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Porosity-Velocity Distribution in Stratigraphic Sequences: The Marion-Yin Model*

By

Juan Florez¹ and Gary Mavko¹ 

Search and Discovery Article #40105 (2003)

*Adapted from “extended abstract” for presentation at the AAPG Annual Meeting, Salt Lake City, Utah, May 11-14, 2003. 

¹Stanford Rock Physics Laboratory, Department of Geophysics, Stanford University

General Statement 

Parasequences and single stratigraphic cycles, the building blocks of larger sequences, present relatively simple lithofacies trends: fining upward, coarsening upward, blocky, or serrated. Both fining-upward and coarsening-upward trends show gradual transitions from clay-rich shale to clean-sand lithofacies. Changes in porosity along these facies transitions can be predicted using either the Marion-Yin model for dispersed mixtures, or arithmetic averages for laminar mixtures. 

According to the Marion-Yin model for dispersed mixtures (Marion, 1992), the porosity of unconsolidated clayey sand decreases in respect to that of clean sands, as clay replaces pore space. Similarly, in respect to pure-clay sediments, the porosity of sandy clay decreases as well, as non-porous sand grains replace porous clay. The lowest porosity is reached when all the pores in the sand framework are replaced by clay (Figure 1). This is also the point of the highest velocity. The velocities of the end members, clean sand and pure-clay, are the lowest and about the same (Figure 2). As sediments are buried, those with clay as the load-bearing material present a high porosity-reduction gradient, whereas those with sand as the load-bearing material normally have a low porosity-reduction gradient. As a result, the pattern of transitional facies changes from clean sand to pure clayey shale in the velocity-porosity plane varies from a linear trend at low confining pressure, to an inverted V shape at high confining pressures (Figure 2). 

The facies transitions shown in the Marion-Yin model resemble the vertical facies tracks observed in single depositional events or cycles (Figure 3). Consequently, the Marion-Yin model predicts that the patterns of stratigraphic sequences in the velocity-porosity plane will change from a collapsed V in unconsolidated sediments, to an inverted V-shape in sedimentary rocks. Similar changes in porosity and velocity occur in bimodal sand mixtures and sands with different grain sizes (Estes et al., 1994). In general these changes can be associated with the effect of sorting on porosity and consequently on permeability (Figures 4 and 5) and velocity (Avseth et al., 2000). However, in the case of sand-clay mixtures the effect is not only textural but also compositional. 

We evaluate the applicability of this model to unconsolidated and consolidated fluvial facies sequences composed of one single fining upward-cycle (Figures 6 and 7). The degree of compaction is deduced from the burial depth. The changes in porosity and velocity within these two sequences correlate qualitatively well with those predicted by the model (Figures 8 and 9). In the consolidated sequence, the slopes observed in the segments of the inverted V differ from those predicted by the model. In the unconsolidated sequence, the flat tail of low-velocity and high-porosity associated with pure clay is absent. In spite of these differences, the Marion-Yin model provides a good estimate for the variation of both porosity and velocity in stratigraphic sequences composed of non-laminar sand-clay mixtures.