Introduction

Site formation process (SFP): preface

An SFP is any event involving interactions of physical forces, human activity and the environment that affect the characteristics of the archaeological record (Sullivan and Dibble 2014). An understanding of SFPs is obligatory for any rigorously assessed scientific reconstruction of the cultural past. As such, SFPs belong among the core concepts of any archaeological inquiry (e.g., Schiffer 1987, 2010; Karkanas and Goldberg 2018). Controlling for the impacts of SFPs is crucial to the discipline because archaeologists use the patterns of artifact dispersal in the ground to infer behaviors (Stein 2001). One of the major challenges, therefore, is the identification of patterns that are created by ancient behaviors as opposed to those created by later cultural and natural processes. In this respect, one of the major research avenues in the study of SFPs deals with post-depositional and recovery processes (e.g., Schiffer 1972, 1983, 1985; Clarke 1973; Sullivan 1978). According to O'Shea (2002: 212), post-depositional theory is concerned with what happens after an object has left the systemic archaeological context; whereas, recovery theory is concerned with how the actual process of archaeological discovery and recovery can distort or bias the perception of the archaeological record. After several decades of intensive research in these areas, however, the basic physics of the forces impacting scattered archaeological remains on and under the surface remains surprisingly understudied.

The archaeological aspects

One of the major pillars of archaeological investigation is the field survey: searching for sites and collecting information about the location, distribution and organization of past human cultures across a large area (e.g., Schiffer et al. 1978; Bintliff and Snodgrass 1988; Banning 2002; Tartaron 2003; Bintliff 2014; Banning et al. 2017). Surface surveys are often complementary to excavations, with the advantage of being less expensive and minimally disruptive (Faust and Katz. 2012; Shai and Uziel 2014). From the spread of artifacts on the surface and their quantitative and typological analysis, the settled areas and relative populations in different prehistorical and historical periods are estimated (e.g., Broshi and Finkelstein 1992; Postgate 1994; Finkelstein 1996; Bintliff and Sbonias 1999; Osborne 2004; Chamberlain 2006). Despite a large range of geomorphic factors, such as the processes of alluviation or colluviation, environmental disturbances (cryoturbation or bioturbation) and developmental processes (e.g., ploughing), the validity of the surface survey for locating archaeological sites has been proven on numerous occasions. For instance, in the archaeology of the southern Levant, this is evidenced in the numerous rescue surveys performed along the route of the Cross-Israel Highway before its construction (Dagan 2010), which correctly attested 125 new sites. Nevertheless, a number of sites were not located during the surface survey, and were only eventually discovered in the course of construction activities or during different stages of salvage excavations (Dahari and Ad 1998). Inconsistencies such as these have been noted in both Israel (e.g., Dagan 2009; Garfinkel and Ganor 2010) and worldwide (e.g., Whallon 1979; Alcock and Cherry 2004; Wossink 2009: 46–48; and references therein). The reasons for these discrepancies have never been properly analyzed or understood.

The other side of the same coin with regard to SFPs concerns the presence of artifacts from earlier levels in the later levels of multi-period and multi-stratum sites (archaeological tells) (e.g., Villa 1982; Finkelstein and Zimhoni 2000). This well-known phenomenon is usually considered to be related to subsequent construction activities, which utilized materials (such as mud) that introduced earlier artifacts into later strata, to differences in erosion between different parts of the site, or to mole rat activity (Sapir and Faust 2016). This may be so and indeed, there are many additional components that may affect SFPs. Nevertheless, before one embarks on clarifying particularities such as these, it is essential to understand the basic physics and dependencies underlying the accumulation of artifacts from different periods on the surface or at boundaries between strata in archaeological sites, and their movements, if any, in different types of soils. Similarly, it is imperative to understand why in certain types of soil, we do not observe archaeological scatters on the surface, despite the presence of archaeological sites beneath.

The physical and geological phenomena

The Brazil nut effect (BNE)

The BNE refers to the phenomenon by which large granular particles, in a bed of small vibrating particles, rise to the top (Fig. 1). The same result occurs with both vertical and horizontal vibrations. Thus, shaking a box of cereal leads to spontaneous ordering of the largest particles toward the upper part of the container, ostensibly against the intuitive assumption that objects will become randomly mixed when jostled. This phenomenon occurs even if the larger particles have a higher density than the smaller ones (Möbius et al. 2001). However, when changing the shaking conditions, the same large particles may sink to the bottom due to what is known as the reverse Brazil nut effect (RBNE) (Breu et al. 2003; Schnautz et al. 2005; Schröter et al. 2006; Garzó 2008). It has also been demonstrated that factors which might at first glance appear inconsequential (e.g., air pressure, starting height, etc.) can change the outcome from a lifting to a sinking. Therefore, these granular systems can be considered out of equilibrium at almost any level (Kudrolli 2004; Shinbrot and Muzzio 2000).

Fig. 1
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Simplified representation of the BNE as a result of vertical vibration. Credit: by I. Ben-Ezra

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Although these phenomena have long been known and abundantly observed and described (e.g., Williams and Shields 1967; Ahmad and Smalley 1973; Rosato et al. 1987), real advances in understanding the physical mechanisms involved have only been achieved in the last two decades (e.g., Möbius et al. 2001; Naylor et al. 2003; Kudrolli 2004; Rémond 2004; Schnautz et al. 2005; Ciamarra et al. 2006; Xu and Zhu 2006; Chung et al. 2013; Wang et al. 2016). The main factors affecting the phenomena are the size ratio (DL/DS) (Rosato et al. 2002) and the density ratio (ρL/ρS) (Möbius et al. 2001) of the large to small particles, where D refers to the diameter; ρ refers to the density; L stands for large object, in our case the archaeological artifact (the intruder); and S refers to the small media, in our case the soil (and see below).

Today, studies of the BNE and RBNE are at the forefront of granular physics, with their implications for early planet-formation processes and the formation of asteroids (Güttler et al. 2013; Matsumura et al. 2014; Perera et al. 2016). Recently, it has been suggested that riverbed armoring, which prevents excessive erosion, should also be seen as an example of a granular segregation phenomenon within the framework of the BNE, where gravel riverbeds typically have an “armored” layer of coarse grains on the surface, which acts to protect the finer particles underneath from erosion. The term “armored layer” has been coined by researchers to describe a situation in which the larger particles can be seen as an armor that protects the riverbed underneath from erosion (Ferdowsi et al. 2017). It had previously been assumed that only fluid mechanics control this pattern, where the river water would wash away the finer particles, leaving the larger particles behind. Experimental results, however, suggested that some riverbed armoring may be due to the granular segregation that follows the BNE from below—rather than fluid-driven sorting from above (Ferdowsi et al. 2017; and see further Seil et al. 2018; Dudill et al. 2018).

Desert pavements (DP)

The presence of rock fragments in topsoils is well known (Poesen and Lavee 1994). According to Poesen's (1990) estimations, these soils are widespread, particularly in the Mediterranean area where they often constitute more than 60% of the land. In some cases, rock fragment contents in the topsoil are attributed to intensive cultivation. Bruder (1982) described the emergence of large stones each year from the soil of agricultural fields in northern Israel following harvest. Similar patterns for the emergence of surface rock fragments following tillage erosion have been reported from other locations, such as southern Spain (Poesen et al. 1997). The same observation applies for archaeological artifacts, where the fresh ploughing of a fallow field brings to the surface considerable quantities of new archaeological material (Tartaron 2003). It seems, however, that in many cases, the main mechanism underlying the creation of surface rock pavements may be related to the process of DP formation. DP is the final stage of a very long geological/pedological process occurring in what is typically known as reg (desert) soils. The typically described DP formation process includes gravel shattering and fragment lifting in the lower, so-called B horizon, the fragments' penetration into the upper Vesicular horizon, and finally, their accumulation as a DP on the surface (Amit et al. 1993; Poesen and Lavee 1994). Amit et al. (1993) suggest to separate the long-term shattering process, in the deep soil into five stages in which the shattering rate turns from logarithmic to asymptotic, thus, most of the shattering process takes place in the first stages in the ground. In other studies (e.g., Grotzinger and Jordan 2010), the DP process is limited to the Vesicular horizon, near the upper surfaces. In that case, the lifting process includes the effect of a wind blowing fine-grained material, rain events during which the microbes living underground produce bubbles that raise the pebbles.

DP has also been reported for many types of rocks and morphological surfaces, such as alluvial fans, basaltic flow, pluvial lake beaches and plain terraces, as well as volcanic structures (e.g. Amit et al. 1993; Al-Farraj and Harvey 2000; Valentine and Harrington 2006; Kianian 2014). DP vertical rising on a continuously thickening sedimentary layer have been assumed to be stable landforms. However, recent works (Dietze and Kleber 2012; Dietze et al. 2012, 2013, 2016; Derkum and Dietze 2019) suggest a further lateral process that possibly indicates desert pavements to be a dynamic rather than a stable landform. The proposed mechanism: rain water infiltration causes soil air pressure to increase, as air cannot escape through the mixture of wet clay and sand surface but through the still dry patches below stones, it lifts stones parallel to the slightly inclined surface. Another model suggests that deposition of wind blown sediments is the major agent of pavement evolution and formation and, accordingly, these pavements are actually borne at the surface (Wells et al. 1995). This model, however, is not applicable for all cases of DP formation as it has been tested only for lava flows in specific locations.

Archaeological pavement (AP)

Subsurface redistribution processes resulting in upward and downward movement of artifacts have been well attested to, primarily in the field of prehistoric archaeology (Staurset and Coulson 2014, with further references). Villa (1982: 287) observed that "considerable vertical movement can occur in the absence of visible traces of disturbance. Such displacement—which may be either postdepositional or contemporaneous with the time of burial—alters the original stratigraphic relationships of archaeological items and creates false stratigraphic associations." According to her, layers and soil should be considered as fluid, deformable bodies through which archaeological items float, sink, or glide. The main forces behind these movements are routinely described not only in terms of biogenic activity, but also by other instances, such as differential stresses in the Aeolian soil column due to consolidation, or due to the wetting and drying of sediments that may cause vertical descent of artifacts into the soil (e.g., Cahen and Moeyersons 1977; Moeyersons 1978; Wood and Johnson 1978; Rowlett and Robbins 1982; Villa 1982; Villa and Courtin 1983; Erlandson 1984; Hofman 1986; Bocek 1986; 1992; Bollong 1994; Leigh 1998; Bueno et al. 2013; Araujo 2013). To deal with this vertical mixing of archaeological deposits, a series of mathematical models, based on assigning probabilities to a variety of artifact specimens' movements between discrete stratigraphic layers, have even been developed (Brantingham et al. 2007). All of these explanations and models, reliable as they are, do not take into account additional major forces that are physical in nature and that, in our view, will have a large effect on any given SFP.

We would like to introduce a new term, "archaeological pavement" (AP), describing the physical process by which archaeological artifacts are lifted by the soil and accumulated on open surfaces, indicating, in most cases, a hidden archaeological site below. The term AP is derived directly from its resemblance to DP appearance on the surfaces. In the following, we suggest that the primary force creating AP is the BNE. Similarly, the forces responsible for the RBNE may explain the phenomenon of reverse archaeological pavement (RAP). This hypothesis enables the use of theoretical and experimental results attained from studies of the BNE to enhance our physical understanding of the lifting process of artifacts in archaeological sites through AP formation.

In what follows, based on laboratory tests, we offer a new SFP model that takes into consideration two opposing and continuous processes: soil coverage of the site soon after human activity has ceased, and a force(s) that tends to lift buried artifacts up to exposed surfaces, acting in accordance with Brazil nut effect (BNE). The model will also address the following questions: (i) why even intensive field surveys occasionally fail to detect significant archaeological sites buried in the ground, and (ii) how we can integrate, in the same model, both the lifting process, BNE that leads to AP and its reverse action, RBNE that leads to RAP?

Methods

Seven typical Israeli soils (as defined by Ravikovitch 1981) from different locations (Fig. 2), were tested for their lifting speed using vertical and horizontal vibrations with the same spherical intruder. Yaalon (1997) demonstrated that all terrestrial soils in the Mediterranean region are affected by the addition of Aeolian dust. This activity started when the Sahara became a desert. Hence, values of up to 50% Aeolian material in limestone soils are reasonable (Yaalon and Ganor 1973). This leads to the existence of a high percentage of small-sized particles in local Israeli soils, enhancing the role of the void-filling mechanism.

Fig. 2
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Map of an area with archaeological sites mentioned in the text. Credit: by I. Ben-Ezra

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Out of seven samples, two samples were collected from sites in which a very close correlation was found between the surface survey and the final excavation results. In other words, the archaeological remains from a number of periods collected during the surface survey and from the buried archaeological strata beneath it were almost a perfect match. The first sample (Table 1: No. 2) came from Tel Hadid (Brand 1998); the second sample (Tables 1: No. 3) was from Tel Ras Abu-Hamid (Shavit and Wolf 2008), both located in the upper Shephelah—a lowland region in southcentral Israel stretching over 10–15 km between the mountains and the coastal plain.

Table 1 Correlation between field surveys and archaeological excavations for the tested soil samples
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Two other samples were taken from sites in the Shephelah, but from slightly different geomorphological locations, which showed a poor correlation between the surface survey and the following excavation. The first sample (Table 1: No. 4) came from Horbat Petora (north). Here, the archaeological surface survey only revealed remains from the Byzantine period; whereas, the following salvage excavation revealed extensive remains from several earlier periods, namely Neolithic, Chalcolithic, Early Bronze I and Roman periods (Gorzalczany and Baumgarten 2005). The second sample (Table 1: No. 1) came from Shoham. This area had been covered by several surveys (Dagan 2010), all of which failed to find any remains of the extensive archaeological site that was found later by accident. The site yielded substantial remains, attributed to eight different periods, namely Late Iron Age/Early Persian, Early and Late Hellenistic, Early Roman, Byzantine, Early and Late Islamic and Medieval periods (Dahari and Ad 1998). Other soil samples (Table 1: Nos. 5–7), with no correlation to attested archaeological remains, were taken for comparative purposes, demonstrating different lifting speeds for additional soil types.

In the first stages of this study, we focused on choosing the best vibrating conditions and selecting the specific artifacts (intruders) to be tested. First, a 2D symmetric loom weight was examined. As this object was not lifted in a horizontal manner during the lifting process, it was difficult to detect the exact moment at which the object was completely separated from the soil. Therefore, a spherical intruder was selected instead, as in this case the completed lifting process is clearly indicated by the roll of the intruder on the surface of the sample. The "lifting time" for the intruder was defined as the time, in seconds, needed for the intruder covered, at the center of the vessel, to reach the top surface and to start rolling freely. Since it was not clear whether the horizontal or vertical vibration is the dominant factor in archaeology, we decided to test all of the samples using both vibrating directions, applying the same vibrating characteristics and using the same object as the intruder.

The preparation procedure of the soil samples and the final protocol of running conditions are as follows:

  1. 1.

    The soils were sampled in the locations described above, after removing ca. 10 cm from the topsoil.

  2. 2.

    The samples were sieved in a screen of 2 mm: to receive a clean material.

  3. 3.

    The samples were heated in an oven at the temperature of 180° C for 60 min to achieve same dry conditions.

  4. 4.

    After the heating, the samples were stored in closed vessels to prevent absorbing the external moisture.

  5. 5.

    Before vibration each sample was mixed in its storing vessel for two minutes to avoid soil's compaction (cf. Grotzinger and Jordan 2010: 129–130).

  6. 6.

    Device: a versatile horizontal and vertical vibrator was used. The dimensions of the conical–cylindrical vessel used to hold the samples were: bottom diameter 93 mm, top diameter 105 mm, height 72 mm (Fig. 3).

    Fig. 3
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    The experimental device with a soil sample and various tested intruders. Credit: by D. Luria

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  7. 7.

    Intruder: a spherical intruder with a diameter of 14.3 mm and density of 0.72 g/ml3.

  8. 8.

    Prior to the tests, the intruder was installed below the surface at the center of the holding device to minimize the effect of the walls and of soil's cycling (cf. Yaalon and Kalmar 1978).

  9. 9.

    Running conditions in both horizontal and vertical vibration: lifting distance for measuring the lifting time, 16.3 mm; frequency 5.92 Hz; amplitude 14 mm.

Soil has unique spectral characteristics, which allow for quantification of organic matter, clays, hygroscopic water, crystalline iron, calcite, etc. (Stoner et al. 1980; Nocita et al. 2015; Viscarra Rossel et al. 2016). Thus, despite it being a very complex matrix (Holliday 2004; Grotzinger and Jordan 2010), the soil's spectral characteristics can simplify its complexity and indicate its characteristics (Ben-Dor et al. 2007, 2017; Viscarra Rossel and Bouma 2016). The samples were measured using Tel Aviv University's protocol (Ben-Dor et al. 2008, 2015), concentrating on three parameters: sand (particle size 2.0–0.05 mm), silt (particle size 0.05–0.002 mm) and clay contents (particle size less than 0.002 mm) that appear to be essential to the lifting and sinking speeds of artifacts (Rosato et al. 2002).

Results

During the laboratory testing, two samples from the sites (Tel Hadid and Tel Ras Abu-Hamid) in which a very close correlation was found between the surface survey and the final excavation results have demonstrated relatively short lifting speed/time for the buried object toward the surface, 10 and 14 s, respectively, under horizontal vibration and 12 and 21 s, respectively, under vertical vibration (Table 2: Nos. 2–3, respectively).

Table 2 Comparison of the lifting time and speed of the soil samples under horizontal and vertical vibrations
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Two other samples from the sites which showed a poor correlation between the surface survey and the following excavation (Horbat Petora and Shoham), have demonstrated comparatively long lifting speed/time for the buried object toward the surface, 17 and 72 s, respectively, under horizontal vibration and 23 and 49 s, respectively, under vertical vibration.(Table 2: Nos. 4; 1, respectively).

The results from both vibration modes (Table 2) demonstrated a close similarity in the order of the lifting speeds, and in the mean lifting velocity (12.4 and 14.5 mm/s × 10, respectively), despite the large qualitative variety of the results (Vmax/Vmin in the horizontal vibration was 15:1 and in the vertical vibration 6:1).

The principal results were that the faster the lifting speed of each examined soil, the closer the correlation between the survey results and the excavation results, and vice versa (Figs. 4, 5). This discovery has important consequences for the theoretical understanding of the SFP at any archaeological site.

Fig. 4
figure 4

Horizontal vibration case. Graphical comparison of lifting speeds and the correlation between field surveys and the subsequent archaeological excavations, where available. Credit: by D. Luria and I. Ben-Ezra

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Fig. 5
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Vertical vibration case. Graphical comparison of lifting speeds and the correlation between field surveys and the subsequent archaeological excavations, where available. . Credit: by D. Luria and I. Ben-Ezra

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The results of spectral investigation for all seven samples are presented in Table 3. The correlation found between lifting speed and sand and silt contents is shown in Fig. 6a, which demonstrates that an increase in the amount of large-size particles (sand) decreases the lifting speed. In contrast, increasing the amount of small-size material (silt), as shown in Fig. 6b, increases the lifting speed. Both findings are in accordance with the BNE and the void-filling mechanism.

Table 3 Lifting speed of the soil samples under horizontal vibration versus values of sand, clay and silt
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Fig. 6
figure 6

Correlations between lifting speed in horizontal vibration and the contents of a sand, and b silt. Numbers refer to the samples defined in Table 1. Credit: by E. Ben-Dor and I. Ben-Ezra

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Analyzing the effect of clay content on the lifting speed ended with very poor correlation: in horizontal vibration: R2 = 0.3 and in vertical vibration R2 = 0.11. In this regard, it should be noted that our work was limited to dry conditions; while in real-field cases, clays tend to swell with the addition of water. Thus, their actual size will vary between dry and wet periods and in most cases, they will be significantly larger than under totally dry conditions (Tariq and Durnford 1993).

Discussion

Assuming that the primary force creating AP is the BNE, we adopt principal experimental and theoretical data attained from three leading BNE teams. These results are schematically described in Fig. 7. For simplification, all of these major BNE studies used spherical intruders adopted also in our experiment. Our model for SFP will include the principal results described in Fig. 7b–d.

Fig. 7
figure 7

Schematic effects of variable particle density ratios (ρL/ρS) and diameter ratios (DL/DS) on the lifting speed of spherical objects under the BNE, and transfer from the BNE region to the RBNE region. Credit: by D. Luria and I. Ben-Ezra, modified after Mobius et al. 2001; Rosato et al. 2002; Breu et al. 2003

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Möbius et al. (2001) demonstrated that the amount of time taken for spheres of the same diameter but different densities to be lifted from a predetermined depth to the free surface is a function of the specific particle density ratio ρL/ρS (artifact/bed media) (Fig. 7a): rising times are smaller at large and small density ratios; whereas, the rising time for moderate density ratios is larger. The maximum rising time is achieved at a density ratio of around 0.5. However, the most important variable in our work is "lifting speed" and not "lifting time". Therefore, in Fig. 7b, "time" is replaced by "speed", without violating the basic premises of Möbius et al. (2001).

Rosato et al. (2002) demonstrated a direct relationship between the diameter ratio DL/DS (artifact/bed particles) and the vertical lifting speed of an object under the BNE (Fig. 7c). A simple explanation for these results is that as the DL/DS ratio increases, the smaller spheres can more easily intrude beneath the large particles, thereby increasing the lifting speed. This process is called void filling.

Breu et al. (2003) defined the regimes under which the classical BNE switches to a RBNE, in which the particles move to the bottom (Shinbrot 2004). The results (Fig. 7d) demonstrate that a high diameter ratio and a low particle density ratio may lead to a BNE situation; whereas, a low diameter ratio and a high density ratio will lead to a RBNE condition.

The proposed SFP model

Two new terms are added to the following discussion: "speed of soil forming" and "critical speed". It is assumed that shortly after an active site is abandoned, it begins to be covered by soil at a constant rate. This rate is affected by geographical location, specific topography, wind patterns and other environmental variables. The "rate of soil forming" is the quantity at which the parent material is covered by a new soil. At the same time, a vertical lifting force (BNE) will begin to act upon the artifacts. Artifacts having a lifting speed that is higher than the rate of soil forming will remain on or near the surface. On the other hand, artifacts with a lifting speed lower than that rate of soil forming will move upward through the new soil cover, but will never reach the open surface—as long as the two separate processes, covering and lifting, are not disturbed or changed. The point at which the specific lifting speed equals the rate of soil forming is defined here as the "critical speed".

Figure 8 presents the theoretical lifting speeds of two different soils—"fast" and "slow"—while assuming an equal rate of soil forming. As a pure theoretical exercise, each soil contains the same nine artifacts.

Fig. 8
figure 8

Lifting speeds of fast and slow soils. Credit: by D. Luria and I. Ben-Ezra, based on modification of the results presented by Möbius et al. 2001

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Following the original results of Möbius et al. (2001), while at the same time considering the process of soil forming, we arrive at the following outcomes: in the slow-lifting soil, only objects 1 and 9 will reach the open surface as their speed is higher than the "critical speed". On the other hand, in the fast-lifting soil, objects 1, 2, 3, 7, 8, and 9 will be fully lifted. Concurrently, the slower objects will also be lifted according to their individual speeds, but they will not reach the topsoil.

Figure 9 presents a model of a site formation composed of fast lifting soil and two archaeological levels. The artifacts (Nos. 1–9) shown here are the same as artifacts described in Fig. 8. Thus, Fig. 9a displays the situation after level 2 has fully developed and before level 1 has begun to accumulate. Level 2 also includes heavy and large objects that will sink to the bedrock by RAP. Figure 9b exhibits the situation after level 1 has fully developed. Theoretically, if a field survey is performed after level 2 has been fully covered (Fig. 9a), artifacts 1, 2, 3, 7, 8, and 9 will be found; whereas, if the field survey is performed after level 1 has fully developed (Fig. 9b), artifacts 1, 2, 3, 7, 8, and 9 from both levels will be found, but not artifacts 4, 5, or 6 from either level. The latter objects might be revealed only through shovel or probe tests. This theoretical description also shows that the slowest artifact of level 2, artifact 5, is still located in the covered soil of level 2; whereas, artifacts 4 and 6 have already crossed to level 1.

Fig. 9
figure 9

The establishment of an archaeological site by fast-lifting soil. Credit: by D. Luria and I. Ben-Ezra

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Figure 10 describes the same situation as in Fig. 9, but with slow-lifting soil. In this case, a field survey performed after level 1 or 2 has fully developed will reveal only artifacts 1 and 9 of both levels.

Fig. 10
figure 10

The establishment of an archaeological site by slow-lifting soil. Credit: by D. Luria and I. Ben-Ezra

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Under more extreme situations, such as when the soil is extremely slow-lifting, only a few or no objects will reach the open ground and even a careful survey might fail to find archaeological remains. This might explain the case of sample No. 1 from Shoham (Table 1), located in an area that was covered by several surveys, all of which failed to find any remains of the buried archaeological site. The above discussion follows the theoretical consequences derived from Fig. 7b only. In addition, Fig. 7c deals with lifting speed versus diameter ratio which also affects artifact's lifting. However, as Fig. 7c has the same right-hand side characteristics of Fig. 7b (i.e., by replacing “density ratio” with “diameter ratio”), the SFP model that would be derived from Fig. 7c will be, qualitatively, the same as the one derived from Fig. 7b. Thus, to avoid redundancy, the SFP results for Fig. 7c are not presented.

A few scholars in the Southern Levant have tried to use shovel testing (Portugali 1982; Shott 1985; Leibner 2009; Faust and Katz 2012; Shai and Uziel 2014), or even boreholes, to enhance the results of the surface survey conducted for tells prior to their excavation. This procedure (more common in North America) which usually consists of digging a random number of pits scattered on the tell's surface to a depth of ca. 20–30 cm provides important complementary information to the results obtained from the surface surveys. Deeper probe tests are intended to be dug from the surface until a buried site is reached. The outcomes of the shovel and probe tests enable to improve statistical indications of the quantitative and qualitative traits of the remains buried underground, as described in Figs. 9 and 10.

Vertical movements of the various artifacts, having different propagation speeds, may produce unexpected results:

  1. (i)

    Fig. 9b: after level 1 is formed and starts to be covered, objects 4 and 6 of level 2 penetrate into level 1 and continue to be lifted by the soil of level 1. At the same time, object 5 of level 1, having the lowest lifting speed among the artifacts, is also lifted. At some point, object 5 from level 1 reaches the same height position as that of objects 4 and 6 from level 2. If an archaeological excavation is performed at that time, the three objects, originating from two different levels, might be considered a "new" level. We term this situation a "phantom level".

  2. (ii)

    Assume, ostensibly, a "stratum" containing artifacts with the same lifting speeds, which are less than the critical speed—for example, objects 4 and 6 shown in Figs. 9a and 10a. This "stratum" might be considered a separate level in an archaeological excavation and it is defined here as an "induced level".

Interestingly, almost four decades ago, Villa (1982: 266, 278) had already reported similar empirical observations, without being able at that time to relate them to any physical explanation:

I realize that the conclusions I have drawn may be called into question […] that layer boundaries through which objects seem to have moved may have existed only in the mind of the excavator who was too zealous in defining bedding planes, stratigraphic boundaries, and living floors. Whatever processes may have caused vertical displacement of artifacts—so the reasoning goes—we would expect layer boundaries to be blurred. This would immediately suggest to experienced eyes some degree of mixing.

We know now that disturbance during burial or following deposition may affect archaeological assemblages to a much larger extent than previously imagined, and that considerable vertical displacement of artifacts (both upward and downward) may occur even when the matrix itself has not been visibly disturbed or displaced.

In view of this, it is clear that a surface survey performed on slow-lifting soils will underestimate portions of the potential artifacts or will even ignore a site's artifact assemblage entirely, with the only alternative to locating them being the use of shovel or probe tests. In addition, it follows that frequent surveys conducted in the same area will tend to "dilute" the archaeological remains and will lead to a gradual degradation of later results. Banning (2002: 220) correctly identifies the effect of numerous surveys performed in the same area as "exhaustion" (contra to Faust and Katz 2012, who consider the archaeological survey to be a non-destructive procedure). Therefore, it is advisable that all past and present surveys conducted in the same area be integrated into a single cumulative databank. Using the same physical rationale discussed above, even the shovel tests cannot be considered to give "true" results (contra to, e.g., Leibner 2009: 68), against which the accuracy of the field survey can be assessed, but rather partial and mostly of the slow lifted objects.

It should be emphasized that in addition to the BNE phenomenon, there are numerous other soil's activities that can cause lifting or mixing of artifacts in archaeological record (see above). For instance, bioturbation of archaeological remains can occur due to burrowing, particularly by rodents, earthworms, ants or termites (e.g., Stein 1983; Erlandson 1984; Canti 2003; Bueno et al. 2013; Araujo 2013; Więckowski et al. 2013; Sapir and Faust 2016), as well as to manuring and mixing (Wood and Johnson 1978). Bruder (1982) demonstrated a substantial effect of mole activity on the pedoturbation of objects in soil. However, the artifacts lifted by moles are limited in size to at most 30 mm across. Therefore, the overall effect of this type of bioturbation on the lifting characteristics of archaeological artifacts is limited. In this regard, Yaalon and Kalmar (1978) assumption that the uniform content of clay with depth is the result of mixing the surface soil and subsoil during a subsequent wetting and swelling is highly relevant. According to them, the differentiation in the non-clay fraction is due to seasonal wetting followed by uplift of the coarse grains (see also Madsen and Müller-Vonmoos 1997).

In addition, we assume that the forces responsible for the RBNE provide an explanation for the creation of reverse archaeological pavement (RAP). Such instances have been detected in specific archaeological assemblages, without acknowledging the reasons for their occurrence (Ben-Yosef 2010), or without considering the RBNE (Hofman 1986; Staurset and Coulson 2014). The situation, in the former case, relates for instance to specific sites for copper production in Wadi Arabah in southern Israel and the "surprising" deposition of heavy slags (Ben-Yosef 2010: 348, levels 6 and 7; 349, Fig. 5.66b; 350, Fig. 5.67b; 559, levels 9 and 8). In this particular case, it may be assumed that before the earliest periods of copper production, a layer of soil covered the bedrock. During periods of copper production, the produced slags were gradually dumped on this topsoil, but over time, these heavy and large particles descended to the bedrock, where they are observed today, in accordance with the RBNE (for additional instances, see Villa 1982).

Throughout this work, we assume that the SFP is the result of two opposite and continuous processes: the first is coverage of the site by soil and the second is a physical force, or a combination of several forces, leading mostly to raising (and sometimes for sinking) of the artifacts. These forces might be attributed to cycles of temperature, seismic, volumetric or pressure within the soil (see, e.g., Ravikovitch 1981; Cahen and Moeyersons 1977; Claudin and Bouchaud 1997; Madsen and Müller-Vonmoos 1997; Chen et al. 2009). All of these postulates are characterized in producing local perturbations, similar to vibration, which leads to BNE. Therefore, we suggest that the main physical factor leading to the creation of AP is the BNE. This claim is supported by following observations:

  1. 1.

    AP and its diverse direction, RAP, demonsrate the same lifting and sinking characteristics as the BNE and RBNE.

  2. 2.

    The results present in Fig. 6 demonstrate that as the amount of large-size particles (sand) increases in the soil, the lifting speed decreases, and vice versa with regard to small particles (silt). These outcomes are in full accordance with BNE characteristic (Fig. 7c).

Successful correlation of lifting mechanisms with different types of soil and their role in the SFP, identified through soil spectroscopy, will have far-reaching implications for many venues of scientific inquiry. Beyond its obvious value for clarifying the hitherto unacknowledged fundamental physical laws governing the SFP, it will assist in estimating the percentage of artifacts that might still be buried in the ground at different sites. This would significantly reduce the estimation error in the calculation of inhabited areas from different periods at any given site, adding a powerful dimension for demographic estimates of ancient populations. It is important to emphasize that the SFP phenomena are far more complicated than the theoretical and experimental state of the art achieved in studies of the BNE. The main reasons for this are the complex nature of soil, the environmental conditions, and the structure of the archaeological objects. Nevertheless, if we tackle the problem from several interdisciplinary angles, the limitations of predictive modeling can be overcome by adopting the simplifications that are already being used in BNE studies together with the implementation of advanced mathematics and statistical techniques, in particular, statistics for incomplete data and possibly hidden Markov models and Tweedie 2009), in which the system being modeled is assumed to be a Markov chain with hidden variables.

Some methodological notes on further SFP modeling

  1. 1.

    In our simplified model, we assumed that the two main opposite processes affecting the AP are continuous and stable over time. This assumption seems to be valid for long durations. On the other hand, it does not take into account the artifacts with high-speed properties which will tend to concentrate on the topsoil (for instance, artifacts 1, 2, 3, 7, 8 and 9 in Fig. 9, and artifacts 1 and 9 in Fig. 10). In such cases, the lifting forces and covering process will be affected differently in different seasons of the year by rain, temperature, Aeolian dust, etc. Thus, these high-speed-lifted objects should be assessed differently in different seasons along the year.

  2. 2.

    At this stage, we are considering only the vertical movement. Under real field conditions, one expects horizontal movement as well, in particular, for asymmetrical objects (Hofman 1986).

  3. 3.

    In our model, we suggest that all of the artifacts reaching the outer surfaces of level 2 (Figs. 9–10) will also reach the surface of the mature level 1. This is, of course, problematic under real field conditions, as it requires that during the whole period in which level 1 is flourishing, the artifacts of level 2 will stay unaffected on the open ground and will not be removed. For a more realistic model, one would have to assume that any early layer will be diluted by activities taking place in a newer layer.

  4. 4.

    Based on the above outcomes, it might be supposed that in a multilayer site, dilution of the deepest level will be greatest, while that of the newest level will be the least. This theoretical assumption has been already been detected by Dagan (2010: *32), without acknowledging the real reasons behind this observed phenomenon.

  5. 5.

    It might be assumed that human activities related to the surface (i.e., ploughing and farming) will increase the lifting speed of the artifacts significantly (cf. Bruder 1982; Tartaron 2003). On the other hand, gradual compaction of soil over time (Grotzinger and Jordan 2010: 129–130) might reduce the lifting speed of the artifacts with time.

Conclusions

A new empirical–theoretical model for SFP based on granular physics, pedology, accelerated tests and archaeological observations, was outlined. It is suggested that the AP phenomenon is an external result of the same internal forces responsible for the BNE and the RBNE. At the same time, an opposite process also occurs: a constant and continuous coverage of the site by external soil. These two processes begin just after a site is abandoned, and continue to the present day. They demonstrate different lifting rates for different types of artifacts, soils and outdoor conditions. The experimental work reveals that the faster the lifting rate of a given soil, the better the correlation between the results of the surface survey and the final excavation outcome, and vice versa. Thus, soil type has one of the most important effects on SFPs.