# CSEM Optimization Using the Correspondence Principle
## 3 Numerical Experiments
### Inversion Results
#### 3.2.3 Marlim Model  
The model we will refer to as Marlim is an adaptation of the MR3D resistivity model constructed by [33] from 3D seismic and well-log data from the Marlim field (Brazilian continental margin). The features of interest in using electromagnetic (EM) methods include a heterogeneous reservoir embedded in a conductive background and a salt body with a resistivity of 1000 Ohm.m. It is a good representation of the type of scenario where the use of the CSEM method might be required, which was also described by [35] when discussing the forward modeling performed from the MR3D model.  
Figure 12: Results of the inversions with (**a**) the steepest descent, (**b**) the momentum method, and (**c**) the L-BFGS-B method, performed using observed data simulated from the MARE model. Black outlines indicate the boundaries of the resistors.  
Figure 13: Curves showing the evolution of the objective function during the inversions for the MARE model, using the steepest descent method (black curve), momentum (blue curve), and the L-BFGS-B (red curve).  
The modifications made relative to the original MR3D model consist of removing the effects of bathymetry and using only the vertical resistivity of the original model (in this case, we considered the model to be isotropic). Figure 14 illustrates the central section of the model (Figure 14a) from which we simulated the observed data through modeling that used a grid of 20 m (vertical) by 100 m (horizontal) and recorded the inline electric field measured by 20 receivers regularly arranged along the line that coincides with the section in Figure 14a (in the interval from 11 km to 30 km). The sources are distributed between 0 to 41 km every 200 m. We discarded data with offsets smaller than 1 km and amplitudes smaller than \(10^{-15}\) V/m, and the inversions used single-frequency data at 0.25 Hz. The initial model is homogeneous, with a resistivity of 2.8 ohm.m (which corresponds to the average background resistivity in the region where the reservoir is in the Marlim model), the same used in calculating the gradient relative to vertical conductivity (Figure 14b) on a mesh with a grid spacing of 100 m (along the vertical) and 200 m (along the horizontal). Note the asymmetry in the gradient shape associated with the location of the resistor in the reference model.  
Using the data and the initial model described, the inversions performed produced the results that will be illustrated below. Using the steepest descent method with gradient precondition 1, we obtained the model shown in Figure 15a. In the inversion with momentum, where we used precondition 2, we obtained the model in Figure 15b, and the inversion with L-BFGS-B (performed using the gradient with precondition 1), resulting in the model shown in Figure 15c. All results indicate the presence of a resistor in the region where the reservoir is located in the Marlim model, each of them presenting its own characteristics. The models obtained with the steepest descent and L-BFGS-B are similar, as they are characterized by an anomaly with higher resistivity in the case of the L-BFGS-B inversion. The result obtained with momentum is better distributed, covering a larger reservoir extent. The curves showing the evolution of the objective function during the inversions are shown in Figure 16, indicating a slightly more effective reduction rate in the case of L-BFGS-B, especially in the first iterations. In contrast, the others show similar behavior, with the momentum method reaching a slightly lower residual value.  
Figure 14: (**a**) Central section of the Marlim model used to simulate the observed data utilized in the inversions. Triangles represent the receivers, and stars represent the sources used in the simulation. Not all sources are represented, and their height relative to the seafloor is illustrative. (**b**) Gradient (at a frequency of 0.25 Hz) relative to vertical conductivity, calculated from the homogeneous medium with a resistivity of 2.8 ohm.m.