Even though I am not an expert, but still can tell about few work which has been used by archeologists, especially in analyzing Rock Art assembledges (Ross and Davidson 2006).
Rappaport, R. 1999. Ritual and religion in the making of humanity. Cambridge University Press.
which has been used by
Ross and Davidson. 2006. Rock art and Ritual: An archeological analysis of rock art in Arid Central Australia. Journal of Archeological Methods and theory. 13(4):305-41.
You can also see a conference proceedings namely "Kurshiburu: A rock Art site of Eastern India" in XXIV Valcamonica Symphosium 2011.
I reference Rappaport (1999) in my article on repetition and ritual in Japan (pdf posted on my profile "Repetition and the Symbolic in Japanese Ancestor Memorial"), but only briefly and more in regard to the problem of time and cyclicality (reproduction and recurrence, and punctiliousness/invariance vs. change). More of a starting point to introduce ritual theory for my article's purposes, but I would like to see RR's incredible work used more!
Regarding repetition; and the core content of all cultural media, including art, myth, ritual and building sites (mainly dedications to gods and angels or saints or ancestors), I have published six articles in the anthropology journal Expression (there are already 16 editions, I have contributed to six). I demonstrate that sixteen archetypes were isolated in rock art, aft and building sites; in five structural layers (attributes; peripheral sequence; spatial relationship between the eyes of characters expressing archetypes being on an axial grid; certain polar markers on limb joints; and relationship of the polar features to the horizontal or vertical plane of the work). See also www.stoneprint.wordpress.com that demonstrates the universal structure of culture in building sites. Some sites are relics of ritual, for example groups of geoglpyhs on the Nazca plains, and in the Atacama desert; and pyramid fields; and temple fields; and durbar (temple) squares. Thus ritual probably extends not only to invocations and various kinds of magic, and funeral facilities; and initiaitions (see the Avebury and Silbury landscape structural analysis; and the Germany Magdalenburg graves mound structural analysis); but to civic squares including markets and the full repertoire of communal life.
I am looking for a way to extend demonstration of this high detailed, subconscious, compulsive structure, or cultural grammar, in ritual. however time sequence probably replaces some of the spatial context, and time sequence is prone to scrambling, as in myth (and movies).
Stylisation probably plays the same role in ritual as it does in art and building sites and language; an inherently meaningless layer allowing and justifying peer pressure and thus tribal or economic polity differentiation, and thus appropriation and exploitation. Thus we have to remove style from data in order to study the core meaning, in the way that JG Frazer compared data; and C Levi-Strauss compared cognition; and CJ Jung compared data from myth and dreams, or theatre of the subconscious; and return to the wisdom of philosophy, particulary the concept of archetype.
this reply comes rather late, but Pascal Boyer and Pierre Lienard have written many fantastic papers on the cognitive and evolutionary foundations of the “obvious” aspects of ritual (repetition, boundaries, stereotypy, etc.) outlined by Rapport. They also identify threat-detection as an important mechanism in the mediation of ritualized behaviour.
cheers
Samuel
Liénard, P., & Boyer, P. (2006). Whence collective rituals? A cultural selection model of ritualized behavior. American Anthropologist, 108(4), 814-827.
Boyer, P., & Liénard, P. (2006). Precaution systems and ritualized behavior. Behavioral and brain sciences, 29(6), 635-641.
Lienard, P., & Lawson, E. T. (2008). Evoked culture, ritualization and religious rituals. Religion, 38(2), 157-171.
Boyer, Pascal, and Brian Bergstrom. "Threat-detection in child development: An evolutionary perspective." Neuroscience & Biobehavioral Reviews 35, no. 4 (2011): 1034-1041.
Boyer, P., & Parren, N. (2015). Threat-related information suggests competence: A possible factor in the spread of rumors. PloS one, 10(6), e0128421.
Veissière, S., & Gibbs-Bravo, L. (2016). Language, Ritual, and Placebo Sociality in a Community of Extreme Eaters. Food Cults: How Fads, Dogma, and Doctrine Influence Diet, 63.