was formed in the same time duration: thicker-than-average cycles are marked on rising limbs of the plots and thinner-than-average on falling limbs (e.g., Read and Goldhammer, 1988; Sadler et al., 1993).
The Lower Ordovician mixed carbonate–shale Dumugol Formation of Korea was analysed to compare the stratal thickness and facies proportion of measured and decompacted successions and to assess the effect of compaction on the interpretation of cyclicity. Metre-scale cyclic units (MSUs) in the formation consist in part of outer-shelf shale, distal to intermediate mid-ramp limestone–shale couplets, and proximal mid-ramp lime mudstone facies. A total of 119 MSUs were recognised in the studied section. Thickness reduction was estimated based on petrographic evidence, including compressed to uncompressed burrows, firm- to hardground surfaces and differentially compacted laminae, and supplementary values of decompaction factors taken from the literature. Five oscillatory units in the apparent Fischer plots consist of thickening- to thinning-upward packages composed of shallowing- to deepening-upward MSUs. Similar thickness–facies relationships were observed in the lower two oscillatory units of the decompacted Fischer plots; these units are rich in shale. In contrast, a transition to an antithetic thickness–facies pattern occurs in the following units, with common occurrences of limestone facies. The different thickness–facies relationships in the measured and decompacted Dumugol successions indicate that a large portion of the major controls on the formation of sedimentary cyclicity changed from sediment accumulation rate to relative sea-level fluctuations. Such modification by compaction of the original sediment column appears to have been caused by early cementation in calcareous sediments, which resulted in differential thinning between limestone and shaly deposits. These findings reveal that diagenetic influences on sequence-stratigraphic and cyclostratigraphic interpretations have been underestimated, with consequent potential effects on associated local to regional geodynamic models, particularly for mixed carbonate–siliciclastic successions.
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In this sense, in order to evaluate cyclicity variations (facies changes, thickness, frequency/pattern) and define key-surfaces, we used the Fischer Plots extension (Fischer, 1964; Sadler et al., 1993; Bosence et al., 2009). This methodology compares the cumulative departure from average cycle thickness and the cycle number to estimate the accommodation space creation rate related to base level variations (Husinec et al., 2008). The Pastos Bons Formation is exposed throughout road cuts, dried drainage beds and small hills with exposures that reach up to 30 m-thick.
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However, several recent wells have good sidewall core coverage across the SCP, and results from two recent whole cores cut within the SCP became available during this study. We have used the software published by Husinec et al. (2008) to construct Fischer plots to analyse trends in the thickness of fourth-order cycles within the SCP. Fischer plots are a widely-used tool for interpreting trends in accommodation space change in successions of cyclic carbonates (e.g. Fischer, 1964; Read and Goldhammer, 1988; Sadler et al., 1993).
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However, these negative effects would be reduced if extra information is included such as systematic facies changes and special facies indicators (subaerial exposure indicators, shales). Fischer plots are conventionally drawn by cumulative departure from a mean cycle thickness against the cycle numbers (> 50) (Read and Goldhammer, 1988; Sadler et al., 1993; Husinec et al., 2008) or cumulative thickness of cycles (e.g., Chen et al., 2001a; Zhang et al., 2015). In this way, thick cycle packages will positively deviate from the mean cycle thickness, and form the rising limbs of the plots, reflecting a long-term increase in accommodation space; whereas thin cycle packages will negatively deviate from the average cycle thickness and form the falling limbs, reflecting a long-term decrease in accommodation space.
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FISCHERPLOTS: An Excel spreadsheet for computing Fischer plots of accommodation change in cyclic carbonate successions in both the time and depth domains☆

Abstract

Introduction

Section snippets

Fischer plots and cyclic carbonate platforms

Program description

Example

Conclusions

Acknowledgments

Accuracy and frequency stability of the Earth's orbital elements during the Quaternary

Some comments on the problem of using vertical facies changes to infer accommodation and eustatic sea-level histories with examples from Utah and the southern Rockies

Lithofacies and cyclicita of the Yates Formation, Permian Basin—implications for reservoir heterogeneity

American Association of Petroleum Geologists Bulletin

Misuse of Fischer plots as sea-level curves

Geology

Numerical forward modeling of peritidal carbonate parasequence development: implications for outcrop interpretation

Basin Research

The Fischer diagram in the depth domain: a tool for sequence stratigraphy

Journal of Sedimentary Research

Aperiodic accumulation of cyclic peritidal carbonate

Geology

The Loffer cyclothems of the Alpine Triassic

Geological Survey of Kansas Bulletin

Landward movement of carbonate mud: new model for regressive cycles of carbonates (abstract)

American Association of Petroleum Geologists Bulletin

The origin of high-frequency platform carbonate cycles and third-order sequences (Lower Ordovician El Paso GP, West Texas): constraints from outcrop data and stratigraphic modeling

Journal of Sedimentary Petrology

Cyclicity and paleoenvironmental dynamics, Rocknest platform, northwest Canada

Geological Society of America Bulletin

Field and modelling studies of Cambrian carbonate cycles, Virginia Appalachians—a discussion

Journal of Sedimentary Petrology

Variation in the earth's orbit: pacemaker of the ice ages

Science