# Robust 3D Joint Inversion of Gravity and Magnetic Data: A High-Performance Computing Approach
## 5 Conclusions  
The inversion results with structural similarity and greater structural direction constraints (Equation (2)) are an improvement with respect to standard separate inversion (Equation (17)), allowing to better estimate of the form and depth of the buried dike (Figure 5). Despite being sensitive to the noise of the input data, they do present structural similarity, in this example, we give prior information in one method through the cuttings of a pair of hypothetical wells (density in two wells) to show how structural similarity regularizer can use this information together with dip and strike to improve magnetization distribution, while both models can justify observed data. In addition to that, our parametric function proved to better estimate the form and depth of different buried bodies (Figure 9) compared to standard separate inversion. Processing time does not depend on the size (dimensions) of the cells but on the size of the matrices needed for processing; the major issue in obtaining higher resolution inversion models is the amount of RAM or VRAM to which one has access, as the amount of memory required for an inversion grows exponentially and is highly dependent on the number of voxels in the 3D domain of the models and, to a lesser extent, on the number of observed data. However, good results can be obtained even with lower resolution models (fewer cells), as the minimum resolution required for studies is defined by the scale of the study, the objectives, and the scope of each study. Having three versions of code allows us to obtain preliminary results within minutes, either by employing the fully parallel or hybrid version of the code, to minimize the total processing time. In cases where the VRAM available on the graphics card falls short, reducing the resolution of the 3D domains during the initial modeling stages proves to be a viable strategy. Once the regularization parameters achieve fidelity to observed data and results align with geologically expected distributions, it is possible to revert to a higher model resolution and utilize the single-core version of the code with associated time-related costs. This is feasible due to the lower cost and ease of obtaining additional RAM instead of VRAM. Through the analysis of performance and computational costs of serial, parallel, and hybrid implementations, we conclude that as the inversion domain expands, the processing speed could increase from 4\(\times\) up to 100\(\times\) times faster, as shown in Table 1, rendering it particularly advantageous for application in larger domains. The following supporting information can be downloaded at: [[https://github.com/abdrg/Gram_Joint_Inversion.git](https://github.com/abdrg/Gram_Joint_Inversion.git)]([https://github.com/abdrg/Gram_Joint_Inversion.git](https://github.com/abdrg/Gram_Joint_Inversion.git)) accessed on 15 August 2023. In this link the repository of the Fortran code and the test data to reproduce synthetic test model 1 can be found under a BSD license to use the source code in non-free software. Conceptualization, methodology, A.D.R.G. and V.Y. ; software, data curation, A.D.R.G. validation, V.Y. ; investigation, V.Y. and A.D.R.G. ; writing--original draft preparation, A.D.R.G. and V.Y. ; writing--review and editing, V.Y. ; discussion, interpretation of physical results and conclusions, all authors; visualization (preparation of figures), A.D.R.G. ; supervision, V.Y. ; project administration, V.Y. All authors have read and agreed to the published version of the manuscript. This work was supported by CONACYT-Fondos Sectoriales Project A1-S-29604 to [PERSON]. [PERSON] received support from CONACYT PhD scholarship with CVU 816921. The APC was partially funded by the Instituto Potsino de Investigacion Cientifica y Tecnologica, A.C.  
Not applicable. This work was partially supported by CONACYT Project A1-S-29604. [PERSON] gratefully acknowledges support from CONACYT Ph.D. scholarship with CVU 816921.