--> Abstract: A Stratigraphic Inverse Simulation Model, by M. A. Lessenger and T. A. Cross; #91004 (1991)

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A Stratigraphic Inverse Simulation Model

LESSENGER, MARGARET A., and TIMOTHY A. CROSS, Colorado School of Mines, Golden, CO

Numerical process-response models of sedimentary basins have the potential for accurately simulating and predicting stratigraphic architecture and facies distributions. Increases in the accuracy of such forward models will require assessment and calibration of two common attributes. First, the correct process variables must be chosen, their interdependencies identified, and responses established. Second, the magnitudes and frequencies of the processes that controlled distribution of lithologies and stratal architecture must be extracted from field-based stratigraphic data.

One approach toward determining the magnitudes and frequencies of process variables that operated in a basin is inversion of real or simulated (modeled) stratigraphic data; this approach has several advantages. First, inversion should estimate not only magnitudes and frequencies of the process variables, but also their ranges and errors of the estimates. Second, inversion provides a means for assessing the sensitivities, interdependencies, and relative importance of the variables in controlling the resulting stratigraphy. Third, it determines the accuracy of the values of the process variables that are extracted from a data set based on known limitations of the forward model, temporal and spatial sampling of the data set, and the degree to which relations between processes and respons s have been established. Finally, it suggests the amounts, types, and sampling frequency of data that will be necessary for more accurate and precise inversions of real-world stratigraphic data.

We are applying Generalized Linear Inversion (GLI), using the Marquardt technique, to a simplified stratigraphic forward model. GLI extracts values for the fundamental process variables of eustasy, tectonic subsidence, sediment supply, compaction, and isostatic response from a limited stratigraphic data set. For this inverse model, stratigraphic data consist of interpreted water depths and stratal thicknesses correlated within a time-stratigraphic framework. This preliminary work will determine the potential utility of applying this method to more realistic field-tested models.

To develop the GLI model, we built a scaled-down, simplified version of our forward stratigraphic model. This simplified model contains many of the primary elements of the more sophisticated model, but does not include sediment supply, compaction, or isostatic response parameters. Eustasy is modeled with a simple sine curve, and the amplitude of tectonic subsidence is modeled with a square root of age curve. Sediment is only deposited seaward of the strand; thicknesses are constrained with an equilibrium slope. Initial depositional topography is modeled with a seaward-sloping line.

In the GLI, the forward model is locally linearized with first-order terms of a Taylor series expansion. Differences between observed and synthetic data are minimized using unweighted least squares. This minimization, a function of the forward model parameters, defines a loss surface. The algorithm searches this loss surface for a minimum guided by a sensitivity matrix. The sensitivity matrix is approximated with finite differences.

Inversion of this simplified forward model was tested by analyzing the speed (number of iterations) and accuracy of convergence to sets of "true" parameters when they were perturbed within the inverse model. We have not yet tested the routine on actual data. The accuracy and speed of convergence was excellent for subsidence amplitude, constraining slopes, and eustatic frequency. However, there was no convergence for eustatic amplitude or phase. Because this particular forward model is fairly insensitive to eustatic amplitude and phase, inversion is difficult; the routine cannot search for minima on a relatively flat surface. In addition, analysis of matrices indicates that the inversion algorithm confuses eustatic amplitude with subsidence amplitude, and the time increment between cor elated horizons with eustatic frequency.

 

AAPG Search and Discovery Article #91004 © 1991 AAPG Annual Convention Dallas, Texas, April 7-10, 1991 (2009)