Determining earthquake magnitude or seismic shaking based on SSDS includes observations of the types and forms of SSDS, maximum liquefaction distance, thickness of a disturbed layer, empirical formulae, and thickness of an rapidly-deposited sand layer (Table.1). Among these, the most commonly used methods are the maximum liquefaction distance (Qiao et al., 2017) and the deformation type (Rodriguez-Pascua et al., 2000). Historical liquefaction method (Sims, 1975) and the thickness of the disturbed layer (Hibsch et al., 1997) are based on the liquefaction deformaton intensity and its relationship with the deformation amplitude of the SSDS layer and the seismic shaking, respectively. These methods only provide the lower limit of seismic shaking, and are used less frequently. The empirical formula (Rodríguez-Pascua et al., 2003) and the thickness of rapidly-deposited sand layer (Moernaut et al., 2014) methods are based on the thickness of the SSDS layer and its relationship with the thickness of the overlying sand layer and the earthquake magnitude, respectively. Due to the complexity of SSDS deformation mechanisms and lacustrine sedimentation processes, this method is still under investigation. The method also has strict requirements on the thickness of the deformed layer (≤15 cm) and thickness of the rapidly-deposited sand layer (≤50 cm) (Zhong et al., 2020c), which limits the scope of its use. In the following paragraphs, we will analyze the applicability, and advantages and disadvantages of each method.
Historical liquefaction cases for determining lower boundary curve for liquefaction occurrence
Controversy remains regarding the lowest limit of earthquake magnitude that can cause liquefaction. Some researchers initially believed that a MS 2–3 earthquake was large enough to trigger liquefaction (e.g., Seed and Idriss, 1971). Later, Scott and Price (1988) proposed that earthquakes with magnitude smaller than 5 do not cause significant liquefaction of sediments. Valera et al. (1994) suggested that the threshold magnitude to induce liquefaction effects in the most susceptible gravel deposits is about 7 (e.g. in the 2008 Wenchuan MS 8.0 earthquake, the liquefaction of gravelly soils accounted for 80-85% of all liquefaction points, see Cao et al., 2010), whereas the threshold magnitude for sands is about 5.5. Marco and Agnon (1995) proposed that the triggering of liquefaction occurs only for earthquake magnitudes larger than 4.5; these values are consistent with the historical case studies (Kuribayashi and Tatsuoka, 1975; Youd, 1977; Galli, 2000). Many researchers (e.g. Allen, 1986; Audemard and De Santis, 1991; van Loon et al., 2016) have suggested that Richter magnitudes larger than 5 are required to produce significant liquefaction effects in near-surface, water-saturated, semi-consolidated to unconsolidated sediments. The duration of ground shaking during seismic events of smaller magnitude (M < 5) is often insufficient to cause liquefaction.
An MMI (Modified Mercalli Intensity Scale) of about VI is the threshold for widespread development of small-scale SSDS features such as folds, pseudonodules, contorted laminations and recumbent folds (Sims, 1975). Although liquefaction effects have occurred at MMI values as low as V and VI (Galli, 2000 reports Io 5-6 MCS, Mercalli Cancani Sieberg scale), Keefer (1984) suggested that the lowest shaking at which liquefaction-induced features can become common is VII. Monecke et al. (2004) found that lake sediments are only affected if they are situated within an area that underwent ground shaking of at least shaking VI to VII. Small-scale SSDS, such as disturbed and contorted laminations as well as liquefaction structures (e.g. dish structures), are generated by earthquakes when M = 5-5.5 (Monecke et al., 2004, 2006). When an earthquake causes liquefaction and/or fluidization of water-saturated sediments, the magnitude could be M ≥ 5 or the MMI greater than VI. The advantage of the historical liquefaction method for assessing seismic shaking is its convenience, speed, and wide range of applicability. The disadvantages are that the accuracy is limited and it only provides the lower limit of seismic shaking. Therefore, historical liquefaction method can be used only as a preliminary seismic shaking estimation method.
Maximum liquefaction distance for determining earthquake magnitude
The sand or soil liquefaction and water ejection features caused by earthquakes show a clear correlation with the magnitude and epicenter distance (Kuribayashi and Tatsuoka, 1975; Qiao et al., 2017). The larger the earthquake magnitude, the wider the distribution of liquefied sites (Papadopoulos and Lefkopoulos, 1993). Paleoearthquake magnitudes have been calculated based on sand-layer liquefaction data for modern and historical earthquakes (Qiao and Guo, 2013). The key is first to establish the location of the epicenter, and then to determine the location of the farthest liquefaction from the epicenter (Qiao et al., 2017). This requires identification of the location of liquefaction deformation that is the furthest from the seismogenic fault that induced the earthquake, when undertaking geological field surveys and paleoearthquake research. Kuribayashi and Tatsuoka (1975) have been commended for their comprehensive compilation of the occurrence and distribution of liquefaction during Japanese earthquakes of the past century (1872–1968), and they produced the first map revealing the relationship between the maximum epicentral distance of liquefied sites (R) and magnitude (M) for at least 44 earthquakes (M > 5.3) and liquefied sites (Fig. 2). Youd (1977) compiled data for 14 earthquakes (M > 5.3) from 1897 to 1976 in the USA, India, New Zealand and Chile; their data support the conclusion of Kuribayashi and Tatsuoka (1975) that there is a maximum distance beyond which liquefaction is not likely to occur for an earthquake of a given magnitude. Liu and Xie (1984) compiled sand-bowls and sand-emission data for the 900 years before 1995, and established a relationship between magnitude and maximum epicentral distance to liquefied deformation in China. Ambraseys (1988) re-examined the 44 events analyzed by Kuribayashi and Tatsuoka (1975) and eliminated 5 cases, then added the further 14 cases reported by Youd (1977) from other parts of the world, 6 by Davis and Berrill (l983) and 7 by Fairless and Berrill (l984), as well as 70 new cases; in total 137 earthquakes known to have caused ground failures due to liquefaction were analyzed. Ambraseys (1988) then established a relationship between maximum epicentral distance of liquefied sites R (km) and moment magnitude M. Galli (2000) updated the Italian catalog of liquefaction (Galli and Meloni, 1993; Galli and Ferreli, 1995) by means of new systematic historical researches. This database, permitted the construction of empirical relationships between the epicentral parameters of the earthquake (Io, Ms, and Mw) and the distance of the observed liquefaction for 317 cases related to 61 different earthquakes in Italy since 1117. The triggering events range from intensity (MCS) 5.5 to 11, from magnitude (Ms) 4.2 to 7.5, and magnitude (Mw) 4.83 to 7.46. Papadopoulos and Lefkopoulos (1993) propose a slight modification of the M/R and M/R relations suggested by Ambraseys (1988). Subsequent revision and addition of further data by Obermeier (1996) and Obermeier et al. (2002) has yielded other widely-used diagram showing the relationship between SSDS and earthquake magnitude. Qiao et al. (2017) produced a detailed plot of maximum liquefaction distance and earthquake magnitude (Fig. 3) which shows an obvious relationship between the earthquake epicenter and the farthest surface liquefaction. We can use the R-M map to estimate earthquake magnitude based on the largest distance between the observed liquefaction points and the earthquake epicenter (or responsible fault) in the field.
Conversely, in the field, it is often difficult to determine whether the observed liquefaction deformation may be the farthest from the epicenter. Nevertheless, the R-M map (Fig. 3) can still be used to estimate the magnitude of the earthquake, because it gives a reasonable range of paleoearthquakes magnitudes triggered by active faults that may have formed SSDS, and once the responsible fault has been identified, the R-M map (Fig. 3) can be applied. The epicenters of paleoearthquake should be distributed along the fault, similarly to epicenters of modern earthquakes. When the epicenter of a paleoearthquake is unknown, we can also project the vertical distance from the furthest liquefaction deformation record (or the location of the liquefied deformation section) to the seismogenic fault onto the R-M map; this provides an estimate of the range of the paleoearthquake magnitude. We note that the R-M map only can provide a quasi-quantitative paleoearthquake magnitude, and cannot be as accurate as modern earthquake magnitudes obtained by seismic wave measurements.
Thickness of disturbed layers for determining seismic shaking
Some attempts (e.g. Sims, 1975) have been made to establish a relationship between seismic shaking and thickness levels, based on SSDS. Guiraud and Plaziat (1993) measured the degree of deformation in seismites observed within the Bima Sandstone Formation of the Lower Cretaceous Beune Basin, Northeastern Nigeria. Hibsch et al. (1997) compared the distribution of coseismic deformation thicknesses (disturbed or contorted layer) and the distribution of historical seismic shaking in the Holocene fluvial-lacustrine sediments of the northern Quito Basin, leading to the proposal of a new method of paleoseismic analysis which achieved relatively good for seismic shaking over VI. Fig. 4 shows the historical seismicity of Quito and attribution of seismic shaking (MMI) to the deformation levels. Considering that the sedimentological characteristics have a greater control than the layers thickness, then for layers with a similar lithology (grain-size, sorting, petrology, compaction, etc.), a stronger seismic shaking should result in a thicker disturbed layers. Disturbed layers thicknesses of 0-8 cm and 27-53 cm could tentatively correspond to seismic intensities of VI and XI, respectively. It is important to note that the disturbed layers occurred at the water/sediment interface, and are identified by the following features: constant thickness of contorted and disrupted layers not related to slumps; horizontal post-earthquake deposits showing the same lithology as that of the deformed horizon (Hibsch et al., 1997). Considering the paucity of the statistical data, and the lack of experimental validation, the accuracy of the disturbed layers thickness methodology is limited. In addition, this method does not consider the effect of the sedimentary layer on seismic waves (amplitude and travel time) (Li et al., 1991). In a specific succession, earthquake-induced seismic waves will deform the same layer (or set of layers), possibily independent of their magnitude. A strong earthquake may deform only a thin layer, and a weak earthquake may deform a thick unit, which need further research.
SSDS can evolve in one liquefiable layer (silt), or concurrently in two (silt and sand), or even in three layers (silt, sand and gravel), as a function of the energy involved (Rodríguez-Pascua et al., 2010). Rodríguez-Pascua et al. (2010) proposed a new methodology (DDI, degrees of intensity deformation) to estimate the intensity of SSDS. Through comparative analysis of multiple SSDS sections in the Tierras Blancas Basin, Rodríguez-Pascua et al. (2010) established a regional paleoseismic isoline by the DDI method, and inferred the seismogenic source of this paleoearthquake. This method can therefore benefit regional seismic hazard assessment. Based on the Kelvin-Helmholtz instability mechanism, Lu et al.(2020) modeling the relationship between soft deposition deformation structure and peak ground acceleration (PGA), and constrain the magnitudes of the six paleoearthquakes (seismites) with intensities of VII (0.18g), VI. (0.13g), VI (0.09g), VII (0.18g), VI (0.09g), and VII (0.18g) as Mw 5.6, Mw 6.1, Mw 6.2, Mw 7.1, Mw 6.0, and Mw 6.9, respectively, which are in line with recorded historic magnitudes.
Empirical formulae for determining earthquake magnitude
Rodríguez-Pascua et al. (2003) found that the frequency-thickness distribution of 73 seismites obeys an exponential law, and that the “b” value of this distribution is the same as the “b” value for the seismicity of the area(b is defined by the Gutenberg–Richter law, and reflects the proportional relationship between large and small earthquakes). In addition, they compared the deformation caused by modern and historical earthquakes in Spain with the deformations caused by paleoearthquakes, and found very similar characteristics. Then they established an empirical relationship between the seismics-related deposit (liquefied layer and disrupted layer) thickness of the studied sediments and the earthquake magnitude, yielding the empirical formula M = T/3 + 3.83, where T (in cm) is the thickness of the seismics-related deposit and M is the magnitude. Three zones characterized by distinctive styles of deformation can be distinguished in a fully-developed seismics-related deposit: an uppermost fluidization zone, an intermediate zone of ductile–fragile deformation (breakage and fragmentation of lamina), and a lower zone showing features typical of ductile deformation (folding of lamina). This lower zone overlies undeformed laminae (Rodríguez-Pascua et al., 2003).
This characteristic seismics-related deposit structure was first defined by Marco et al. (1994) for laminated sediments of the Pleistocene Lisan Formation in the Dead Sea region (Middle East). Marco and Agnon (1995) suggest that the seismics-related deposit are composed of fine-grained matrix-supported texture and tabular laminated fragments, underlain by asymmetrical and recumbent folds, and overlain by undeformed sand layers. Marco and Agnon (2005) changed the term “seismics-related deposit” to “breccia-layers”, and interpreted them as seismites. Undisturbed laminated layers between these breccia layers represent inter-seismic intervals. To separate observations from interpretations, “intraclast” refers to the clasts that were reworked from within the sedimentary section; Agnon et al. (2006) replaced the term “breccia-layers” with “intraclast breccia layers” and stressed that the term “breccia” refers to the texture of the deposit. In addition, they considered the formation of intraclast breccias, proposing that earthquakes are the main mechanism. The Dead Sea intraclast breccias have many similarities to seismites described in a lacustrine environment (Zhong, 2017), as well as glacial deposits (Davenport and Ringrose 1987). Based on field observations and research experience, we propose that the seismics-related deposit (named breccia layer by Agnon et al., 2006) should comprise a liquefied or fluidized layer and overlying detrital layer, but should not include the overlying undeformed sand layer with a grain size change in vertical section.
No clear standard has been defined for the thickness of the seismics-related deposit (Rodriguez-Pascua et al., 2003), thus limiting its application. Many empirical data show that the magnitude is not strictly linear with the logarithm of earthquake frequency (Fu, 1997), and a robust error estimation and confidence interval calculation is needed for “b” values. Mugnier et al. (2011) found that the lithology, grain size, sedimentary environment and acceleration can all influence the thickness of seismites, and also the number of individual shocks and number of cycles (earthquake recurrence cycle) can affect the final thickness of the deformed layer. Meanwhile, numerical simulations indicate that, firstly, deformation intensity increases with increasing ground acceleration and decreasing layer thickness; and secondly, the duration of the earthquake affects the deformation geometry, rather than the deformation amplitude (Wetzler et al., 2010). Therefore, the relationship between coseismic shaking and thickness of the seismics-related deposit is very complex and is not single-valued (Mugnier et al., 2011); as such, one should be very careful in applying the empirical formula.
Types of SSDS for determining earthquake magnitude
In water-saturated and unconsolidated sediments, different seismic shaking and deformation mechanisms (liquefaction, fluidization, thixotropy etc.) can result in different types of deformation structure. For example, gravity and liquefaction can gradually form load, flame, ball-and-pillow and pillow-bed structures. Firstly, the superposition of coarse-grained sand (heavy) on fine-grained sand (light) is analogous to gravitational instability (Anketell et al., 1970), allowing coarse-grained sediment to sink into fine-grained sediment when the fine-grained (underlying) material liquefies, resulting in load casts. Secondly, as a load cast develops, the underlying, finer sediment compensates its loss of space with upward intrusions forming flame structures. Thirdly, at the base of the source layer, horizontal motion generates horizontal shear stress in the over-pressurized fine-grained layer, and causes the laminae to convolute within the clay to form contorted layer (Suter et al., 2011). Fourthly, with stronger and/or longer seismic shaking, the heavy sand completely sinks into the light sand, forming pseudo-nodules (Anketell et al., 1970) and ball-and-pillow structures (Owen, 1987), and eventually forming pillow-bed structures (Qiao and Li., 2008). Sims (1973) suggested that the evolution of the load cast phenomenon towards pseudonodule formation may be an indication of stronger and/or longer seismic shaking. Under identical conditions (i.e. in the same sedimentary environments), the seismic shaking required to create ball-and-pillow structures should be greater than that required to create load cast and flame structures, while the shaking needed to create pillow beds should be larger than that needed to generate the ball-and-pillow structures (Owen, 1987).
Rodríguez–Pascua et al. (2000) summarized the various types of SSDS and their relationships with earthquake magnitudes, suggesting that seismics-related deposit, pseudonodules and ball-and-pillow structures correspond to magnitudes of 5.5–6.5, 6.5–8 and 6–8, respectively (Fig.5). Taking into account the distances to seismogenic faults, Neuwerth et al. (2006) tentatively postulated that the earthquake magnitude required to generate SSDS is 5-7. Berra and Felletti (2011) concluded that an earthquake should have a Richter magnitude of between 6 and 8 if it is to be capable of generating ball-and-pillow structures or irregular, contorted stratification. Qiao and Guo (2013) used the relationship between earthquake magnitude and the maximum distance from epicenter established by Liu and Xie (1984) and Obermeier (1996), and suggested that liquefaction or fluidization deformation (droplets and a homogenized layer) in early Jurassic lacustrine sandstones in the Wuqia region of the SW Tianshan Mountains may have recorded paleoearthquake magnitudes ranging from M 6.5 to 7. In addition, a large number of load and ball-and-pillow structures have been reported from a liquefied deformed layer with the same age (Qiao and Guo, 2013). Zhong et al. (2017) proposed that the load and ball-and-pillow structures were triggered by earthquakes with magnitudes of 6-7. It is possible to obtain the seismic shaking through comparative analysis of similar types of SSDS triggered by earthquakes in the same sedimentary environments with similar lithology.
Thickness of rapidly deposited sand layer for determining earthquake magnitude
The MS 8.0 Wenchuan earthquake struck on 12 May 2008, triggering more than 190, 000 landslides and collapses along ridges and hillslopes of the Longmen Shan (Sichuan, China) (Xu et al., 2014). These detrital materials still remain in the hillslopes and valleys of the earthquake area. The transfer of a large amount of landslide material from the hillslopes to the river network resulted in a large number of dams and associated lakes that formed immediately after the Wenchuan earthquake (Fan et al., 2012). Wang et al. (2015) used suspended sediment (<0.25 mm) concentration measurements from several rivers (Minjiang River, Fujiang River and Tuojiang River) in the epicentral area to analyze the evolution of suspended sediment flux; their results showed suspended sediment discharge increased by factors of 3-7 after the Wenchuan earthquake relative to 2006-2007 levels. Furthermore, 10Be mixing budgets indicate that the sediment flux of the 0.25–1 mm size fraction increased by up to six-times following the Wenchuan earthquake (Wang et al., 2017). Across the Longmen Shan, at the present rate of post-earthquake fluvial export, Wang et al. (2015) estimate that it will take 33±24 yr to remove all material <0.25 mm delivered by coseismic landslides, and coarse sediment (> 0.25 mm) will take about 1000 yr. The entrance of the Zipingpu reservoir at the highest water level is ~2 km downstream from the epicenter of the 2008 Wenchuan earthquake, which can captures a significant portion of the landslide material associated with the 2008 Wenchuan earthquake. The deposition record in the Zipingpu reservoir core shows the grain size and magnetic susceptibility have an abrupt coarsening (increasing) and upward fining (decreasing) after the 2008 Wenchuan earthquake (Zhang et al., 2019). However, these changes (grain size and magnetic susceptibility) were delayed until 2 years after the event. Based on this delay, Zhang et al. (2019) emphasized the importance of the interplay between a major earthquake and the prevailing monsoonal climate, highlighting the central role of runoff as an erosional agent in removing earthquake-triggered landslide material and in creating a corresponding depositional signal of the earthquake. After the 2008 Wenchuan earthquake, the large quantities of dust in many of the landslides and collapses also caused frequent dust storms. This dust accumulated on local roads, reaching several centimeters in thickness (Liang and Jiang, 2017). Based on the geochemistry, quartz particle scanning electron microscopy and grain size, Jiang et al. (2014) proposed that lacustrine sediments in east Tibet were transported by wind and trapped in lakes; most of this material originated from local wind-blown sediments. From these results it can be hypothesized that large earthquakes in east Tibet might have caused widespread rockfalls and landslides, leading to exposure of fine-grained sediments that have accumulated on mountain slopes before undergoing aeolian transport into the lake. Interestingly, post-seismic vegetation recovery at landslide sites indicates that the Wenchuan earthquake's impact on regional post-seismic landslide frequency may disappear within two decades of a major event (Yang et al., 2018). This implies that the amount of detrital material released in the area gradually decreases after an earthquake.
The above discussion shows that, strong seismicity (M ≥ 5) can cause not only liquefaction and/or fluidization of water-saturated sediments, resulting in various types of brittle and/or ductile deformation, but can also generate a large amount of debris (landslides, dust, etc.), which is rapidly transported into lakes by wind and/or rivers, and deposited as a series of turbidites (Howarth et al., 2012; Moernaut et al., 2014; Archer et al., 2019; Fan et al., 2020; Molenaar et al.,2021). Seismic shaking may also trigger sedimentary instabilities on the steep slopes of lake basins (Katz et al., 2009) or lake seiches (Beck, 2009; Avşar et al., 2014), resulting in mobilized masses at proximal sites (i.e., slides, slumps, debris flows) (Zhang et al., 2014) and deposition from induced turbidity currents at distal sites (i.e., seismoturbidites). When an earthquake occurs, pre-existing unconsolidated lake deposits (below the event horizon) may deform and generate various SSDS (Fig. 6), followed by the deposition of medium- to coarse-grained particles released by earthquake-induced processes to form a so-called event layer (rapidly-deposited sand layer formed by material supplied due to effects of the seismic shock) above the event horizon (Jiang et al., 2014; Zhong et al., 2020c) (Fig. 6). Event layers were found to have varying thicknesses in the upper part of the SSDS in the Lixian lacustrine sediments, east Tibet (Jiang et al., 2017). In these SSDS, the grain-size and magnetic susceptibility repeatedly show abrupt coarsening and upward fining, probably because frequent earthquakes have generated a large amount of debris in the lacustrine sediments of the present study area, resulting in an abrupt increase in the terrigenous flux of coarse-grained (magnetic material) in the Lixian dammed paleo-lake (Jiang et al., 2016, 2017). Such earthquakes (M >5.0/5.5) have not always resulted in the formation of SSDS in lacustrine sediments, perhaps due to their greater distance from the epicenter (Owen and Moretti, 2011) or the higher sand/mud ratio of lacustrine sediments (Jiang et al., 2017); nevertheless, they can still generate a large amount of debris within the lake basin. A positive correlation between the thickness of the seismites and the seismic shaking has been identified (Hibsch et al., 1997; Rodríguez Pascua et al., 2003), but it remains unclear whether there is a correlation between the thickness of the event layer (post-seismics deposit) and the seismic shaking.
Keefer (1984) produced the first map to show the area affected by landslides during earthquakes of different magnitudes for 40 historical world-wide earthquakes covering the years 1811 to 1980. The correlation between magnitude (M) and landslide distribution shows that the minimum magnitude likely to trigger landslides is M≈4.0. This limit was subsequently revised and constrained with further data by Rodríguez et al. (1999) and Xu et al. (2014). Bommer and Rodríguez (2002) presented data for earthquake-triggered landslides in Central America but noted that their characteristics can be compared with global relationships between the area of landslides and earthquake magnitudes (Fig. 7a). Malamud et al. (2004) confirmed the results of Keefer (1984) and proposed that the minimum earthquake magnitude required to trigger landslides is Mw = 4.3 ± 0.4. Under the same geological conditions, the stronger the earthquake, the larger the area and volume of landslides. A strong earthquake can induce tens of thousands of landslides, especially in alpine valleys (Xu et al., 2014; Zhang et al., 2017).
By establishing a high-resolution Holocene seismic history of the Dead Sea Transform, Migowski et al. (2004) found the thickness of the disturbed layer has reasonable correlation with magnitude. This disturbed-layer sedimentary pattern is punctuated by successions of disturbed sedimentary structures that typically consist of aragonite fragments ‘‘floating’’ in a silty detrital matrix without any indication of transport. Furthermore, Moernaut et al. (2014) found that a turbidite’s spatial extent and thickness are a function of the local seismic shaking and can be used for reconstructing paleo-intensities. They also established a linear correlation between cumulative turbidite thickness and seismic shaking of the causative earthquake. Theoretically, a larger magnitude earthquake produces more debris (landslide, dust etc.) and a thicker rapidly deposited sand layer (event layer) in local water bodies. Initial conditions should also be considered: for example, the degree of gravitational instability of the sedimentary body; textural parameters; depth of sliding surface; etc.
To assess this theory, we assimilated data on the thicknesses of rapidly deposited sand layers from 32 historical world-wide earthquakes (France, Turkey, New Zealand, and Chile) covering the years 181 to 2010. For more details on determining the genesis and thickness of sand layers, based on abnormal changes in sedimentary indexes, see Avşar et al. (2014) and Jiang et al. (2014). Next, we established a linear correlation between the cumulative sand layer thickness and magnitude of the causative earthquake (Fig. 7b), yielding a residual mean square of 0.40. Correlation between magnitude (M) and cumulative sand layer thickness shows that the minimum thickness likely to be affected by debris material in a sand layer increases from approximately zero at M = 5.0 to 50 cm at M = 8.0. A cumulative sand layer with a thickness of 1 cm corresponds to earthquake magnitudes of ~4.0-6.0. A cumulative sand layer with a thickness of 10 cm corresponds to earthquake magnitudes of ~5.8-8.4. If the debris (landslide, dust etc.) in the lake drainage basin is induced by earthquakes, and is transported into the lake, then the correlation between the cumulative sand layer thickness and the magnitude can be used to determine the magnitude or shaking of the seismic event under study.
Considering that the denudation mechanism of debris in a lake drainage basin is complicated, and that other factors such as provenance, topography, meteorological conditions and hydrodynamic conditions can also affect the sediment transport, we note that most lake sediments comprise mixtures of sediment populations derived from different sources and transported to the site of deposition by different mechanisms. Therefore, it is difficult to assess the true significance of variations in sediment properties, especially when considering that the provenance of lake sediments may also be influenced by extreme weather events (e.g. rain storms, sand storms, etc.). Consequently, we propose that components of the lake sediments should be separated (see the end-member modeling method: Weltje, 1997), by distinguishing tectonic and climatic components, when studying a seismic event layer and its thickness, for the purpose of determining the seismic shaking. Admittedly, this method is only based on statistical results of the data, it require more data support and further examination. Therefore, the method of rapidly deposited sand layer thickness can only be used to gain a rough magnitude estimate with limited accuracy, and needs to be compared with alternative methods of verifying seismic shaking.
Two independent methods for determining earthquake magnitude are numerical simulations and shaking table experiments. Wetzler et al. (2010) carried out field observations in the Lisan Formation sediments (Dead Sea) and numerical simulations based on peak ground acceleration and its relationship with deformed layer thickness and deformation morphology. Their results reveal that deformation morphology is controlled by ground acceleration and deformed layer thickness. Shaking table experiments are not only limited by the available instruments and equipment, but are also affected by the sediment materials, grain size, porosity and permeability during the experiment (Shen, 2014). Considering the complex rheologies involved, and because the developing structures are impossible to observe in sediments (Harrison and Maltman, 2003), shaking table experiments are used less frequently than other methods mentioned above.
The other method is based on geotechnical engineering techniques at sites of marginal liquefaction (a critical state of liquefaction), to constrain the peak accelerations as a function of epicentral distance: these accelerations can then be compared with predictions from seismological models, and used for back-calculating prehistoric magnitudes (Obermeier, 1996, 1998).