THERMAL STATE OF THE LITHOSPHERE OF PATAGONIA VIA DATA OF THE XENOLITHS

. Ultramafic xenoliths and minerals present in intrusive rocks make it possible to infer the temperature and pressure of the upper mantle and lower crust, since they preserve their physical and chemical characteristics while being transported by magmatic processes. Thermal models incorporating thermo-barometric data have been developed to estimate the thermal field. Thus, the objective of this work is to use mineralogical temperature and pressure equilibrium information to estimate lithospheric thermal field in the Patagonian region bounded by latitudes 40º - 52º S and longitudes 67º - 71º W, these coordinates correspond to the Argentine provinces of Río Negro, Chubut and Santa Cruz. Experimental mineral temperature data indicate ranges of 917-1029 ºC in the Chubut province, 877-1253 ºC in the Río Negro region and 728-1196 ºC in the Santa Cruz province. The average heat flux and temperature values at the Moho depth are 40 mWm -2 and 734 ºC, respectively. Río Negro province has the highest temperature (760 ± 45 ºC) and the lowest thermal thickness value (75 ± 11 km), while Santa Cruz province has the highest heat flux (44 ± 7 mWm -2 ) at Moho depth, which indicates that there are possibly two plumes responsible for the deposition of xenoliths in the region: one in Río Negro province and the other in Santa Cruz.


INTRODUCTION
Ultramafic xenoliths (peridotite-pyroxenites) and eclogitic minerals present in intrusive rocks such as kimberlites, lamproites and alkaline basalts are widely used to infer the temperature and pressure of the upper mantle and lower crust (Kukkonen & Peltonen, 1999;Russell & Kopylova, 1999;Russell et al., 2001;Harder & Russell, 2006;Aulbach et al., 2004;Howarth et al., 2014;Dymshits et al., 2020;Alexandrino et al., 2022).As xenoliths preserve their physical and chemical characteristics while being transported by magmatic processes, we can use this information to estimate the thermal field of the lithosphere using the thermo-barometric equilibrium condition of xenoliths.The method was used by Rudnick et al. (1998) in a global study with the purpose of investigating the thermal regime in Archaean terrains.Russell et al. (2001) evaluated radiogenic heat production and basal heat flow in the Slave Craton region of Canada via thermo-barometrical xenoliths data.A similar D r a f t method also was used by Dymshits et al. (2020) to estimate the thermal state, thickness and composition of the Siberian Craton.These studies show that the information extracted via equilibrium conditions from samples of xenoliths of man-made origin constitutes an efficient way to infer geothermal parameters in the lithosphere, especially in the upper mantle and lower crust.
In this context, the region of Patagonia in Argentina provides an opportunity to infer geothermal parameters.at Moho's depth being covered by geologically recent basaltic volcanism it provides samples of ultramafic xenoliths directly from the upper mantle from data compiled in works published in the past two decades (Mallmann, 2004;Bjerg et al., 2005;Ntaflos et al., 2007;Rieck et al., 2007;Schilling et al.. 2017).
Therefore the objective of our study is usefulness of the information of temperature and pressure of mineralogical balance of the to estimate the thermal state of the crustal lithosphere and the mantle.

GEOLOGIC SETTING
The study area is located between the latitudes 40º and 52º S and longitudes 67º and 71º W.
These coordinates delimit the Patagonian region, the focus of this work which also includes the southern stretch of the Andes as described in figure (1) where the main pre-Jurassic tectonic elements are the Northern Patagonian and the Deseado Massifs (Giacosa et al., 2012;Caminos et al., 1999).
In these regions there is a Jurassic rhyolitic volcanic rock domain which forms one of the largest siliceous provinces in the world (Pankhurst et al., 1998).
The siliceous volcanic field of Patagonia extends from the Atlantic coast to the Chilean Andean region.Eastern Patagonia is geologically divided into stable areas in which the volcanic rocks are now exposed in the Northern and Deseado Patagonian massifs and the intermediate areas covered by the Cretaceous and Tertiary sedimentary rocks of the San Jorge and Magellan Basins (Pankhurst et al., 1998;Caminos et al., 1999).
The basement rocks occupy a larger area in the Northern Patagonian Massif.The main types of rocks which occur on the western edge of the massif in Paleozoic granite intrusions are Shales and Gneiss.In the southwestern part of the massif carboniferous and Permian gneisses occur (Caminos et al., 1999;Pankhurst et al., 1998;2006).
In the Deseado massif a series of small outcrops occur that reveal sequences of micaceous materials and amphibolitic shales possibly of pre-Cambrian or late Cambrian age Permo-Triassic conglomerates fill small basins and represent the oldest evidence of an extensional regime that became more pronounced during the Triassic period with the regional formation of NNW -SSE trend graben throughout Patagonia (Pankhurst et al., 1998).
Tables (1) to (3) present the pressure and temperature information, as well as the types of dominant minerals present in xenoliths samples in the provinces of Río Negro, Chubut and Santa Cruz, compiled from various works as described in the references.Details on the geothermometers and geobarometers used to estimate the pressure and temperature of equilibrium can be consulted in the references from which the information was compiled.

MODEL DESCRIPTION
Regarding the main mode of heat transfer in the lithosphere is conduction, we can develop a model to estimate the thermal field of the lithosphere from the following parameters: temperature, heat flow, radiogenic heat production and thermal conductivity.
The model proposed in this work is composed of two layers, as described in figure (3).This analysis is similar to that proposed by Russell & Kopylova (1999); Lewis et al. (2003); The layer (2) represents the lithospheric mantle.The top of this region is the ZM position and the base at the ZA position.ZM is Moho's depth, this way it also represents the crustal thickness.The radiogenic heat production AM in layer ( 2) is assumed to be constant, but thermal conductivity λ(T) is a function of temperature, while B is the coefficient of variation of thermal conductivity with temperature.
TM and qM are respectively the temperature and the heat flow at Moho's depth.
The ZA position physically represents the thickness of the thermal lithosphere which is the region of the lithosphere by definition, where the main mode of heat transfer is conduction.In this position the temperature TA has a value of approximately 1300ºC and qA the heat flow from the asthenosphere.
Based on the schematic representation presented in figure (3) we can formulate the temperature distribution in the lithosphere for the layers (1) and ( 2) from the one-dimensional equation of heat in permanent regime.In these conditions equation (1a) can be considered as representative of the thermal field for layer (1).The equation ( 1b) and (1c) are the contour conditions.In this layer the thermal conductivity and the radiogenic heat production are assumed to be constant.
where T1 represents the temperature and the other variables are those described and informed in ( ) Equation ( 2) represents the temperature distribution for the layer (1).The equation (3a) shows the formulation for layer (2).The equation ( 3b) and (3c) are the boundary conditions and the equation (3d) shows the variation of thermal conductivity with temperature.The radiogenic heat production in this layer is assumed to be constant.
( ) where T2 represents the temperature and the other variables are those described and informed in Figure (3).The solution to the boundary value problem described by equations (3a) to (3d) is that presented in equation ( 4).
The equation (4) represents the temperature distribution for the layer (2).The solution of equation ( 1) was obtained by applying conventional methods for solving differential equations with these characteristics.The solution of equation (3a) was obtained by applying Kirchhoff Transform to remove nonlinearity and consequently transform the nonlinear problem into a linear one (for details see Özisik, 1980).This technique was used by Dipple & Kopylova (2000) and Russell et al. (2001) to determine the production and flow of heat in the region of Slave Craton.Canada.

METHODOLOGY TO ESTIMATE THE GEOTHERMAL PARAMETERS.
In order to use the model proposed in this work is necessary to know some initial information.
This information is the one in table (4).T0 is the average annual surface temperature of the study area.Thermal conductivity λ0 and density ρ have similar values to those used by Russell and Kopylova (1999), Lewis et al. (2003), Harder & Russell (2006), and Greenfield et al. (2013).
According to Chulick et al. (2013) and Lloyd et al. (2010) the crustal thickness ZM in the Patagonia region is between 28 and 32 km.
Results from numerical simulations indicate that small variations in the value of ZM do not significantly affect estimates of lithospheric thicknesses.Thus, we assume the average value of 30 km as the characteristic of the crustal thickness of the region.Below we describe the sequential process to estimate the geothermal parameters of interest:

Geothermal parameters at Moho depth.
To estimate the geothermal parameters at the depth of Moho such as temperature TM, heat flow qM, radiogenic heat production AM and the coefficient of variation of thermal conductivity with temperature B at the depth of Moho we use the pressure and temperature balance data described in tables (1), ( 2), (3), the physical parameters described in table (4) and equation ( 4) to form a system of equations.
The system of equations formed from temperature and pressure balance data allows us to estimate TM, qM, AM and B at Moho depth using appropriate numerical methods.In this work we use the RNLIN routine available in IMSL.The RNLIN routine uses a modified Levenberg-Marquardt method.

D r a f t
Radiogenic heat production in the surface A0.
To estimate the heat production at the surface we derive the equation ( 2), thus obtaining the equation ( 5).
( ) We evaluate the equation ( 5) at the Z=ZM position and multiply the resulting equation by λ0.
Following this procedure we arrive at equation ( 6) and thus we can estimate A0.
Geothermal heat flow in the surface q0.
To estimate the value of the heat flow at the surface, we multiply the eq.( 5) by λ0 evaluated at position.Z=Z0=0.

RESULTS AND DISCUSSION
Tables ( 5) to ( 7) present the results of geothermal parameter estimates for the provinces of Río Negro, Chubut and Santa Cruz.The values of the coefficient of variation of thermal conductivity with temperature and radiogenic heat production in all provinces are compatible with those expected for these parameters (Jaupart and Mareschal, 1999;Kukkonen and Peltonen, 1999;Russell et al., 2001;Artemieva and Mooney, 2001;Dymshits et al., 2020).
In the province Río Negro, Table (5) the heat flow varies from 73 to 84 mWm -2 and the radiogenic heat production from 1.0 to 1.3 µWm -3 in the surface.At Moho's depth the temperature and the heat flow have average values of 750 ºC, 44 mWm -2 respectively and 75 km is the value of the thermal thickness of that province.The lowest thermal thickness estimated in this work.

D r a f t
ZA (km) 65 86 75 11 The Table ( 6) shows the geothermal parameter estimates for Chubut province.In this province the estimated thermal thickness is between 76 and 102 km.The average values of heat flow and radiogenic heat production at the surface are respectively 78 mWm -2 and 1.4 µWm -3 .In the depth of Moho 36 mWm -2 is the value of the heat flow and 693 ºC the temperature.These are the lowest values of geothermal parameters at Moho's depth between the three provinces.
ZA (km) 76 102 87 13 For the province of Santa Cruz, the parameter values are those shown in the Table (7).In this province the heat flow varies from 78 to 91 mWm -2 and the radiogenic heat production from 1.2 to 1.8 µWm -3 in the surface.These are the highest values when compared to the other provinces.At Moho's depth the parameters vary as follows: temperature between 715 and 804 ºC and heat flow from 34 to 47 mWm -2 .The average thermal thickness estimated for the province was 82 km.

D r a f t
The uncertainties in the estimates of the magnitudes listed in Tables ( 5) to ( 7) come from a number of sources, including uncertainties of ZM crustal thickness, pressure, temperature and composition of the xenoliths samples listed in tables (1) to (3) and the value of thermal conductivity λ0.
To minimize these problems a model of radiogenic heat production and constant thermal conductivity in the crust (layer 1 of figure 3) and constant heat production in the lithospheric mantle (layer 2 of Figure 3) were chosen in order to reduce the number of variables in the model and consequently obtain more robust results.
Because the value of temperature at the Moho's depth TM is associated with crustal thickness, and the value of heat flow at the Moho's depth qM is associated with the value of thermal conductivity, all cases were simulated considering ZM = 30 km and λ0 = 3.0 W m -1 ºC -1 in the lithospheric mantle (layer 2, figure 3).Therefore, the quantities TM and qM (equation 4), are influenced only by the production of AM radiogenic heat and the coefficient of variation of thermal conductivity B.
In relation the production of radiogenic heat in the mantle, the global data indicates that the values of this parameter are in the range of 10 -6 < AM < 0.06 µWm -3 .This represents a variation of ± 5.0 ºC in the temperature value TM and ± 2.0 Wm -2 in the value of the heat flow qM.
The other constraint used to solve equation ( 4) was to establish a difference between the observed temperature TOBS and TMODEL below or equal to 20ºC.

D r a f t
This value was chosen due to the uncertainty in the thermobarometry calibration estimated at ± 20 °C and ± 0.3 GPa for the geothermometer proposed by Brey and Köhler, 1990. Figures (4)      Therefore, the values of the geothermal parameters near surface are: 81 mWm -2 and 1.4 µWm -3 for the heat flow and radiogenic heat production respectively, at the Moho depth, the values are: heat flow 40 mWm -2 , radiogenic heat production 2x10 -2 µWm -3 and temperature 734 ºC.The thermal thickness was estimated at 81 km and coefficient of variation of thermal conductivity with temperature 2x10 -4 W m -1 ºC -2 .
The value of heat flow at the surface is similar to those estimated by Vieira and Hamza (2019), Ávila and Dávila, (2018), Cardoso et al. (2010), radiogenic heat production and the parameter of variation of thermal conductivity at Moho's depth are within the range of expected values, so we can consider that the model presents coherent results, which may better show the applications of the model when more accurate data are available.
Santa Cruz province has the highest heat flow at the surface and also the highest temperature value at Moho depth, Río Negro province has the lowest thermal thickness value and the highest heat flow at Moho depth, this indicates that there are possibly two plumes heads responsible for xenoliths deposition in the region: one in Río Negro province and another in Santa Cruz.

ACKNOWLEDGMENTS
Information about this item was purposely obtained to avoid identifying the authors.If the article is approved for publication, this item will be rewritten.
Figure (2) shows the occurrences of xenoliths in the provinces of Río Negro, Chubut and Santa Cruz.Argentina.

Figure 3 -
Figure 3 -Schematic representation of model for conductive heat transfer in the crust and mantle lithosphere.

Figure ( 3
Figure (3).The solution to the boundary value problem described by equations (1a) to (1c) is the one shown in equation (2).
to (6) show the results of the temperature distribution for the provinces Río Negro, Chubut and Santa Cruz.In the figures we can observe the maximum and minimum values of the modelled temperature profiles, as well as the observed data.

Figure 4 -
Figure 4 -Temperature distribution of the Río Negro province, red line represents the upper limits, blue line the lower limit and black line the best fit.The limits were established with 95% confidence.Gray dotted line represents the isotherm of 1300 ºC and the green dots are the observed data.

Figure 5 -Figure 6 -
Figure 5 -Temperature distribution of the Chubut province, red line represents the upper limits, blue line the lower limit and black line the best fit.The limits were established with 95% confidence.Gray dotted line represents the isotherm of 1350 ºC and the green dots are the observed data.

Figure ( 7
Figure (7) shows that using the strategy of fixing ZM and λ0 and to refine the values of AM and B within the range of expected values for these quantities.It was possible to estimate the variables in equation (4) TM, AM, qM, and B in order to obtain the difference between TOBS and TMODEL within the range of uncertainties of the geothermobarometer.

Figure 7 -Figure 8 -
Figure 7 -Residue (difference between observed and modelled temperature) versus observed temperature.The residues are below 15 ºC.Imposing these restrictions, we obtain a good quality of the adjustment, as can be verified by the analysis of figure (8) where we can observe that the correlation coefficient R 2 > 0,99 a value that confirms a strong correlation between the observed data and those predicted by the model.
bibliographic review, elaboration of the computational model, figures and tables, elaboration of the text and formatting of references; TARRILLO, C.A.M.: bibliographic review, elaboration of the computational model, figures and tables, elaboration of the text; SILVA, A.F.: bibliographic review, elaboration of the computational model, figures and tables;

Table 1 -
Pressure and Temperature (P-T) data on mantle xenoliths in the Chubut Province.

Table 2
-Pressure and Temperature (P-T) data on mantle xenoliths in the Río de Negro Province.

Table 3 -
Pressure and Temperature (P-T) data on mantle xenoliths in the Santa Cruz Province.
Hamza (2008)used this technique to estimate the thermal field of the Brazilian geological province of San Francisco.

Table 4 -
Physical parameters used in the model

Table 5 -
Sumary of model results for geothermal parameters of the Río Negro province.

Table 6 -
Sumary of model results for geothermal parameters of the Chubut province.

Table 7 -
Sumary of model results for geothermal parameters of the Santa Cruz province.