Stochastic asymmetry properties of 3D gauss-lagrange ocean waves with directional spreading

In the stochastic Lagrange model for ocean waves the vertical and horizontal location of surface water particles are modeled as correlated Gaussian processes. In this article we investigate the statistical properties of wave characteristics related to wave asymmetry in the 3D Lagrange model. We present a modification of the original Lagrange model that can produce front-back asymmetry both of the space waves, i.e. observation of the sea surface at a fixed time, and of the time waves, observed at a fixed measuring station. The results, which are based on a multivariate form of Rice’s formula for the expected number of level crossings, are given in the form of the cumulative distribution functions for the slopes observed either by asynchronous sampling in space, or at synchronous sampling at upcrossings and down-crossings, respectively, of a specified fixed level. The theory is illustrated in a numerical section, showing how the degree of wave asymmetry depends on the directional spectral spreading and on the mean wave direction. It is seen that the asymmetry is more accentuated for high waves, a fact that may be of importance in safety analysis of capsizing risk

Enterolithic folds in evaporites as microbially induced sedimentary structures: New model of formation and interpretation in the geological record

Enterolithic structures are stratigraphically localized folds in gypsum beds found in certain saline evaporitic sedimentary units in a wide variety of basins. Different models of formation have been proposed, all related to inorganic processes. These models include: diagenetic transformation of gypsum beds producing either displacive growth of crystals or volume changes; mechanical folding caused by compressional stress; and folding produced by slumping. The analysis of three Cenozoic evaporite sequences in Spain reveals that none of the previous models explains their origin and existence. In these outcrops, gypsum enterolithic structures occur in horizontal beds with parallel troughs and crests of the folds. They appear in shoreline facies of lacustrine environments and did not undergo major diagenetic transformations after the primary lithification of the original sediment. Based on these observations, together with the study of a modern analogue in Minorca, Spain, a new model is proposed for the genesis of enterolithic structures. This new model is based on the existence of a microbial mat exposed to brine concentration–dilution cycles and strong wind events. The high wind flow events enhanced folding of the microbial mat that became subaerially exposed and lithified due to subsequent evaporation. Therefore, the presence of enterolithic structures could be used as an indicator of shallow water environmental conditions subject to variations in brine concentration in areas with strong wind flow events. Previous studies of some evaporitic successions should be revisited, taking into account the proposed model, which would imply new depositional environment interpretations. At the same time, the proposed model could explain the existence of Kinneyia‐type structures, also known as wrinkle structures, formed beneath microbial mats in peritidal zones. Moreover, considering enterolithic structures as microbially induced sedimentary structures could be useful as evidence of microbial life in the ancient geological record and on other planets such as Mars