the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 Aug 2024
The roles of surface processes on porphyry copper deposits preservation
Abstract. Porphyry copper deposits typically originate within subduction zones at 2 to 5 km depths. These deposits are exhumed due to the influence of tectonic forces and climate-driven erosion. Porphyry copper deposits are currently only mineable at relatively shallow depths, and their prospectivity relies on a balance between the rate of exhumation and preservation. In this study, we evaluate the impact of surface processes on the preservation or exhumation of porphyry copper deposits. To do so, we rely on a global-scale numerical model (goSPL), which simulates landscape dynamics and associated erosion and deposition patterns over geological time scales. High-resolution Cenozoic simulations incorporate published open-source global paleo-climate and paleo-elevation datasets, and have been fine-tuned using contemporary data. We then calculate exhumation rates by comparing the ages of known porphyry copper deposits and their simulated emplacement depths based on modelled erosion-deposition values. Obtained average exhumation rates vary from 10−2 to 10−1 km/Myr, with an overall difference of 0.04 mm/yr when compared to independent erosion rate estimates available from published studies. The predicted global mean emplacement depths range from 1 to 3 km. To highlight the influence of paleo-reconstructions on exhumation rate estimates, we analyse simulated erosion rates across the Andean region using two distinct paleo-climate models and find significant spatial and temporal differences across the Central Andes. While our landscape evolution model successfully predicts the known emplacement depths for the North and South Andean deposits younger than 20 Myr, it also predicts depths exceeding 6 km for Central Andean deposits older than 60 Myr. We attribute these mismatches to a combination of limitations related to model assumptions and input resolutions. Our results show the intricate connection between deposit preservation and surface processes. Our method offers an addition to the traditional porphyry copper exploration toolkit that links geological observations to plate tectonics dynamics and paleo-climatic reconstructions.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1868', Anonymous Referee #1, 10 Sep 2024
This is a unique study in which a very special geologic feature (porphyry copper deposit) has been used to test model approaches to quantifying exhumation rates. The results provide insights both to estimates of exhumation rates in different climate regimes and to factors that might control the depth of emplacement of porphyry copper deposits. The authors have provided excellent background informationl on porphyry copper deposits, including factors that control estimates of their depth of emplacement. I cannot comment on the modeling methods used here, but can say that the results of are of considerable interest from the perspective of mineral deposit geology.
Citation: https://doi.org/10.5194/egusphere-2024-1868-RC1 -
CC1: 'Comment on egusphere-2024-1868', Victor Sacek, 11 Apr 2025
The manuscript presents the use of a sophisticated numerical code of high-resolution global-scale landscape evolution model applied to quantify the preservation or exhumation of porphyry copper deposits (PCDs). With the input from published palo-climate and paleo-elevation data, the authors predicted the exhumation rate by comparing the age of known PCDs and the simulated emplacement depth.
I recommend this article for publication after minor revisions.
I have a few points to discuss about the numerical approach:
i) In equation (1), the term related to the fluvial processes considers the local precipitation P and the upstream total area A. In line 84, the authors define the water flow as the product P times A. However this is only true if the precipitation P is spatially constant.The correct flow discharge should be calculated as the integration of the precipitation in each upstream numerical cell. Therefore, the water flux in one point of the mesh depends on the upstream precipitation and not on the local precipitation.
This is specifically important in the eastern side of the Andean Cordillera where orographic precipitation can create significant lateral variations in precipitation rate. Therefore, I think it is important to discuss more about this in the manuscript, and how the adopted simplification can affect the results.
ii) Please, give some description of how the tectonic forcing was added in the model. Give details of how the U term is calculated to simulate the tectonic correction to reach the dynamic equilibrium. The authors referred to Salles et al. (2023), but I think a short description in the paper can contribute to the understanding of the mathematical procedure adopted in this work.
iii) The paper does not mention any isostatic compensation. Therefore, I assume that the model does not take into account isostasy (local or regional). My question is: how does the vertical displacement of the plate, caused by the load of the cordillera and sedimentary layers in the foreland basins, affect the present results of exhumation rates? The authors briefly commented on this on line 385, discussing about the effect of re-burial, but I think that flexural effects can significant impact the exhumation rate, aspect not explored in the text.Citation: https://doi.org/10.5194/egusphere-2024-1868-CC1 -
RC2: 'Comment on egusphere-2024-1868', Victor Sacek, 14 Apr 2025
The manuscript presents the use of a sophisticated numerical code of high-resolution global-scale landscape evolution model applied to quantify the preservation or exhumation of porphyry copper deposits (PCDs). With the input from published palo-climate and paleo-elevation data, the authors predicted the exhumation rate by comparing the age of known PCDs and the simulated emplacement depth.
I recommend this article for publication after minor revisions.
I have a few points to discuss about the numerical approach:
i) In equation (1), the term related to the fluvial processes considers the local precipitation P and the upstream total area A. In line 84, the authors define the water flow as the product P times A. However this is only true if the precipitation P is spatially constant.The correct flow discharge should be calculated as the integration of the precipitation in each upstream numerical cell. Therefore, the water flux in one point of the mesh depends on the upstream precipitation and not on the local precipitation.
This is specifically important in the eastern side of the Andean Cordillera where orographic precipitation can create significant lateral variations in precipitation rate. Therefore, I think it is important to discuss more about this in the manuscript, and how the adopted simplification can affect the results.
ii) Please, give some description of how the tectonic forcing was added in the model. Give details of how the U term is calculated to simulate the tectonic correction to reach the dynamic equilibrium. The authors referred to Salles et al. (2023), but I think a short description in the paper can contribute to the understanding of the mathematical procedure adopted in this work.
iii) The paper does not mention any isostatic compensation. Therefore, I assume that the model does not take into account isostasy (local or regional). My question is: how does the vertical displacement of the plate, caused by the load of the cordillera and sedimentary layers in the foreland basins, affect the present results of exhumation rates? The authors briefly commented on this on line 385, discussing about the effect of re-burial, but I think that flexural effects can significant impact the exhumation rate, aspect not explored in the text.Citation: https://doi.org/10.5194/egusphere-2024-1868-RC2 -
AC1: 'Comment on egusphere-2024-1868', Beatriz Hadler Boggiani, 10 May 2025
We thank both reviewers for their insightful comments and their efforts in helping improve our manuscript. We are particularly grateful that both reviewers found the study valuable and only suggested minor revisions. Referee #1 describes this as “a unique study” and notes that “the results are of considerable interest from the perspective of mineral deposit geology.” Referee #2 highlights “the use of a sophisticated numerical code of high-resolution” and suggests useful modifications to clarify the limitations inherent to the model, as well as to provide a more detailed explanation of the main equations and how simplified formulations might affect the interpretation of results. We have addressed these comments in the revised manuscript and believe the resulting version is significantly improved.
In the following, we address the technical points and minor issues raised by the reviewers, outlining the suggestions and the corresponding modifications made to the manuscript.
Response to Comment 1: We thank the reviewer for their careful observation. We agree that assuming water flux as the product of local precipitation and upstream area is only valid under spatially uniform precipitation—an assumption that does not hold in many real-world settings, particularly where orographic effects lead to strong lateral precipitation gradients, such as the eastern Andes.
In response, we have revised Equation (1) to better reflect how goSPL handles spatially variable precipitation across the catchment. In the updated formulation, the flow discharge at each cell is calculated as the sum of the local rainfall contribution (local precipitation multiplied by the local area) and the accumulated upstream discharge. This explicitly shows that the water flux at a given mesh point depends not only on local precipitation but also on all upstream precipitation contributions.
The original mass continuity equation was:
where the water flux was simplified as PA, assuming spatially constant precipitation.
In the revised manuscript, we define the local change in elevation over time as:
where the local flow discharge Qi is expressed as:
Here, Ai is the area of cell i, Pi is the local precipitation, and the summation is for all nodes j that belong to the upstream set (up). This revised equation makes explicit that the water flux Qj depends on both the local precipitation and the cumulative discharge from upstream nodes. We have clarified this change in the revised manuscript (lines 79 – 81, and lines 91- 92), highlighting its relevance for regions with significant precipitation gradients.
Response to Comment 2: Following the reviewer’s advice, a description of how tectonic forcing U has been incorporated into the model has been added at line 132 of the revised manuscript:
“The second and final round of simulations are run considering the same initial input files, however with the computed tectonic forcing, added to it (Salles et al., 2023) (Fig. 1). The tectonic forcings is computed from the mismatch between the model predictions and a geologically reconstructed target location. The mismatch indicates that either surface processes parameters (erodibility) need to be tuned, or that other forcings such as dynamic uplift or subsidence need to be considered. If the second is decided, a new tectonic forcing based on the filtered mismatch map which only consider long wave lengths and short amplitudes, is imposed. Mismatch percentages and correlation coefficients guide the calibration of the paleo-elevation maps.”
This addition outlines the calculation of U and how the correlation coefficients and mismatch percentages guide the dynamic equilibrium based on Salles et al. (2023).
Response to Comment 3: We appreciate the reviewer’s comment regarding the omission of explicit isostatic compensation (local or regional) in our modelling framework. Indeed, as correctly noted, the current version of goSPL does not directly account for flexural isostasy or lithospheric flexure in response to erosional unloading or sedimentary loading.
However, our data assimilation approach implicitly captures some of these effects by iteratively adjusting the evolving topography to remain consistent with independent paleo-elevation reconstructions (mismatch maps). This means that vertical motions such as regional uplift or subsidence - whether driven by tectonics or flexural loading - can be partially integrated into the model through these boundary conditions, although we cannot, with confidence, ascribe the uplift to a specific driver such as tectonic motion or flexural loading.
That said, we agree that flexural responses to sediment loading in foreland basins and unloading in orogenic regions can strongly influence exhumation rates, especially over >105 -year timescales and regional scales of hundreds of kilometres. These feedbacks are not fully captured in our current model setup, and therefore, the exhumation rates presented here may underestimate or misrepresent areas where flexural effects dominate the vertical signal.
In future work, coupling goSPL with a flexural isostasy module or using dynamic lithosphere models would improve the treatment of these processes and refine estimates of both burial and exhumation in foreland settings. We clarify this limitation in the revised manuscript in lines 70 to 74:
“Flexural responses due to erosional unloading and depositional loading influence long-term drainage evolution, landscape rejuvenation, and sedimentation, reflecting lithospheric strength and mantle buoyancy (Sacek, 2014). While goSPL does not explicitly model these processes, the assimilation method implicitly accounts for them by aligning modelled elevations with paleo-elevation reconstructions (Salles et al., 2023). As an example, the approach captures subsidence patterns near large deltaic systems (e.g., Amazon, Bengal fans, Pelotas Basin).”
And expand the discussion accordingly in lines 401 to 405:
“Re-burial processes can also initiate flexural responses, which are indirectly accounted for in the model. These processes are particularly significant in the Northern Andes, where the interplay between flexural isostasy and surface processes helps explain the drainage reversal of the Amazon River (Sacek, 2014). The isostatic effect of volcanic loading can induce local subsidence, which if not taken into account, may lead to overestimation of the final exhumation rates. Conversely, neglecting flexural isostasy associated with sediment unloading can result in an underestimation of exhumation rates.”
Additional alterations:
Errata: Figure 2 was incorrectly referenced in section “Paleo-elevation and paleo-precipitation forcings”, the correct figure to be cited is Figure 3. The alterations have been made to the manuscript accordingly.
Line 397: We have altered the initial text from “The re-burial process associated with the pilling of rocks and sediments due to volcanic activity is not accounted for in our study.” To “The re-burial process associated with the overlaying of volcaniclastic rock is not accounted for in our study” for enhanced readability.
Citation: https://doi.org/10.5194/egusphere-2024-1868-AC1
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-1868', Anonymous Referee #1, 10 Sep 2024
This is a unique study in which a very special geologic feature (porphyry copper deposit) has been used to test model approaches to quantifying exhumation rates. The results provide insights both to estimates of exhumation rates in different climate regimes and to factors that might control the depth of emplacement of porphyry copper deposits. The authors have provided excellent background informationl on porphyry copper deposits, including factors that control estimates of their depth of emplacement. I cannot comment on the modeling methods used here, but can say that the results of are of considerable interest from the perspective of mineral deposit geology.
Citation: https://doi.org/10.5194/egusphere-2024-1868-RC1 -
CC1: 'Comment on egusphere-2024-1868', Victor Sacek, 11 Apr 2025
The manuscript presents the use of a sophisticated numerical code of high-resolution global-scale landscape evolution model applied to quantify the preservation or exhumation of porphyry copper deposits (PCDs). With the input from published palo-climate and paleo-elevation data, the authors predicted the exhumation rate by comparing the age of known PCDs and the simulated emplacement depth.
I recommend this article for publication after minor revisions.
I have a few points to discuss about the numerical approach:
i) In equation (1), the term related to the fluvial processes considers the local precipitation P and the upstream total area A. In line 84, the authors define the water flow as the product P times A. However this is only true if the precipitation P is spatially constant.The correct flow discharge should be calculated as the integration of the precipitation in each upstream numerical cell. Therefore, the water flux in one point of the mesh depends on the upstream precipitation and not on the local precipitation.
This is specifically important in the eastern side of the Andean Cordillera where orographic precipitation can create significant lateral variations in precipitation rate. Therefore, I think it is important to discuss more about this in the manuscript, and how the adopted simplification can affect the results.
ii) Please, give some description of how the tectonic forcing was added in the model. Give details of how the U term is calculated to simulate the tectonic correction to reach the dynamic equilibrium. The authors referred to Salles et al. (2023), but I think a short description in the paper can contribute to the understanding of the mathematical procedure adopted in this work.
iii) The paper does not mention any isostatic compensation. Therefore, I assume that the model does not take into account isostasy (local or regional). My question is: how does the vertical displacement of the plate, caused by the load of the cordillera and sedimentary layers in the foreland basins, affect the present results of exhumation rates? The authors briefly commented on this on line 385, discussing about the effect of re-burial, but I think that flexural effects can significant impact the exhumation rate, aspect not explored in the text.Citation: https://doi.org/10.5194/egusphere-2024-1868-CC1 -
RC2: 'Comment on egusphere-2024-1868', Victor Sacek, 14 Apr 2025
The manuscript presents the use of a sophisticated numerical code of high-resolution global-scale landscape evolution model applied to quantify the preservation or exhumation of porphyry copper deposits (PCDs). With the input from published palo-climate and paleo-elevation data, the authors predicted the exhumation rate by comparing the age of known PCDs and the simulated emplacement depth.
I recommend this article for publication after minor revisions.
I have a few points to discuss about the numerical approach:
i) In equation (1), the term related to the fluvial processes considers the local precipitation P and the upstream total area A. In line 84, the authors define the water flow as the product P times A. However this is only true if the precipitation P is spatially constant.The correct flow discharge should be calculated as the integration of the precipitation in each upstream numerical cell. Therefore, the water flux in one point of the mesh depends on the upstream precipitation and not on the local precipitation.
This is specifically important in the eastern side of the Andean Cordillera where orographic precipitation can create significant lateral variations in precipitation rate. Therefore, I think it is important to discuss more about this in the manuscript, and how the adopted simplification can affect the results.
ii) Please, give some description of how the tectonic forcing was added in the model. Give details of how the U term is calculated to simulate the tectonic correction to reach the dynamic equilibrium. The authors referred to Salles et al. (2023), but I think a short description in the paper can contribute to the understanding of the mathematical procedure adopted in this work.
iii) The paper does not mention any isostatic compensation. Therefore, I assume that the model does not take into account isostasy (local or regional). My question is: how does the vertical displacement of the plate, caused by the load of the cordillera and sedimentary layers in the foreland basins, affect the present results of exhumation rates? The authors briefly commented on this on line 385, discussing about the effect of re-burial, but I think that flexural effects can significant impact the exhumation rate, aspect not explored in the text.Citation: https://doi.org/10.5194/egusphere-2024-1868-RC2 -
AC1: 'Comment on egusphere-2024-1868', Beatriz Hadler Boggiani, 10 May 2025
We thank both reviewers for their insightful comments and their efforts in helping improve our manuscript. We are particularly grateful that both reviewers found the study valuable and only suggested minor revisions. Referee #1 describes this as “a unique study” and notes that “the results are of considerable interest from the perspective of mineral deposit geology.” Referee #2 highlights “the use of a sophisticated numerical code of high-resolution” and suggests useful modifications to clarify the limitations inherent to the model, as well as to provide a more detailed explanation of the main equations and how simplified formulations might affect the interpretation of results. We have addressed these comments in the revised manuscript and believe the resulting version is significantly improved.
In the following, we address the technical points and minor issues raised by the reviewers, outlining the suggestions and the corresponding modifications made to the manuscript.
Response to Comment 1: We thank the reviewer for their careful observation. We agree that assuming water flux as the product of local precipitation and upstream area is only valid under spatially uniform precipitation—an assumption that does not hold in many real-world settings, particularly where orographic effects lead to strong lateral precipitation gradients, such as the eastern Andes.
In response, we have revised Equation (1) to better reflect how goSPL handles spatially variable precipitation across the catchment. In the updated formulation, the flow discharge at each cell is calculated as the sum of the local rainfall contribution (local precipitation multiplied by the local area) and the accumulated upstream discharge. This explicitly shows that the water flux at a given mesh point depends not only on local precipitation but also on all upstream precipitation contributions.
The original mass continuity equation was:
where the water flux was simplified as PA, assuming spatially constant precipitation.
In the revised manuscript, we define the local change in elevation over time as:
where the local flow discharge Qi is expressed as:
Here, Ai is the area of cell i, Pi is the local precipitation, and the summation is for all nodes j that belong to the upstream set (up). This revised equation makes explicit that the water flux Qj depends on both the local precipitation and the cumulative discharge from upstream nodes. We have clarified this change in the revised manuscript (lines 79 – 81, and lines 91- 92), highlighting its relevance for regions with significant precipitation gradients.
Response to Comment 2: Following the reviewer’s advice, a description of how tectonic forcing U has been incorporated into the model has been added at line 132 of the revised manuscript:
“The second and final round of simulations are run considering the same initial input files, however with the computed tectonic forcing, added to it (Salles et al., 2023) (Fig. 1). The tectonic forcings is computed from the mismatch between the model predictions and a geologically reconstructed target location. The mismatch indicates that either surface processes parameters (erodibility) need to be tuned, or that other forcings such as dynamic uplift or subsidence need to be considered. If the second is decided, a new tectonic forcing based on the filtered mismatch map which only consider long wave lengths and short amplitudes, is imposed. Mismatch percentages and correlation coefficients guide the calibration of the paleo-elevation maps.”
This addition outlines the calculation of U and how the correlation coefficients and mismatch percentages guide the dynamic equilibrium based on Salles et al. (2023).
Response to Comment 3: We appreciate the reviewer’s comment regarding the omission of explicit isostatic compensation (local or regional) in our modelling framework. Indeed, as correctly noted, the current version of goSPL does not directly account for flexural isostasy or lithospheric flexure in response to erosional unloading or sedimentary loading.
However, our data assimilation approach implicitly captures some of these effects by iteratively adjusting the evolving topography to remain consistent with independent paleo-elevation reconstructions (mismatch maps). This means that vertical motions such as regional uplift or subsidence - whether driven by tectonics or flexural loading - can be partially integrated into the model through these boundary conditions, although we cannot, with confidence, ascribe the uplift to a specific driver such as tectonic motion or flexural loading.
That said, we agree that flexural responses to sediment loading in foreland basins and unloading in orogenic regions can strongly influence exhumation rates, especially over >105 -year timescales and regional scales of hundreds of kilometres. These feedbacks are not fully captured in our current model setup, and therefore, the exhumation rates presented here may underestimate or misrepresent areas where flexural effects dominate the vertical signal.
In future work, coupling goSPL with a flexural isostasy module or using dynamic lithosphere models would improve the treatment of these processes and refine estimates of both burial and exhumation in foreland settings. We clarify this limitation in the revised manuscript in lines 70 to 74:
“Flexural responses due to erosional unloading and depositional loading influence long-term drainage evolution, landscape rejuvenation, and sedimentation, reflecting lithospheric strength and mantle buoyancy (Sacek, 2014). While goSPL does not explicitly model these processes, the assimilation method implicitly accounts for them by aligning modelled elevations with paleo-elevation reconstructions (Salles et al., 2023). As an example, the approach captures subsidence patterns near large deltaic systems (e.g., Amazon, Bengal fans, Pelotas Basin).”
And expand the discussion accordingly in lines 401 to 405:
“Re-burial processes can also initiate flexural responses, which are indirectly accounted for in the model. These processes are particularly significant in the Northern Andes, where the interplay between flexural isostasy and surface processes helps explain the drainage reversal of the Amazon River (Sacek, 2014). The isostatic effect of volcanic loading can induce local subsidence, which if not taken into account, may lead to overestimation of the final exhumation rates. Conversely, neglecting flexural isostasy associated with sediment unloading can result in an underestimation of exhumation rates.”
Additional alterations:
Errata: Figure 2 was incorrectly referenced in section “Paleo-elevation and paleo-precipitation forcings”, the correct figure to be cited is Figure 3. The alterations have been made to the manuscript accordingly.
Line 397: We have altered the initial text from “The re-burial process associated with the pilling of rocks and sediments due to volcanic activity is not accounted for in our study.” To “The re-burial process associated with the overlaying of volcaniclastic rock is not accounted for in our study” for enhanced readability.
Citation: https://doi.org/10.5194/egusphere-2024-1868-AC1
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Beatriz Hadler Boggiani
Tristan Salles
Claire Mallard
Nicholas Atwood
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(62063 KB) - Metadata XML