. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography PHI UNITS (b) FIGURE 1. Grain-size frequency distributions as a product of a retention vector and an admittance vector. See text for explanation. From Swift et al. (1972b). If P]n is an element in an admittance vector, where j denotes thej'th station in the transport path and n de- notes one of n grain-size classes, and if P'}n is a corre- sponding element in a retention vector for the same station, then the product of the two probabilities, Pjn( 1
. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography PHI UNITS (b) FIGURE 1. Grain-size frequency distributions as a product of a retention vector and an admittance vector. See text for explanation. From Swift et al. (1972b). If P]n is an element in an admittance vector, where j denotes thej'th station in the transport path and n de- notes one of n grain-size classes, and if P'}n is a corre- sponding element in a retention vector for the same station, then the product of the two probabilities, Pjn( 1 — P'jn) gives the probability that the particle in the local input enters but does not leave the station. The product of the input vector with all corresponding ele- ments in the admittance and retention vectors for a sta- tion gives the frequency distribution for that station (Fig. 1). This is a restatement, in probabilistic terms, of the intuitively apparent fact that the modal diameter of a deposit is that grain size most likely to arrive and least likely to be carried away from the place of deposition under prevailing flow conditions; progressively coarser sizes are progressively less frequent because they are less likely to arrive, and progressively finer sizes are progres- sively less frequent because they are more likely to be carried away. In Fig. la, the two linear numerical filters (admit- tance and retention vectors) are applied to a local input frequency distribution that is uniform in nature and a symmetrical retained frequency distribution results. If, however, the local input has a skewed distribution (Fig. lb), then the retained distribution is still skewed, al- though it has been modified by the station probabilities. If the filters are not linear, then further modification of the input vector occurs. In Fig. 2, various hypothetical input distributions are subjected to sorting down the stations of a hypothetical transport path according to the probabilistic a
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