Fractal Features of Fan-Shaped Depositional Bodies

Key words: 
• fan-shaped depositional body /
• fractal dimension /
• nonlinear dynamics /
• fractal-kriging simulation

Abstract: Fan-shaped depositional bodies are those mainly composed of terrigenous coarse deposits and fan-shaped in morphology, including alluvial fan, fan delta, delta and subaqueous fan and so on. They are important exoil-gas targets in oil and gas-bearing basins in Mesozoic and Cenozoic interior and offshore in China, which are the problems deeply concerned with by oil-gas exploration department to show quantitatively the features of their morphological distribution and inner structure parameters. Recent researches on fan-shaped bodies are results combining static, qualitative and megascopic methods with dynamic, quantitative and microscopic approaches. Great efforts were made in quantitative modeling and in simulating of structural parameters of sedimentary bodies, but there have been still few of published documents about how to build morphological and simulating models of sedimentary bodies up to now. With fractal theory applied widely to sedimentology , it may be considered from a new point of view to solve the problems. The growing of fan-shaped depositional bodies is a complex nonlinear dynamics process and a fractal. Fractal dimension may reflect the complexity of their outer morphology and inner structure, and predict some information about tectonic and depositional setting. It will be one of the most important ways to realize nonlinear dynamics building models and simulation of depositional bodies combined fractal with chaos theory. On the bases of analyses of sedimentological features of more than twenty faulted basins at home and abroad, the paper probes the growing dynamic process of fan-shaped depositional bodies, summarizes their fractal features, and establishes the model of shape fractal growing and structural fractal. The structural fractal box dimensions are determined. Simulations of morphologies of the fan-shaped bodies are made by fractal, and of their structures by fractal-Kringing. The main conclusions are as follows： 1.Fan-shaped sedimentary bodies are complex nonlinear systems. Their forming processes are both a depositional dynamics of growing, crevassing, abandoning and a complex stochastic, nonlinear dynamics. Crevasses can be viewed as a kind of bifurcation and fluctuation; the choice of branches and the interaction of the fluctuation quantities are the important causes to form the complex and various morphological features and inner structures of fan-shaped bodies. 2.The box dimension of morphology fractal of a fan-shaped body is generally 1.1-1.4, that of structure fractal is generally 1.25-1.45. 3.The different box dimensions show different tectonic and depositional setting. Fractal dimensions represents the structural anisotropism of sedimentary bodies. 4.Fractal-Kriging proves to be useful method for modeling morphology and inner structures of sedimentary bodies, it can better reveal the local features and anisotropic change in the bodies by adjusting fractal dimension D, horizontal and vertical range.