Quantification of physical and chemical paleoweathering at the microscale: a new concept

Weathering is a basic geological process that refers to the breaking down or dissolving of rocks and minerals on the surface of the earth. However, weathering characteristics may vary among different lithologies even under similar conditions. To evaluate and quantitatively compare the physical and chemical index of alteration among different types of rock, new concepts of paleo-weathering such as the absolute weathering degree and the relative weathering degree are proposed for microscale studies. For the quantification of physical weathering, the index of physical weathering (IPW) is introduced. The index is defined as the ratio between the area of the fractures formed during different weathering stages and the total area of the thin section under the polarizing microscope and it is corrected by the corresponding rock strength. To quantitatively compare the chemical weathering intensity among different types of rock and minerals, the following two new concepts are introduced: total weathering mass (TWM) and chemical weathering ability (CWA). While the TWM is an integral function of weathering rate and weathering time for minerals, the CWA is the sum of the TWM of each mineral in rock within a certain time period. As a case study, this concept is applied to the weathered crystalline basement below the post-Variscan nonconformity in southwestern Germany. The petrography and geochemistry of three drillings penetrating the nonconformity were investigated by polarizing microscopy, X-ray diffractometry (XRD), scanning electron microscope (SEM), X-ray fluorescence (XRF) and inductively coupled plasma-mass spectrometry (ICP-MS). The investigations illustrate how to better extract quantitative information for both, physical and chemical weathering.


Introduction
Weathering as a consequence of physical and chemical factors is one of the most fundamental processes of the Earth's surface system (Riebe et al. 2003;Babechuk et al. 2014). For decades, traditional indices for the evaluation of weathering degrees, such as the CIA (chemical index of alteration) (Nesbitt and Young 1982), PIA (plagioclase index of alteration) (Fedo et al. 1995), CIW (chemical index of weathering) (Harnois 1988) and Σ bases/Al ratio (Retallack 1999), have been used to interpret the influence of chemical regime (Nesbitt and Young 1989), time of exposure (Gallagher and Sheldon 2013;Jian et al. 2019), climatic conditions (Sinisi et al. 2014), environment and influence of vegetation (Drever 1994;Pokrovsky et al. 2005) on the formation of hiatal surfaces. However, among different types of rock mineral compositions, textures and susceptibility to physical and chemical weathering differ significantly (Nesbitt and Young 1984;White et al. 2001). This leads to the fact that even under the same weathering intensity, the weathering degree for different types of rock is different. When investigating hiatal surfaces at the regional scale, the results from different types of rock may be contradictory and not comparable, which makes comprehensive conclusions impossible. If it would be possible to normalize weathering patterns quantitatively for different rock types, regional-scale reconstructions of the conditions forming a hiatal surface would be possible. Such consistent results would allow for quantifying the duration and kind of sediment production processes, which can improve the mass balancing of sediment routing systems and sediment distribution models in basin analyses. Additionally, a quantitative and comparable measure of alteration in terms of mineralogical composition, permeability and porosity will enhance the accuracy of related reservoir models.
To find a method for the normalization of the chemical weathering index to mirror the chemical weathering intensity among different lithologies, the relationship of the weathering rate among different minerals must be considered. Experimental setups in the laboratory or field delivered a wealth of mineral-specific dissolution rates (e.g. Chou and Wollast 1985;White and Brantley 2003). These results can be used to determine the susceptibility to chemical weathering among different rock types. With the susceptibility, the chemical weathering indices can be normalized.
An integrated concept of paleo-weathering also needs to consider physical weathering. In the natural environment, physical and chemical weathering are mutually reinforcing (Matsuoka 1995;Moon and Jayawardane 2004). In contrast to the widely used indices for chemical weathering, quantitative evaluation of physical weathering is fairly scarce. One method for the quantification of physical weathering in a modern environment is to compare the relative content of primary Fe(II) silicates in the dust source (Shoenfelt et al. 2019); other methods quantified the physical weathering with the characteristics of suspended particulate material in the river (Qin et al. 2006). However, these methods are only suitable for investigations on a regional scale, and investigations of the physical weathering degree and the physical weathering intensity for specific paleo/weathering profiles at the local scale are still hesitant. Most previous studies on the physical weathering degree of paleosols are based on the Rock Weathering Classification diagram summarized by Aggisttalis et al. (1996). The diagram qualitatively describes the following seven different weathering degrees: fresh, faintly weathered, slightly weathered, moderately weathered, highly weathered, completely weathered and residual soil according to the exposed modern weathered profile, which is somehow a result of both features of physical and chemical weathering. Subsequent researchers optimized the table to five degrees by removing faintly weathered and residual soil (e.g. Ceryan et al. 2008a, b, c). With the development of engineering, the form was enriched by parameters such as uniaxial compressive strength (UCS) (e.g. Chiu and Ng 2014). Some of the researchers introduced the major elements and/or chemical weathering indices into their studies (Tugrul and Gurpinar 1997;Ceryan 2008Ceryan , 2008a. The geochemical data are applied to estimate the mechanical properties of the rock under the five summarized weathering degrees. However, a physical index specifically for modern and paleoweathering profiles has yet to be created. Nevertheless, the relationship between the geochemical data and mechanical properties provides an ideal dataset to evaluate the susceptibility to physical weathering degree among different rock types. This study uses an integrated quantification of chemical and physical weathering from the covered paleo-surface of the Variscan basement in southwestern Germany. The quantification of the physical weathering degree is mainly based on the detailed fracture characteristics at the microscale, and the results are expressed as the index of physical weathering (IPW). The normalization of IPW and chemical weathering indices is based on the susceptibility of different lithologies to weathering, and the results are supposed to reflect weathering intensity.

Physical weathering degree quantification
Physical weathering is a ubiquitous process in the upper crust and is crucial for providing materials for sedimentary rock and landscape modification (Camuffo 1995;Matsuoka et al. 1996). However, an index for physical weathering is still not available. The physical weathering degree is reflected by the fracture density and width, as well as fragmentation of the rock matrix (Camuffo 1995). The higher the physical weathering degree is, the denser the spacing and wider the fractures. Therefore, the physical weathering degree can be expressed, in principle, by the ratio between the fracture and the total area within a specific zone. This study concentrates on the microscale and uses petrographic analysis of thin sections. The quantification of the physical Fig. 1 Workflow for physical weathering degree quantification weathering degree and intensity is performed in five steps, as shown in Fig. 1, and detailed in the following sections.

Fracture recognition and classification
Fractures may be formed due to weathering and/or other factors, such as tectonic stress in the natural environment. Regardless of whether the fractures are formed due to physical weathering or tectonic stress, they may be filled by secondary minerals, which may be products of chemical weathering and/or the minerals are formed due to burial diagenesis. The minerals formed during chemical weathering have different mineralogical and geochemical characteristics compared to those formed by burial diagenesis (Bauluz et al. 2008;Dill 2010), which can be used to distinguish them. However, the fillings of fractures cannot be used to conclude whether the fractures are formed due to physical weathering or tectonic stress. To fix this problem, the method for tectonic fracture recognition with fracture angle or orientation proposed by Gol'braykh et al. (1966) is applied. In this case, the fractures are divided into four groups based on the mineralogical and geochemical characteristics of the fillings in the fractures and the angles of the fractures: (i) fractures formed due to tectonic stress; (ii) fractures formed before and/or during chemical weathering; (iii) fractures formed at the end of chemical weathering; (iv) Fractures overprinted by burial diagenesis (Fig. 2).
(i) Fractures formed due to tectonic stress The tectonic fractures may be formed before, during and/or after the chemical weathering process together with the fractures formed due to physical weathering. The fractures tend to have a preferential orientation and angle due to the influence of tectonic stress, while the fractures formed due to weathering, and orientation and/or the angle tend to show a random pattern (Scarpato 2013;Caspari et al. 2020). Therefore, to recognize the preferential directions of the fractures, the rose diagram can be applied to illustrate the angle of the fracture along the drill cores. When the rose diagram shows a preferential angle, it indicates that the weathering profile con- tains both tectonic and weathering fractures. In this case, the fracture area of the tectonic fractures along the weathering profile within the thin sections corresponds to those fractures located in the parent rock (Fp). (ii) Fractures formed before and/or during chemical weathering The weathering products may be composed of stable minerals including clay and oxide (e.g., Fe 2 O 3 , TiO 2 ), and unstable minerals such as calcite (Goldich 1938). The fractures formed before and/or during chemical weathering include both tectonic and physical weathering fractures and therefore are filled by products of weathering, such as clay minerals, oxides and calcite. These fractures are classified as Fcl (fracture, clay), Fx (fracture oxide) and Fc (fracture calcite). Whereas stable minerals persist, unstable minerals will gradually be depleted (Harriss and Adams 1966). Meanwhile, the unstable minerals formed during hydrolysis may transfer and precipitate, accompanied by stable minerals filling fractures in the lower part of the weathering profile (Nesbitt et al. 1980). These fractures formed before and/or during the weathering process are defined as Fw. (iii) Fractures formed at the end of chemical weathering While the chemical weathering process comes to the latest stage with a significantly lower rate, the physical weathering process and/or tectonic process may continue, and new void fractures may form (Fv). (iv) Fractures overprinted by burial diagenesis (Fb) For a weathering profile that is overprinted by burial diagenesis, the void fractures may be filled by secondary minerals. If secondary mineral types are the same as unstable weathering products, such as calcite, which may be formed during both weathering and burial stages, the method proposed by Michel and Tabor (2016) can be applied. This method uses stable C and O isotopes of carbonates to distinguish the process of formation.

Quantification of the fracturing
The fracture area is analyzed under a microscale by a polarizing microscope. In our case, the best results were obtained under 10 eye pieces with 10 objective lenses. The pictures were taken by a single-lens reflex camera connected to the microscope and controlled by Olympus Stream Basic software with a plotting scale. The resolution of the photograph was 2560*1920. To measure the fracture and the inspected area, the thin-section photo taken under the polarizing microscope with a plotting scale was opened by the software ImageJ. To acquire the ratio between the fractures and the whole picture, three steps are shown in Fig. 3 and illustrated in the following paragraphs.
Step one: after opening the picture with ImageJ, the pixel unit can be seen in the upper left corner. With the "straight" button of the menu bar, A straight-line coincidence with the plotting scale line should be first drawn. To ensure that the line that draws has the same length as the plotting scale line, the magnifying glass in the menu bar can be selected, and then, the plotting scale part can be clicked to amplify to an appropriate scale; then, the line can be drawn more accurately.
Step two: after drawing the line, the length of the line according to the plotting scale should be defined. To define the length, the "Analyze" button should be selected, and click the "set scale" in the submenu, fill the "Known distance" with the number of the plotting scale, in the example the number is 100, and "Unit of length" in this case is "μm". By clicking "OK" in the plane, the length of the line can be defined. Now, the pixel unit in the top-left corner changes to length unit (μm), and with the length and width of the photograph, the area of the total inspected area (A (Ft) ) can be calculated.
Step three: Select the "Polygon selections" and outline the fractures manually on the digital photograph. Similar to drawing the straight line, the fracture can also be magnified to ensure the accuracy of the outline, if necessary. After selecting the "Analyze" button and clicking "Measure" in the submenu, the area of the outlined area will appear to the right of the photograph. For the void fracture, the area is defined as A (Fv) , the fractures filled by calcite are defined as A (Fc) , the fractures filled by clay minerals are defined as A (Fcl), the sum of the area of filled fracture in the weathering zone is defined as A (Fw) , and the area of the fractures within the parent rock is defined as A (Fp) . The statistical error is less than 250 µm 2 with a mean value of approximately 55 µm 2 . With the area of both fractures and the photograph, the IPW (area ratio) can be acquired.

Quantification of the influence of chemical alteration on the rock strength
The susceptibilities to physical weathering among different lithologies are intrinsically different. Previous studies indicate that the higher the strength of a rock is, the more resistant it is to physical weathering (Jayawardena and Izawa 1994; Thomson et al. 2014). Therefore, the susceptibility of different lithologies to physical weathering can be represented and normalized by rock strength to enable the comparison of physical weathering intensity among different lithologies.
Rock strength is an engineering geological term that is concerned with mineral composition, structure, texture and jointing (Golodkovskaia et al. 1975). It can be specified in terms of uniaxial tensile strength (UTS), uniaxial compressive strength (UCS), shear strength, and impact strength. The formation of fractures during weathering is more related to the UTS than UCS (Aadnøy and Looyeh 2019). While the UTS of rock refers to the required pulling force to rupture a rock sample divided by the area of the cross section of the sample, the UCS is the capacity of a rock to withstand loads tending to reduce size (Aggisttalis et al. 1996;Aadnøy and Looyeh 2019). These two parameters are always in a linear relationship with the UTS at approximately 0.1 times the UCS (Gupta and Rao 2001;Cuccuru et al. 2012;Aadnøy and Looyeh 2019). This enables both UCS and UTS to be applied for the normalization of IPW. Within the previous studies, the UCS data are much better available than UTS. Hence, to acquire more data for a more accurate result, the UCS is applied for normalization in this study.
In a natural environment, physical and chemical weathering processes always interfere. The cracks formed due to physical weathering may provide pathways for fluids and accelerate the chemical weathering process (Bland and Rolls 1998). Meanwhile, meteoric water and pore fluids can also penetrate the basement rock through the rock fabric and further increase the chemical index of alteration (Di Figlia et al. 2007). With the ongoing chemical weathering process the rock strength will gradually decrease (Khanlari et al. 2012;Chiu and Ng 2014). The decreased rock strength will clearly enhance the formation of the physical cracks which is rock-type specific. Therefore, the chemical index of alteration needs to be considered when the physical weathering degree is normalized. Since the twentieth century, quantitative correlations between rock strength and chemical index of alteration have been developed (Tuǧrul 1997;Ündül and Tuǧrul 2012;Korkanç et al. 2015). Different researchers Fig. 3 Quantification of the fracturing with ImageJ software. For details of the procedure see the text correlated physical parameters, such as UCS and P-wave velocity with chemical parameters, such as loss on ignition (LOI), weathering potential index (WPI) and other indices (Gupta and Rao 2001;Mert 2014;Ündül and Tuğrul 2016). Moreover, previous studies developed empirical formulae of the relationship between the physical strength and the chemical weathering degree for basaltic and granitic rocks, among these chemical weathering indices, the Chemical Index of Alteration (CIA) has a strong relationship with the rock strength (e.g. Arel and Tugrul 2001;Tuǧrul 2004). Therefore, based on these formulae and data for basaltic and granitic rock (Ceryan et al. 2008a(Ceryan et al. , 2008bErişiş et al. 2019;Khanlari et al. 2012;Thomson et al. 2014;Tuǧrul 1997), this study compiled data and created a regression out of two rock-specific empirical relationships between UCS and the chemical index of alteration (CIA) (Fig. 4): With these two empirical formulae, the UCS of basaltic and granitic rock under different chemical indices of alteration can be assessed.

Calculation of the index
The index for the quantification of physical weathering is defined as the index of physical weathering (IPW). As the fractures along the weathering profile may contain both tectonic fractures and weathering-fractures, the tectonic fractures increase the area of the fractures within the weathering zone, which need to be eliminated. The area of the tectonic fractures can be represented with those in the parent rock. The fractures created by physical weathering in the weathering zone can be (1) UCS basaltic rock = 39186e −0.106CIA (r = 0.83), (2) UCS granitic rock = 2E + 6 * e −0.187CIA (r = 0.82).
corrected as A( Fw) + A (Fv) -A (Fp) , and the IPW can be expressed as follows: where A (Fw) and A (Fv) represent the area of the fractures formed before and during weathering process and void fractures in the weathering zone, respectively, A (Fp) is the area of the fractures within the parent rock, and A T is the area of the total inspected area.
The IPW in Eq.
(3) reflects the physical weathering degree and can be used to compare the physical weathering intensity for a specific rock type. However, the variation in the rock strength among different lithologies makes a quantitative comparison of the IPW impossible. To solve this problem, one method is to normalize the IPW with the corresponding susceptibility to physical weathering for each type of rock. The susceptibility is represented by UCS (see Sect. "Quantification of the influence of chemical alteration on the rock strength").
As different types of physical weathering fractures exist, they should be normalized by their corresponding individual UCS. For basaltic and granitic rock, the UCS can be acquired with Eqs. (1) and (2), respectively. For the void fractures, the rock strength at the weathered sampling position is applied, which is expressed as UCS w , However, as it is difficult to determine the specific CIA value while the fractures were formed, the rock strength that the fractures represent is represented by the average rock strength between the parent rock (UCS p ) and the weathered sampling position (UCS w ), which is defined as UCS A and expressed as follows: When the weathering profile is influenced by tectonic fractures, the normalization process can be divided into the following two situations:  Thomson et al. 2014;Tuǧrul 1997) 1 3 (i) Tectonic fractures preexisting or formed during chemical weathering For preexisting tectonic fractures, their mineral filling is often related to successive processes, i.e., fluid flow and water-rock interaction during burial and uplift. This may include different generations of secondary minerals that are unstable and usually dissolve during uplift. As a consequence, the tectonic fractures experience the same process as the preexisting physical weathering fractures. When tectonic fractures form during the chemical weathering process, they would also experience the same process as fractures formed by physical weathering during the same period. The same process leads to the same fractures characteristics. Therefore, to normalize the IPW, first, for the stage before and during chemical weathering, the area of the fractures in the weathering zone (A (Fw) ) should subtract the area of the fractures within the parent rock (A (Fp) ), then divide the area of the total inspected area (A T ) and normalized by UCS A . The stage at the end of chemical weathering should be the sum of the area between the fractures overprinted by burial diagenesis and void fracture divided by the total inspected area (A T ) and normalized by the rock strength of the sampled weathering part (UCS W ). Therefore, the final IPW N can be expressed as follows: (ii) Tectonic fracture formed at the end of chemical weathering and/or during burial diagenesis When tectonic fractures form at the end of the chemical weathering process or during burial diagenesis, they should be the fracture area formed at the end of the weathering process, which contains the void fractures, and the fractures overprinted by burial diagenesis subtract the fracture area in the parent rock (A (Fp) ) and then normalize by UCS w . Together with the fractures formed before and/or during chemical weathering, the IPW N can be expressed as follows:

Accounting for spatial heterogeneity
Due to the heterogeneity of fracture distribution in the thin section, one view may not be able to represent the physical weathering value over the whole thin section. To determine the most appropriate strategy for acquiring the representative IPW N value, tiles of 3*3, 3*5, 4*5 over all areas of the thin section were applied. The results indicate that the variation in the average value of the IPW approaches stable values after 15 visions independent of rock type. Therefore, a grid of 3*5 is applied (Fig. 5). (6)

Chemical weathering ability (CWA)
The quantification of chemical weathering has been well developed and widely applied (e.g. Nesbitt and Young 1982;Mclennan 1993;Fedo et al. 1995;Schoenborn and Fedo 2011;Babechuk et al. 2014). The common indices can be regarded as the absolute chemical weathering degree of a certain lithology. Furthermore, weathering rates for individual minerals, such as plagioclase, K-feldspar, biotite and hornblende have been quantified (e.g. Schott et al. 1981;Riebe et al. 2003). Previous studies have put much effort into determining weathering rates of fresh minerals in the laboratory (e.g. White et al. 2001;Martinez et al. 2014).
Mineral weathering in the natural environment, however, is a continuous process from fresh to weathered. White and Brantley (2003) concluded that the weathering rate of a mineral decreases with time. Based on an experiment with both fresh rock and weathered rock that lasted 6.2 years, they proposed an equation to depict the alteration rate (R/mol m −2 s −1 ) in the natural environment for different minerals (Table 1) as follows: With the alteration rate among different minerals, this study develops an equation to depict the total weathering mass (TWM) between the times t 1 and t 2, which corresponds to the integral function of the weathering rate as follows: Based on the TWM of mineral types and the mineralogical composition of a rock, its ability to weather chemically can be described as its chemical weathering ability (CWA). It is calculated as the sum of the TWM for each type of mineral with the coefficient of its proportions in a rock-type as follows: where p is the proportion of each type of mineral within the rock, which can be acquired by XRD. The formula provides a measure that rocks with higher CWAs are more easily to be weathered under the same natural environment. Therefore, the CWA can be applied to evaluate the susceptibility of different rock-types to chemical weathering. Due to this calculation, the sensitivity of CWA to "unweatherable minerals" is low. This study considers 'unweatherable' minerals as those showing a chemical weathering rate in natural environments lower than 10 -14.5 to 10 -15.1 mol m −2 s −1 (e.g. quartz), which is several orders of magnitude slower than for other primary silicate minerals (Schulz and White 1999). The CWA of a certain rock type is mainly sensitive to "weatherable minerals", such as plagioclase and biotite. Therefore, using the CWA in this study, the quartz proportion for different types of rock is excluded. Hence, the formula provides a measure that rocks with higher CWAs are more easily weathered under the same natural environment.
In conclusion, CWA can be applied to assess the susceptibility of different types of rock to chemical weathering.

Normalization of chemical weathering indices using CWA
The CWA for different igneous parent rocks provides a chance to determine the relationship for the chemical weathering degree under the same weathering intensity. As the chemical weathering degree can be well quantified by chemical weathering indices, such as CIA, PIA and CIW, to compare the chemical weathering intensity among different rock types, the final purpose is to normalize a chemical weathering index and make the values among different lithologies comparable. To do that, an appropriate solution is to first set a reference rock, and evaluate the chemical index of alteration of the reference rock under the same weathering conditions of the rock to be normalized based on the CWA relationship (Fig. 6).
The methods for the quantification of the chemical index of alteration in previous studies are mainly based on the ratio between the sum of residual "mobile elements" (such as Na, Ca and K) and "immobile elements"(such as Al) (Nesbitt and Young 1982;Harnois 1988;Fedo et al. 1995). As Na, Ca, K and Al exist in most common weatherable rock-forming minerals (Deer et al. 2013), the classic chemical weathering index CIA (Nesbitt and Young 1982), which contains all these elements, is taken as an example for the explanation of the chemical index of alteration normalization. The normalized values mirror the chemical weathering intensity among different lithologies. Therefore, the results can contribute to quantifying the climate variation even with lithologies that show intrinsically different susceptibilities to chemical weathering. For the normalization of CIA values of the sampled rock, a reference rock is needed (Sect. "Normalization of chemical weathering indices using CWA ", first paragraph). The normalization process is divided into three steps as follows: (i) First, the difference in the CIA values compared to fresh parent rock values is calculated (CIA f ): this difference is called the deviation degree (λ): The same formula is applied for the sampled rock. For the reference rock, the deviation of the CIA is defined as λ r , and for the sampled rock to be normalized is defined as λ s . Normalize the deviation range of CIA for the sampled rock type By definition, the maximum CIA value is 100 if the mobile elements Na, Ca, and K are completely leached and only silicates are left over. However, for different minerals, the proportions of Na, Ca, K and Al within the silicate are different. As a result, the CIA values vary with rock types and mineral types, e.g. the CIA value for feldspars is 50; for biotite between 50 and 55, for hornblende 10 to 30 and for pyroxene between 0 and 20 (Nesbitt and Young 1984;Mclennan 1993). This means that chemically fresh mafic rocks dominantly composed of pyroxene or hornblende, show CIA values lower than those of felsic rocks, mainly consisting of feldspars and biotite. Thus, a correction coefficient n is introduced to correct the variation range of CIA between the reference rock and the sampled rock, which is normalized to the same range as follows: where CIA fs refers to unweathered fresh part of the sampled rock and CIA fr refers to the unweathered fresh part of the reference rock.
(iii) Normalization of CIA for sampled rock type with CWA With the correlation coefficient n, the variation range of CIA between the sampled rock and reference rock is corrected to the same range. However, due to the difference in the susceptibility to chemical weathering, the deviation degree should further consider the discrepancy in the CWA between the sampled rock and the reference rock. Therefore, λ s should be normalized based on the CWA between the sampled rock (CWA s ) and reference rock (CWA r ) and the correction coefficient n. The result is defined as λ N as follows : It is noticeable that the maximum CIA value for different types of rock is 100. To maintain the accuracy, it is better to also keep the CIA value of the sample with a CWA lower than 100 after normalization. Therefore, it is better to set the rock with a lower CWA as the reference rock. Putting all calculation steps into a final formula, the CIA values of the sampled rock can be normalized (CIA N ) using the CIA value of the fresh part of the reference rock (CIA fr ) and λ N .
The CIA N represents the chemical index of alteration for the reference rock but under the same weathering conditions as the sampled rock. As the different types of rock are all normalized by the reference rock, the chemical weathering intensity can be compared. However, fresh rock needs different chemical weathering intensities to reach the same chemical index of alteration (CIA) value within the same time. This means that with a given CIA Relationship and definition of total weathering mass (TWM) chemical weathering ability (CWA) and chemical index of alteration (CIA). The contribution to the weathering index CIA of each type of mineral is represented by the area of the gray part of the triangle (example based on granite and basaltic andesite in this case) value, the shorter the weathering period is, the more intense the chemical weathering must be.

Integrative evaluation of weathering conditions
Previous studies on weathering degree in paleoenvironments emphasize the absolute chemical weathering degree mostly via CIA, CIA-K and Σ Bases/Al values (Maynard 1992;Fedo et al. 1995;Retallack 1999;Zhou et al. 2017). The characteristics formed by physical weathering are less considered.
This study pursues a twofold strategy to improve this deficit in paleoweathering studies as follows: (i) petrographic analysis of physical weathering via fracture analysis and (ii) normalization of the CIA to rock types. The detailed workflow is depicted in Fig. 7.
For chemical weathering, the weathering index (CIA) for chemical weathering is first calculated. Second, the time scale of the supergene alteration and reference rock is evaluated. Then, the TWM and CWA can be calculated based on the time scale and the composition of the parent rock. After that, the deviation degree of the CWA (λ) is acquired based on the reference rock. With these three parameters, the weathering indices can be normalized following Eqs. 10-13 to quantitatively assess the chemical weathering intensity among different lithologies.
For physical weathering, the fractures under the microscope are analyzed. The ratio between the fracture area and total area and the index of physical weathering (IPW) are acquired. To normalize the IPW, the formation processes of the fractures are evaluated and normalized with the corresponding rock strength. The corresponding rock strength (UCS) is calculated based on the relationship between CIA values and UCS. Finally, the IPW N can be acquired as the sum of the product between the ratio of different stage fractures with the total area and the corresponding UCS (Eqs. 5 and 6). With both, the physical and chemical weathering characteristics, the integrative weathering regime of the rock sample is quantitatively determined.

Geological setting
To apply and test the quantification of paleoweathering a widely developed paleoweathering surface was selected. For this attempt, a set of drill cores penetrating through the post-Variscan nonconformity in Central Europe were chosen. For the selection of drill cores, the imprints by modern weathering were avoided.
The weathered crystalline basement of the Variscan nonconformity belongs to the so called Mid-German Crystalline Zone (MGCZ) formed during the Variscan orogeny from ca. 360 to 320 Ma (Kroner et al. 2007). After the Variscan orogeny, the MGCZ was a highland, which was continuously weathered and eroded until the Permo-Carboniferous (Willner et al. 1991;Zeh and Brätz 2004). In the study area, sedimentation started in the early Permian, which can be concluded from contemporary volcanic rocks in the Saar Nahe Basin that are dated to approximately 290 ± 6 Ma (Lippolt and Hess 1983). At this time, the basement became covered by biomodal volcanic rocks that interfinger with Rotliegend sediments and are overlain by coarse-grained, arkosic alluvial fan to fluvial deposits (Becker et al. 2012). These rocks belong to the Rotliegend Group. Between the youngest basement rocks and the basal Rotliegend a time gap of ca. 30 Myr exists during which weathering must have taken place (McCann et al. 2006;Opluštil and Cleal 2007). From the late Carboniferous to early Permian, the climate gradually changed from humid-ever wet to a progressively enhanced seasonal and arid climate in central Europe (Izart et al. 2006;Michel et al. 2015). The trend was interrupted by several deglaciation events that converted the climate to relatively more humid conditions (Roscher and Schneider 2006). After a roughly concordant hiatus in the mid-Permian, the region was flooded by a saline, epicontinental sea, the socalled Zechstein, at approximately 257 Ma (Hagdorn and Mutter 2011;Stolz et al. 2013). The study area was at the southern margin of an embayment of the basin's center in the north (South Permian Basin) and only thin dolomitic and marly sediments were deposited (Becker et al. 2012). Around the Permian-Triassic Boundary, the deposition of several hundred meter-thick fluvial, lacustrine to aeolian redbeds of the Buntsandstein started. From the Middle Triassic to Jurassic, the sediments mainly consisted of clastic rock, carbonate and evaporites (Ziegler 1982;Ziegler and Dèzes 2005). Since the Eocene, the Upper Rhine Graben has been formed and filled with various fluvial, lacustrine and marine sediments (Schwarz and Henk 2005).
Three drill cores for this study that fulfil the following criteria were selected: (a) penetration through the Variscan nonconformity at a depth of at least 13 m to rule out modern weathering (Liang et al. 2021), and (b) the basement rock should be different for each drilling. The selected drill cores were from north and south of the MGCZ. Two drill cores were from the north and were located on the Sprendlinger Horst. Its basement rocks belonged to the northern extension of the Bergsträsser Odenwald and were mainly composed of felsic plutonic rocks. On the uplifted fault block of the Spendlinger Horst, a succession of Rotliegend of up to 250 m was conserved (Marell 1989). All younger sediments were eroded during exhumation (Matte 1991; McCann 1999) (Fig. 8). According to thermochronologic studies, the maximum subsidence depth was achieved in the Lower Cretaceous, which makes it probable that some Cretaceous deposits were also present (Ziegler et al. 2004;Cloetingh et al. 2006).
The Rotliegend sediments in this area are divided into the Moret and Langen Formations. The latter contains volcanic rocks (Menning et al. 2005). Previous studies assigned the Rotliegend sediment of the two drill cores GA2 and GA1 to the Moret Formation and the Langen Formation with basaltic andesite, respectively (Liang et al. 2021). The weathering depth in the basaltic andesite is approximately 6 m, in the gabbroic diorite basement is approximately 6.5 m, and in the GA1 drill core, the weathering depth in the GA2 basement is approximately 8.2 m.
Drill core BK2/05 is located on a valley floor in the southernmost part of Odenwald, where the Variscan basement is composed of Heidelberg Granite and the weathering depth is approximately 2 m. The Rotliegend sediments overlying the granite in BK2/05 belong to the Michelbach Formation, for which an age between 290 and 280 Ma is assigned (Edgar and Hubert 2009) (Fig. 9). The Rotliegend is followed by 30 m thick Zechstein deposits and then 6 m of basal Buntsandstein. Xenoliths in a Late Cretaceous volcanic pipe approximately 15 km east of the drill site prove a sediment succession up to the Middle Jurassic, which is eroded down to the upper Buntsandstein (Geyer and Nitsch 2011). It is estimated that approximately 650 m of sediments are missing, which sums up to a total maximum sediment cover of approximately 1000 m in the south (Menning et al. 2005;Geyer and Nitsch 2011).

Analytical methods
In total, 52 samples were collected around the nonconformity. In detail: Seventeen samples were from the GA1 drill core, which were split into 6 from the weathering profile of basaltic andesites (5 paleosol, 1 bedrock) and 11 gabbroic diorites (5 paleosol, 6 bedrock).
Thirteen samples were from the weathering profile of granodiorite in GA2 (6 paleosol, 7 bedrock).
All these samples were collected from paleosols in the top to fresh parent rock in the bottom for each weathering profile. The sampling interval was approximately 1 m for the samples from basaltic andesite and theGA1 and GA2 basement. To acquire the detailed variation in weathering characteristics, the interval was reduced to 40 cm at the topmost part. Due to the low weathering degree of BK2/05 and to express trends of weathering at a more precise scale, the interval was reduced to approximately 20 cm.
Thin sections were made to analyze the petrological features of the samples under a polarizing microscope (PM) and scanning electron microscope (SEM). Another part was Fig. 9 Lithological section of the GA1, GA2 and BK2/05 drill cores with emphasis on the weathered interval. Blue stars indicate the sampling locations. Note, the weathering degree: "extremely weathered, intermediate weathered, incipient weathered and fresh" is based on Fedo et al. (1995) milled into powder with an achate mill and analyzed for major and trace elements as well for mineral composition. Geochemical analysis including major and trace elements and C and O isotopes of the carbonate within the samples, was performed at the State Key Laboratory of Isotope Geochemistry, Guangzhou Institute of Geochemistry, Chinese Academy of Science. The detailed processes for the measurement of major and trace elements are documented in Liang et al. (2021). For the measurement of C and O isotopes, the powder was first roasted in vacuum at 400 ℃ for 4 h to remove organic contaminants. The roasted powder was then reacted with 100% phosphoric acid (H 3 PO 4 ) at 25 ℃. For the samples containing both calcite and dolomite, the CO 2 released during the first 30 min after a reaction was assumed to have come from the calcite part, and the CO 2 gas evolved from 30 min to 72 h and was collected as the dolomite part. The gas was measured by a MultiPrep-GV Isoprime II mass spectrometer. Both the δ 13 C and δ 18 O are expressed in per mil (‰) relative to the PDB standard. The international reference material NBS-19 was applied for the calibration, and the analytical precision for C was better than 0.2‰, and for O was 0.3‰. Bulk powder was analyzed by XRD at Goethe University Frankfurt. The powder was carefully back-loaded to reduce the preferred orientation and analyzed by a PANalytical X'Pert diffractometer equipped with a Bragg-Brentano goniometer (copper beam). The mineral-phase proportions were estimated by weighted XRD peak intensities after conversion with their typical reference intensity ratios (RIRs), as found in the powder diffraction file (PDF-2 and PDF-4 of the International Centre of Diffraction Data) with MacDiff software (Petschick et al. 1996).
As the fracture data were collected from drill cores, it was difficult to measure the fracture orientations. Alternatively, the angle within the fractures can act as a useful tool to assess the tectonic fractures, as they indicate a preferential angle with a smooth fracture surface, while the fractures formed due to weathering show random angles (Scarpato 2013;Caspari et al. 2020;Feng et al. 2021). In this study, fracture angles were measured clockwise and started from the horizontal direction. The results were analyzed by rose diagram to document whether the fractures have preferential directions.

Petrological and mineral characteristics
The lithologies among the three drill cores include the following four rock types: gabbroic diorite, basaltic andesite in GA1, granodiorite in GA2 and granite in BK2/05. To better illustrate the variations in the weathering profile, the petrological characteristics acquired from microscopy and mineral compositions from XRD are depicted together.
Gabbroic diorite (GA1): The fresh part of the granodioritic basement in GA1 at 6 m depth below the nonconformity is coarse-grained (~ 6 mm) and consists of plagioclase (43%), amphibole (19%), biotite (23%) and quartz (15%). Fractures are fairly scarce and are all closed (Fig. 10). Toward the nonconformity, the density and width of the fractures and the ratio of the secondary minerals all increase at the expense of the primary minerals. For example, at a depth of 2.9 m, the density of the fractures increases significantly and the average width of the fractures increases to approximately 25 μm. The fractures are filled by clay minerals and calcite, accompanied by a small proportion of void fractures. In addition, weatherable primary minerals such as plagioclase and biotite are altered and partly replaced by secondary minerals, such as clay minerals and carbonate minerals (Fig. 10A2). In the topmost part, at a depth of 0-0.9 m below the nonconformity, the fractures are ubiquitous with a width between 5 and 100 μm (Fig. 10A3). The proportions of plagioclase and biotite decrease to approximately 7% and 10%, respectively, with secondary minerals increasing to approximately in total 75% (Fig. 8). Most fractures are filled by carbonate, some by clay minerals, and a minority are void (Fig. 10A3).

Fig. 11
Mineral characteristics along the drill core profiles; the lithology legend refers to Fig. 9 Basaltic andesite (GA1): For basaltic andesite, the fresh part at a depth of 5.4 m shows an amygdaloid texture. The matrix contains plagioclase crystals, whereas the amygdaloid is filled with calcite, zeolite and chalcedony. Fractures in this part are rare (Fig. 10B1). Toward the surface, such as at approximately 0.4 m, the primary minerals which are mainly plagioclase, are gradually altered and transferred to clay minerals, the content of the primary minerals gradually decreases from 81.5% at 5.4 m to 72.5% at 0.4 m below the weathering surface (Fig. 11), and fractures are very limited (Fig. 10B2). In the topmost part of the basaltic andesite (13.9 m) which is in the weathering surface, nearly all primary minerals are transferred into secondary minerals, the shape of the primary mineral grains is well preserved, the density of the fractures is still limited, all the fractures are void and the width of the average fractures is approximately 30 μm (Fig. 10B3).
Granodiorite (GA2): The fresh granodiorite in GA2 at a depth of 17.6 m is coarse-grained (approximately 5 mm) and consists of plagioclase (35%), biotite (10%), K-feldspar (15%), quartz (30%) and 10% other minerals (Fig. 8C1). From bottom to top, the primary minerals have an overall decreasing trend while the secondary minerals such as the mixed layer I-S and carbonate increase (Fig. 11). Toward the surface of the basement, the density and width of fractures also increase. In the fresh part of the granodiorite, the fractures are very limited (Fig. 10C1). At 5.8 m, fractures are frequent with widths of approximately 10 μm, and most of the fractures are filled by clay minerals, with a minority of fractures filled by carbonate (Fig. 10C2). In the topmost part of GA2, fractures are more frequent with a width of approximately 25 μm. The fractures are mainly filled by clay minerals, accompanied by a small proportion of void fractures and only a minority of fractures are filled by carbonate minerals (Fig. 10C3).
In the bottom part, no fracture is found (Fig. 10D1). At the position 0.5 m above the fresh part, there is one fracture throughout the thin section with a width of approximately 100 μm. The fracture is filled by clay minerals, carbonate and voids along the edge. The widths of the other fractures are approximately 8 μm and filled by clay minerals (Fig. 10D2). In the topmost part of the granite, fractures are frequent and have an average width of 15 μm, some as low as 5 μm. All the fractures are mainly filled by clay and carbonate minerals. Primary minerals, such as plagioclase and biotite, are highly altered and accompanied by secondary clay minerals. (Fig. 10D3).

Fracture characteristics and IPW
The detailed fracture angle and fracture area under microscale data are given in Supplementary B (Tables S3 and  S4, respectively). In total, 162 fractures along three drill cores are recognized and analyzed, among which 59 are for the basaltic andesite part of GA1, 64 are for the gabbroic diorite part of GA1, 37 are for GA2 and 2 are for BK2/05. The statistics of the fracture angle orientation are illustrated in Fig. 12. Fractures along the entire drill cores indicate a random distribution of angles. A preferential angle distribution does not exist. This indicates that the fractures along the three drill cores all formed due to physical weathering. The contribution of other factors is insignificant (Scarpato 2013).
The ratio between the average values of the fracture areas and the total area of the pictures are visualized in Fig. 13. The fracture area ratio (IPW) values are represented by the average of 15 values from each thin section. In the gabbroic diorite, the physical weathering depth is 6.5 m, the area of void fractures is limited to the upper part (0-2.9 m), and the proportion of void fractures at 2.9 m is 0.83%, increases to 2.0% at 0.9 m and decreases to 0.18% at the surface. The proportion of fractures filled by carbonate increases rapidly from 0% at a depth of 4.9 m to 13.0% in the topmost part. The proportion of fractures filled by clay minerals gradually increases from 0.16% at 6.5 m to 5.4% in the topmost part, and in the fresh part, no open fractures exist. In basaltic andesite the physical weathering depth is limited in the top part which is from 0 to 0.4 m and only void fractures are observed. Their measured area shows an overall increasing trend toward the top with a sharp increase at the topmost part.
Along the GA2 drill core, the physical weathering depth is approximately 10.8 m below the paleosurface, and the void fractures are limited to the topmost part with a proportion of 0.78% of all observed fractures in this part. The fractures filled by carbonate are only observed at a depth of 2.6 m, which yields a value of 3.5%, while the fractures filled by clay minerals exhibit a trend from 0.27% at the bottom (9.2 m) to 4.6% at the top. All types of fractures are not found in the fresh part (17.6 m). In the BK2/05 drill core, the physical weathering depth from 0 to 0.8 m is documented, and the void fractures are also observed only in the topmost part, with a value of 0.31%. The area of the fractures filled by carbonate yields a value of 0.79% at 0.8 m and 4.72% at the topmost surface. The fractures filled by clay minerals decrease from 0.97% at 0.8 m to 0.28% at 0.2 m and increase to 1.02% at the topmost part. In the fresh part (10.8 m), fractures also do not exist.
In the basaltic lava part of GA1, the IPW A values increase from the bottom to the top, with a dramatic increase to 1.56 in the topmost part. Both the gabbroic diorite and However, thin sections from the fresh rocks at all drillings do not show fractures. Therefore, the ratios between the total area of the fractures and the view area in this case can be considered as the true value of IPW, i.e. all observed microfractures are caused by physical weathering.

Determining the IPWN
The fractures among the investigated drill cores consist of the following three types: fractures filled by clay minerals, fractures filled by carbonate and void fractures. To evaluate the IPW N values, the key point is to determine the fractures formed during chemical weathering to calculate the corresponding UCS for each fracture type. The UCS for fractures filled by clay minerals is represented by the average UCS value between the unweathered and the sampling position. For the void fractures, the UCS at the sampling position is applied. The UCS for basaltic (basaltic andesite) and granitic (granodiorite and granite) rock under different weathering degrees (CIA value) can be calculated based on Eqs. 1 and 2.
Since the nonconformity experienced burial diagenesis, for the fractures filled by carbonate, it is important to decide whether the carbonate was formed during the weathering stage or the burial stage. The fractures filled by carbonate formed during the weathering process should be treated similarly to fractures filled by clay minerals (Sect. "Fracture recognition and classification"). Fractures filled by carbonate formed during burial diagenesis should be treated as void fractures.
To distinguish the source of the carbonate, the C and O isotope compositions of the carbonate within the fractures are analyzed (Fig. 14). The δ 18 O composition of carbonateforming fluid was determined based on the method proposed by Michel and Tabor (2016) to assess the influence of the overprint of burial digenesis. Based on the fluid composition, the isotope fractionation between calcite and water is calculated after Friedman and O'Neil (1977) as follows: In Eq. 14, T refers to the temperature on the Kelvin scale. lnα cc-w equals ln[(δ 18 O cc + 1000)/(δ 18 O w + 1000)], δ 18 O cc refers to the measured δ 18 O value of calcite, and δ 18 O w is the δ 18 O value of coexisting water. As all δ 18 O in Eq. (14) are related to SMOW (Craig 2013), the δ 18 O (PDB) acquired from the measurement is transformed to the SMOW standard after Eq. 15 based on Friedman and O'Neil (1977) as follows: The results are listed in Supplementary B (Table S6) and visualized in Fig. 14.
If all the calcite within the weathering profile of GA1 and GA2 was formed during surface weathering under the temperature of 25 ℃, the estimated δ 18 O SMOW of the calcite-water yield values between − 10.8 and − 6.08‰. However, the presence of coexisting authigenic minerals, such as dolomite and quartz, indicate the weathering profile should be overprinted by a higher temperature. Previous studies indicates that the weathering profile experienced a maximum temperature up to approximately 290 ℃ (Wagner et al. 1990;Burisch et al. 2017). Under this temperature, the estimated δ 18 O SMOW values range between 12.73 and 16.50‰. The value range is clearly higher than that of the meteoric water but is highly likely for geothermal and/or hydrothermal fluids (Ruddiman 2008;White 2009;Stataude et al. 2012). Therefore, the calcite within GA1 and GA2 should all have formed during burial diagenesis rather than chemical weathering. In addition, dolomite is a typical mineral that precipitated during burial diagenesis (Stimac et al. 2015). The fractures filled by carbonate (calcite and dolomite) should be originally void and should be treated as void fracture and normalized by the UCS under the present chemical index of alteration.
The normalized index of physical weathering (IPW N ) is visualized in Fig. 15. The IPW N values of the granodiorite in the GA2 drill core increase from 0.22 at the bottom to 3.85 at the top. The physical weathering trend is mainly controlled by fractures filled by clay minerals. An exception is the sample from 2.6 m, where fractures are mainly filled with carbonate. Based on the characteristics of the thin (14) 10 3 ln cc−w = 2.78 10 6 T −2 − 2.89.   (Friedman and O'Neil 1977) section, the lithology in this position is close to gabbro. The CIA value for the fresh gabbroic rock is approximately 35 (Fritz 1988), and the CIA of this sample yields a value of 45.1. Using the results of the fracture analysis and mineral characteristics (Figs. 10C2 and 11), the sample was slightly weathered. For the slightly weathered gabbroic rock or the slightly weathered gabbroic rock previous studies using 26 samples indicate a UCS between 36.6 and 69.6 (Aggisttalis et al. 1996). Here, the arithmetic average value of 43.1 was applied. The results show a gradually decreasing trend of physical weathering from top to bottom.
In the basaltic andesite part of the GA1 drill core, only tiny void fractures were observed. Here, the IPW N values range from 0 to 0.022 from bottom to top, which indicates low physical weathering intensity.
The IPW N values of the granite in BK2/05 range from 0.16 to 1.04. From 1.8 m below the weathering surface the IPW N values first decrease from 1.04 to 0.16 at 0.2 m and then increase to 0.63 at the topmost surface.

Characteristics of major elements
The results of bulk major element concentrations are listed in Supplementary B (Table S1), and the representative elements and CIA values along the profile are visualized in Fig. 16.
For the basaltic andesite in the GA1 drill core, element concentrations of Al, K and P have a decreasing trend from top to bottom, while Ca and Na increase. In the gabbroic diorite part, the element concentrations of Al and P fluctuate in the top part (0-0.9 m) but display an overall increasing trend from top to bottom. Both K and Na indicate a significant shift between the top part (0-0.9 m) and the lower part (1.9-7.9 m), while the concentration of K decreases from top to bottom and Na increases from top to bottom.
For the GA2 drill core, except for the samples from 2.6 m and 5.8 m, the concentration of Al is almost constant. In contrast, Na and Ca show an overall increasing trend from top to bottom, whereas K decreases.
The results from BK2/05 indicate that the concentrations of Al and Ca increase from top to bottom, while Ca is almost constant and K has a decreasing trend. All the elements have an abnormal value in the sample at 1 m below the weathering surface, with the relative content values of Al and Na being lower and Ca and K being higher than any other position along the drill core.

Determining and normalizalizing of the chemical index of alteration
The results acquired by Liang et al (2021) indicate that the weathering profile in the area was overprinted by K-metasomatism. This affects chemical weathering indices such as CIA (Fedo et al. 1995;Zhou et al. 2017;Fàbrega et al. 2019). Previous studies proposed several methods to eliminate the effect of K-metamorphism (e.g. Harnois 1988;Maynard 1992;Panahi et al. 2000). Both Harnois (1988) and Maynard (1992) eliminated the inconsistent behavior and/or the metasomatism of K by removing K 2 O from the CIA equation directly. The elimination of the K component does not account for the associated aluminum; hence, the method works well for evaluating the chemical index of alteration of plagioclase. However, it is not appropriate to evaluate the weathering degree of the parent lithologies that contain K-feldspar and/or biotite, especially when the parent rock is not completely weathered. Since the samples in this study include granite (BK2/05) and granodiorite (GA2), the A-CN-K diagram was applied to assess the chemical index of alteration under K-metamorphism (Nesbitt and Young 1984) (Fig. 17). Previous studies indicate that the weathering trend for the upper continental crust should be in accordance with the A-CN axis given the depletion rate among Ca, Na and K (Nesbitt and Young 1984). However, while the weathering profile was overprinted by K-enrichment diagenetic fluids (so-called K-metamorphism), the weathering trend was shifted to the K-apex (Fedo et al. 1995). As shown in Fig. 17A, the weathering trend for all three drill cores extends to the K apex. Similar results were found by Schmidt et al. (2021).
To correct the K content within the weathering profiles, the method proposed by Panahi et al. (2000) was applied. The detailed method is expressed as follows: where A w and CN w refer to the Al 2 O 3 and (CaO* + Na 2 O) contents in the weathering zone, respectively, while In Eq. (17), the K, A and CN values for m are from the unweathered parent rock sample.
With the correction, the weathering trend for all the drill cores was parallel to the A-CN joint, and the effects for CIA values from the burial diagenesis were removed.
The age of the weathering surface may be younger than the exposure age of the basement, as the weathering surface will be renewed by continuous erosion (Riebe et al. 2003). The post-Variscan nonconformity represents a diachronous time gap between tens and hundreds of millions of years in central Europe (Zeh and Brätz 2004;Kroner et al. 2007). However, a precise chemical weathering scale is uncertain due to the effect of erosion. Therefore, a wide range for the duration of weathering from ten thousand to one million years was applied. This assumption also enabled the determination of the CIA sN variations for a certain rock type under different weathering intensities. The TWMs produced in these time periods for plagioclase, K-feldspar, hornblende and biotite are calculated with Eq. (7). For the weathering rate of pyroxene, Franke (2009) indicated that the weathering ratio between pyroxene and hornblende is 1:1.5, and Hausrath et al. (2008) suggests that the weathering rates between pyroxene and plagioclase is 1:5. Applying Eq. (6), these two results match perfectly with each other. The corresponding CWA for different types of rock is calculated by Eq. (9), based on the mineral proportions in the fresh part. Due to the lack of mineral proportions of the fresh rock for the sample at 2.6 m below the weathering surface (58.3 m) in the GA2 drill core, the result for this sample is ruled out. To normalize the CIA value and make weathering intensity over all rock types comparable, fresh granite samples from drill core BK2/05 are set as the reference lithology. This is because the CWA of the granite is moderate compared to the other three lithologies. After normalization, the CIA sN range for other lithologies will not exceed 100. With the parameters λ, n and λ sN , the original CIA was normalized to CIA s and CIA sN . All the relevant parameters and results are listed in Supplementary B (Table S5) and the original CIA, CIA corrected by n (CIA s ), and CIA sN values are visualized in Fig. 18. For all three lithologies, after normalization to the granite from BK2/05, all the normalized CIA values show an overall similar trend to the original values. As the CIA, CIA s and CIA sN from all the drill cores show an overall decreasing trend, the chemical weathering depth changed from 6.45, 3.9, 5.4 and 2.1 m in the GA2, gabbroic diorite and basaltic andesite parts of the GA1 and BK2/05 drill cores.

Integrative weathering evaluation in the research area
The post-Variscan nonconformity in central Europe represents a time gap of millions years (Opluštil and Cleal 2007). It was formed after the Variscan orogenesis and was successively buried by continental and marine sediments due to the onset of basin formation at approximately 320 Ma and ongoing subsidence up to the Triassic period. The alteration at this first order nonconformity was studied only locally with a focus on petrophysical properties. Littke et al. (2000) pointed out that porosities and permeabilities increased due to supergene alteration. This is confirmed by hydrothermal and geothermal studies, but the authors found significant heterogeneity (Bons et al. 2014;Schäffer et al. 2021). To date, this has been not linked to specific rock types as addressed in this paper. In our research area, the nonconformity crops out and different Variscan crystalline rocks underlie lower Permian basaltic rocks, as well as proximal immature clastic rocks. A series of cored drillings hit the nonconformity at depths of 13-62 m which guaranteed that recent alteration was negligible. Figure 19 summarizes trends of corrected CIA and IPW for the basement beneath the first-order post-Variscan nonconformity, as well as for an intra-Permian lower-order unconformity of the basaltic to andesitic lava flow. The first-order nonconformity was represented by the weathering surface of the gabbroic diorite basement in GA1, granodiorite basement in GA2 and granite basement in BK2/05. As expected IPW and CIA N all show a decreasing trend with depth, i.e., physical and chemical weathering intensity decreases with depth. The normalized IPW N , however, shows opposite trends for the granite. This was probably due to the heterogeneity in the weathering profile.
The granodiorite at GA2 (Fig. 19A) shows decreasing values with depth for IPW and IPW N values. The fractures were mainly filled by clay minerals except at 2.6 m depth where diagenetic carbonate fills the void (see also Fig. 10). After the normalization of IPW, the gradually decreasing IPW N values from top to bottom suggest that the physical weathering intensity decreased with increasing depth.

Fig. 19
Comprehensive weathering characteristics for GA2, GA1 and BK2/05; note that A to D are based on chronological order. Numbers are ratios of indices. The legend refers to Figs. 9 and 17 1 3 CIA N also decreased with depth from approximately 70 to 50 depending on the age model.
For the gabbroic diorite in the GA1 drill core (Fig. 19B), only the IPW was calculated because this rock type does not belong to either granitic rock and or basaltic rock. Thus, the relationships between CIA and UCS in this case are not suitable for the rock type in GA1. The IPW again decreases with depth. It has the highest values of all basement rocks which means strong fracturing. The CIA N decreases from approximately 80 to 55. Compared to the granodiorite the decrease is not gradual, but shows an abrupt decrease to less weathered rock at a depth of approximately 2 m. The intraformational basaltic andesite in the GA1 section (Fig. 19C) over the post-Variscan nonconformity shows much lower physical weathering indicated by IPW and IPW N . Fractures are voids, which indicates that the fractures were formed during the very latest stage of chemical weathering and that the physical weathering intensity is very limited. The CIA N , however, is very high at the top which reflects the higher weatherability of the aphanitic volcanic rock. It drops abruptly at a depth of 0.4 m. This shows the shorter time interval for weathering of the lavaflow compared to basement rocks at the post-Variscan nonconformity.
The granite in drill core BK2/05 shows relatively little weathering which penetrates only some decimetres. Fractures are mainly filled during burial diagenesis with calcite and dolomite. Clay minerals are almost absent. Weak chemical weathering is confirmed by the CIA which declines from approximately 78-55 at a depth of 0.4 m. Figure 20 shows the relationship between the physical and chemical weathering indices. Although in all cases a positive correlation can be observed, the inclination of the regression line is different for each rock type. This means that the balance of physical vs. chemical weathering is clearly rock dependent. Figure 20B shows that the positive relationship enhanced after normalization, particularly for basaltic andesite and granite. As expected, this indicates that the physical weathering process will enhance the chemical weathering intensity due to the fractures formed under physical weathering. The process increases the specific surface area of the rock and provides pathways for meteoric water (Migoń and Lidmar-Bergström 2002).

Implications for paleoclimate research and for heterogeneity assessment of nonconformity reservoirs
The results gained with the methods introduced in this study can be related to paleoclimate data, such as the mean annual temperature (MAT) and mean annual precipitation (MAP), which offers additional fields of applications and quantitative comparisons in paleoclimate research. Previous studies indicate that the physical weathering process refers to an arid climate, while under a humid climate, the chemical weathering process dominates (Bland and Rolls 1998). The results of this study show that the overall physical weathering intensity shows a decreasing trend and then increases from granodiorite (GA2) and basaltic andesite (GA1) to granite (BK2/05), while the chemical weathering intensity shows the opposite trend. Hence, it can be stated that the climate exhibits a gradual trend toward more humid conditions reflected by the increase in chemical weathering intensity accompanied by the decrease in physical weathering intensity.
However, to extend the field of applications and to show the robustness of the methods and results proposed in this study, the major elements employed in this case study are used to apply the methods proposed by Retallack (2006) and Sheldon (2006). The methods make use of the CIA-K and the "clayness (C)", which is expressed as the ratio between Al and Si in the mole fraction. This ratio is directly correlated with paleoclimate conditions indicated by the B-horizon of the soil profile. (Retallack 2006;Sheldon 2006;Sheldon and Tabor 2009). While the CIA-K can be applied to assess the mean annual precipitation (MAP), the "clayness (C)" is a useful tool for the estimation of mean annual temperature (MAT) as follows: Fig. 20 Relationship between the IPW and CIA and CIA sN . Legend refers to Fig. 17 1 3 In addition to Eqs. (18) and (19), a data-driven paleosolpaleoclimate model (PPM) was proposed by Stinchcomb et al. (2016). Their model was developed based on 685 samples from the B horizon from different soil profiles. The investigated elements comprised K, Al, Si, Ca, Na, Al, Ca, Na, Fe, Mg, Mn, Ti and Zr, which were analyzed by combining partial least squares regression (PLSR) and nonlinear spline. The output results of this model include both MAP and MAT. However, the model does not consider the overprint of burial diagenesis. Thus, to apply this model to weathering profiles influenced by burial diagenesis, elements that are preferentially affected such as Ca and K should be corrected.
To apply the PPM model of Stinchcomb et al. (2016), paleosol samples from the topmost part of the weathering profile, with the parent rock of basaltic andesite and gabbroic diorite in GA1, granodiorite in GA2 and granite in BK2/05 were selected. For both methods, the CaO was corrected based on Mclennan (1993). The K 2 O content for PPM is corrected based on Panahi et al. (2000). The comparison of the results from these two studies and the method proposed in this study is listed in Table 2.
Using the PPM of Stinchcomb et al. (2016) rock types comprising granodiorite (GA2), gabbroic diorite (GA1), basaltic andesite (GA1), and granite (BK2/05), the MAP shows an increasing trend from 542 to 1522 mm/year followed by a decreasing trend to 1109 mm/year. The MAT gradually increases from 10.3 to 21.3 ℃ and then decreases to 10.3 ℃. Overall, these trends in MAP and MAT coincide well with the trends of IPW N and CIA N in this study. Hence one can make use of this quantitative relationship to additionally assess MAP and MAT with the same database as used for the methods suggested in this study.
For the results calculated based on the method proposed by Sheldon (2006), the MAT shows a similar trend as the weathering intensity from this study. The MAP of the paleosols weathered from basaltic andesite and gabbroic diorite fits well with the model of Stinchcomb et al. (2016) and with the chemical weathering intensity. However, the samples from the other two drill cores, especially the paleosols weathered from granite in BK2/05, show a clearly higher MAP close to basaltic andesite. The value of CIA-K is 94.7, while the petrographic and mineralogical characteristics indicate that the sample is only moderately weathered (Figs. 7D, 8). An explanation is that the parent rock (granodiorite and granite) of the samples contains K-feldspar, which leads to a higher value of CIA-K compared to its actual chemical index of alteration (Fedo et al. 1995). Nevertheless, our results still show a positive correlation with the variation in both MAP and MAT.
In conclusion, both models coincide with CIA N and IPW N trends, meaning that the increases in precipitation and temperature indicate a warm and humid climate. Subsequently, a more intense chemical weathering environment with a relatively lower rate of physical weathering processes appears (Camuffo 1995;Ruddiman 2008).
In addition to paleoclimate evaluation, the CIA N and IPW N may also be applied for the evaluation of the heterogeneity of nonconformity reservoirs. With the alteration of the meteoric environment, the petrophysical properties of the weathering zone along the basement rock change (Gardner 1940;Walter et al. 2018). Note that both physical and chemical weathering are sensitive to different lithologies, which causes a specific response of petrophysical properties. Therefore, when working on a weathered basement comprising different lithologies, the weathering intensity (IPW N and CIA N ) should be calculated as suggested in this study. Then, on a regional scale, the weathering intensity and the weathering degree of different lithologies distributed along the nonconformity can be assessed to find suitable assets in terms of reservoir quality. In addition, based on the relationship between the weathering degree and petrophysical characteristics (Wu et al. 2013;Walter et al. 2018) the heterogeneity of the nonconformity reservoir can be evaluated.

Perspectives
The suggested theoretical and practical concept for the rock-specific quantification of physical and chemical weathering in this paper opens new avenues to study the Table 2 Results from the methods proposed by Sheldon (2006), Stinchcomb et al. (2016) and this study. Note the unit for MAP is mm and MAT is ℃

Samples
Sheldon ( complex processes at nonconformities but also for paleosols in the sedimentary stratigraphic record. A high applicability is given because it is designed for studies on drill cores and at the microscale. However, there is still a potential for improvements. First, the relationship between UCS and CIA values for more rock types could be developed in the future. With these relationships, the physical weathering intensity for more rock types could be compared. Second, the strategy for sampling could be restricted, e.g., all the samples should avoid macro/mesoscale fractures along drill cores. While the samples are more unified, the weathering degree results should be more representative. Last, the effect of the weathering intensity on the petrophysical characteristics of different types of rock is only weakly discussed here. The influences of both physical and chemical weathering intensity on the porosity and permeability of different rocks are still uncertain. Relevant work, such as the petrophysical characteristics of different igneous rocks under a variety of weathering intensities, could be measured in the future. With the results, the heterogeneities of the nonconformity reservoir may be quantified and the results may contribute to reservoir quality assessment.

Summary and conclusions
Both physical and chemical weathering are significant processes on the surface of the earth. This study suggested a new index of physical weathering (IPW) to quantify physical weathering in paleoweathering profiles at the microscale. Using the IPW, an integrated concept to quantify the weathering intensity for both physical and chemical weathering is proposed. The suggested quantification method is designed for drill core investigations using petrographic and computer-aided textural thin section analysis, combined with standard mineralogical XRD, as well as geochemical XRF and ICP-MS analyses. This study also introduces a normalization procedure for physical weathering, the IPW N , as well as a procedure to normalize the CIA to rock types expressed by the CIA N . The introduction of the new indices IPW N and CIA N and its corresponding workflow allows for the first time the simultaneous quantification of the physical and chemical weathering intensity at subaerial paleo-surfaces in the geological record. This makes the effects of weathering comparable at the regional scale regardless of rock type in terms of paleoclimate and heterogeneity assessment, as well as alteration of petrophysical properties.
As a case study, three drill cores from the first-order post-Variscan nonconformity in southwestern Germany were taken hitting the nonconformity in several tens of meters, which excludes the overprint of recent weathering. At the nonconformity, Precambrian to Paleozoic magmatic rocks (granodiorite, gabbroic diorite and granite) were weathered and diagenetically altered and overlain by Permo-Carboniferous volcanic and sedimentary rocks. A basaltic andesite lava flow within the Rotliegend also shows weathering at the top which has been investigated in addition. The calculated IPW N and CIA N trends of these sections coincide well with trends of paleosol-paleoclimate models revealing mean annual temperature (MAT) and mean annual precipitation (MAP), which illustrate the potential to synchronize the suggested indices with other paleoclimate proxies. This offers a completely new spectrum of possibilities to quantitatively compare weathering and climatic conditions at the regional scale, regardless of lithologic constraints.