Basin and petroleum system modeling allows geoscientists to examine the dynamics of sedimentary basins and their associated fluids to determine if past conditions were suitable for hydrocarbons to fill potential reservoirs and be preserved there. Commonly geological models are created using simple assumptions about the superposition of sedimentary layers during deposition. However, for prograding sequences foreland basin and passive margin settings in particular, this results in simplistic models with limited geological validation of thicknesses or facies distribution.

Stratigraphic forward modeling is a quantitative approach to create a geological model by simulating dynamic sedimentary processes, such as erosion, sediment transport, and deposition, while maintaining mass balance. By suitably varying parameters that represent paleogeographic conditions (such as sea level, sediment input, and major tectonic events) stratigraphic forward modeling can generate a realistic three-dimensional model and predict the distribution of sediments and their properties.

This chapter appears in Geostatistical and Geospatial Approaches for the Characterization of Natural Resources in the Environment, available for purchase from Springer. This book explores the current state of the art and informs readers about the latest geostatistical and space-based technologies for assessment and management in the contexts of natural resource exploration, environmental pollution, hazards and natural disaster research. The content covers 3D visualization, time-series analysis, environmental geochemistry, numerical solutions in hydrology and hydrogeology, geotechnical engineering, multivariate geostatistics, disaster management, fractal modeling, petroleum exploration, geoinformatics, sedimentary basin analysis, spatiotemporal modeling, digital rock geophysics, advanced mining assessment and glacial studies, and range from the laboratory to integrated field studies.

Mathematics plays a key part in the crust, mantle, oceans and atmosphere, creating climates that cause natural disasters, and influencing fundamental aspects of life-supporting systems and many other geological processes affecting Planet Earth. As such, it is essential to understand the synergy between the classical geosciences and mathematics, which can provide the methodological tools needed to tackle complex problems in modern geosciences.

The development of science and technology, transforming from a descriptive stage to a more quantitative stage, involves qualitative interpretations such as conceptual models that are complemented by quantification, e.g. numerical models, fast dynamic geologic models, deterministic and stochastic models. Due to the increasing complexity of the problems faced by today's geoscientists, joint efforts to establish new conceptual and numerical models and develop new paradigms are called for.