# Robust 3D Joint Inversion of Gravity and Magnetic Data: A High-Performance Computing Approach
## 1 Introduction  
Geophysical methods are one of the main ways to study the Earth's crust and search and explore the mineral resources in the Earth's interior [1; 2; 3]. Geophysical methods can be classified based on the physical fields used in their application. Gravity and magnetic methods thus belong to the so-called potential methods of geophysics since they are based on potential theory [4; 5; 6; 7]. One of the fundamental challenges in geophysics is the calculation of distribution models of physical properties in the subsurface that can accurately reproduce measurements obtained in the field, in turn, these models are geologically possible in the context of the study area, which is known as inverse modeling. Any inversion problem is subject to three constraints: (1) the solution must exist, (2) the process is unstable, and (3) the solution is not unique [4; 8; 9; 10; 11]. The informativeness and reliability of the interpretation of geophysical data depend greatly on the method of their inversion. Many studies have been devoted to this topic;we will briefly try to summarize different techniques of joint inversion, their advantages, and their disadvantages. At the same time, it is important to realize that the inversion of different methods may differ in the mathematical apparatus used for their joint processing. For example, in petrophysical inversion [12; 13], a reliable result can be achieved using Newton-Gauss iteration [14]. The authors note that separate inversion of electromagnetic or seismic data is highly ambiguous and leads to great ambiguity in determining porosity and fluid saturation. Using the Gauss-Newton algorithm equipped with multiplicative regularization and a proper data-weighting scheme in the example with real data, the authors showed that up to 20% errors in the saturation and porosity exponents in [PERSON]'s equations do not cause significant errors in the inversion results [12; 13]. [PERSON] [15] in his work on this topic points out that in petrophysical data inversion, it is necessary to apply two levels of initial data, the accuracy and representativeness of which influence the final result. [PERSON] [16] introduced so-called weight coefficients (regularization terms) for this purpose. As a result, when applying this type of joint inversion, it is necessary to introduce two regularization levels. Level 1 (conductivity, seismic velocity, and density) and Level 2 (porosity and water content). The disadvantage of this approach is that a lack of accuracy or number of measurements of Level 1 parameters will result in an unreliable inversion as a whole. [PERSON] et al. [17] analyze the compatibility of different methods in the joint inversion of geophysical data in a study of the Namibian continental margin. They note that electrical resistivity models obtained by inversion of marine data at shallow water depths are characterized by poor resolution for lithologic boundaries. To address this important problem, the authors use a joint inversion of magnetotelluric, gravimetric (fixed structural density model coupling with satellite gravity data), and seismic (fixed gradient velocity model) data. The number of iterations varies from 283 to 380; the Final MT and gravity data RMS are 3.01 and 1.52, respectively. In turn, [PERSON] & [PERSON] [18] proposed a joint inversion of magnetotelluric and seismic data, applying this method to the interpretation of geologic features such as sedimentary basins, crustal and upper mantle structures, oil reservoirs, etc. The joint inversion of these data with added noise has led to good results, but its numerical implementation is often unstable and requires regularization [15]. The main disadvantage of this method is the need for structural semblance of the models and too much computer core memory, especially for three-dimensional inversion. It is important to note that inversion can be interactive or sequential. [PERSON] [19; 20] describes this process in detail, using the construction of a velocity model following a tomographic inversion.