Approaches to the study of attenuation with distance were applied in a variety of other regions worldwide, and these studies have been ably summarized by Torrence (1986: 10-37). A valuable theme in these studies has been the exploration of deviations from Renfrew's Law of Monotonic Decrement, and suggestions for improvement of distance decay models. Gary Wright (1970) proposes that predictions made by the LMD could be improved by controlling for variations in consumption through time and between types of consumer sites, and he emphasizes that investigators consider the influence of alternative materials in the study area, such as the effects of local flint on demand for imported obsidian. Wright (1970;Wright and Grodus 1969: 47-52) also advocates using weight of a non-local good as a measure of abundance, rather than count or percentage of each artifact class. For time periods prior to the domestication of beasts of burden in the Near East, when the weight of artifacts was borne directly by human carriers, weight would more likely influence behavior and discard patterns. Renfrew also considers weight in his analysis, but he observes that weight would be influenced by stylistic and functional factors.

Geographical relationships are considered in more detail in subsequent research. Jonathon Ericson (1977;1977;1981;1982) conducted an exhaustive study of California obsidian distributions and, by focusing on deviations from the LMD, and using regression analysis, he was able to assess the strengths and weaknesses of the approach. Ericson uses trend surface analysis available in the early raster-based mapping system SYMAP to produce maps showing isometric distributions of obsidian types in consumption sites (Ericson 1977: Figures 1-4). In comparing this form of analysis with Renfrew's distance decay graph distributions Ericson states that "in two-dimensional analysis only the magnitude of an observation and its distance from a source is considered, the spatial position of the observation is not considered in its local context; and this simplification masks significant variability in the data" (Ericson 1977: 110). Ericson's density maps demonstrate that, while distance from source is a primary determinant of obsidian type, the distributions of obsidian consumption locations are not symmetrical around the source areas. Ericson explores the spatial relationships by superimposing trail systems, alternative material distributions, and ethnolinguistic group boundaries (Kroeber 1925) on the obsidian consumption density maps and finds that these spatial phenomena influence obsidian distributions.

Similar to Ericson's implementation of trend surface analysis, Findlow and Bolognese (1982: 60-70) perform a SYMAP analysis using the percentage of lithic assemblages represented by obsidian throughout their study region. Their maps are useful in that they show the changing territoriality and direction of obsidian procurement through time in the region. However, as their obsidian percentage isolines only display aggregated obsidian versus not obsidian data, and do not differentiate between source types of obsidian, the maps are difficult to interpret in terms of exchange distances from the sources through time.

Quantitative data available for Ericson's (1977: 121-123;1977: 249-257) analysis include isotropic distance calculations between discard locations and geological source areas, and estimated population by consumption area. A multiple linear regression analysis using the percentage of obsidian from a single source showed that, as stated by the LMD, the distance from the source had the highest predictive power. However, the estimated population in a given consumption area had only slightly less power in predicting the source of the obsidian being used than did distance to the closest source, and the distance to the second closest obsidian source had virtually no predictive power. Ericson interprets these data in terms of the degree of utilitarian use of a commodity and level of necessity for the average person in the community. Thus, in the proximity of the geological source of a raw material widely used in the community, the source types with high population levels in the immediate vicinity of the source would have been more widely used in exchange systems (Ericson 1977: 120).

An improvement in the calculation of effective distance with an incorporation of the influence of topographic relief in the cost accumulation with fall-off curves was first explored by Findlow and Bolognese (1980;1982). In their study in the U.S. Southwest the authors manually develop the linear solutions known today in GIS as "Least-cost paths" or, as Findlow and Bolognese (1980: 239) express it, "the line between the site and the source that at once minimized distance and topographic relief". They find that when these paths are used in the cost function then variability is accounted for more strongly than when using an isotropic distance estimate.

The technology of transport can dramatically alter the effective distance, and changes in mode of transportation have been proposed as explanations for variability in distance decay curves through time (Hodder and Orton 1976: 113,117-118;Renfrew 1977: 73). Torrence (1986: 122-123) reviews the issue and she also discusses boat transport (1986: 135-136). The adoption of river and sea-going vessels in Mesoamerica are discussed by Sidrys (1977: 103-105), and in the Mediterranean by Ammerman (1979;1978). Gary Wright (1970) mentions the importance of considering the weight of transported material for the period before the domestication of cargo animals and the availability of caravan trade networks in the Near East. Similarly, working in the Andes, Richard Burger and his co-authors (2000: 348) consider the impact of camelid domestication and llama caravan networks on obsidian distributions.

The prediction, following the LMD, that artifact size or weight should diminish with distance from the source area (Wright 1969: 47-52;Wright 1970;Wright and Grodus 1969) is not necessarily supported in cases where the form of the artifact, such as projectile points or bladelets, take precedence over effective distance from source. Angela Close (1999) found that at early Neolithic sites in southwestern Egypt flint backed bladelets, even very close to the source, were produced to be very narrow due to hafting requirements, defying the prediction of LMD. Close (1999) also found that among the late Neolithic sites unretouched, unbroken flint debitage did not conform to the LMD either, a situation that she attributes to the probable use of domestic cattle in transporting flint cores (Close 1996). With formal tools, such as projectile points, artifact form may take precedence over size. Hofman (1991) found with Folsom points that did not diminish in size with distance from the raw material source. However, incidence of resharpening can be expect to increase with distance from the source, affecting tool size (Andrefsky 1994).

The gravity model was another approach borrowed from geography and applied to the study of regional artifact distributions (Chappell 1986;Hallam, et al. 1976;Hodder 1974;Renfrew 1977: 87-88). Gravity models are used in situations where artifacts made from raw materials from a number of competing sources are found in a given consumption site. The claim is that the approach quantifies the "attractiveness" of a given material type over other types available to the consumers in a site by comparing actual proportions with expected proportions of the material given the predictions of the LMD. However, as Torrence (1986: 27) observes, "in reality, the gravity model is merely a means for describing and comparing distributions which are already reasonably well documented." While gravity models could be useful in parsing complex temporal patterns in raw material use in production and consumption at a given site, the approach does not provide a means of inferring the character of exchange relationships between consumption sites in prehistory.

Throughout the 1970s, the regional exchange literature shows an increasing awareness of the limitations of a purely spatial approach to inferring modes of exchange through formal geographical regression analysis. Renfrew's ambitious models linking geographical distance-decay with substantive modes of exchange connected to an associated evolutionary socio-political level, were meant to be sufficiently general to operate through time and in different cultural contexts. However, from simulation studies and from archaeological applications, researchers observed that it was necessary to incorporate supplementary information along with the geographical data on long-distance exchange and consumption, in order for distance decay studies to be useful. The view that chemically derived exchange data must be considered in association with information about archaeological context was first expressed by Wright (1969) and was widely echoed in the contributions to Ericson and Earle's (1982) volume "Contexts for Prehistoric Exchange" as well as in later volumes on exchange including Ericson and Baugh (1993) and Baugh and Ericson (1994). Preserving the strengths of geographical analyses from the 1970s period of investigation and combined with a greater consideration of artifact form, regional variation in reduction strategies and site-specific contexts of consumption, offers a fruitful way forward.