# Development of a Deep Neural Network Model for the
### Seismic Source Inversion Techniques  
Relocation of microseismicities rely on the inversion of seismic signals. This process essentially uses recordings from geophysical acoustic wave transducers that measure the motion of ground caused by the proxy seismic events as input. The arrival times of the waves, the shape and amplitudes of the waveforms, and the energy and frequency spectra all contain information on the sources of the event and properties of the geological materials between the sources and the recorders. Thus, we can invert these measurements for the source locations and the surrounding geological materials' physical properties [29]. Inversion techniques can be broadly classified into linear inversion and nonlinear inversion [30]. Linear inversion relies on pre-calculated ray paths, assuming a simplistic model where the changes in the seismic waves' travel times linearly correlate with changes in the subsurface properties [31]. This method is efficient and straightforward, suitable for scenarios with relatively homogenous geological structures. However, its simplicity also limits its applicability to more complex subsurface conditions. Nonlinear inversion goes beyond the assumptions of linear models by allowing for a more intricate relationship between the seismic data and the subsurface properties [32]. This approach does not assumea direct, linear correlation between the changes in wave travel times and the subsurface structure, accommodating more complex geological scenarios. However, this increased accuracy comes at the cost of higher computational demands and the need for initial guess models that are close to the true subsurface conditions to avoid local minima in the solution space [33; 34]. Several issues pose significant challenges to the effectiveness of seismic inversion techniques. Particularly, varying and unknown velocity structures are of concern; the Earth's subsurface is rarely uniform, featuring layers and anomalies with differing velocities. These variations can significantly affect seismic wave propagation, making it difficult to accurately model and predict seismic events. Seismic waves do not always follow straight paths. Their trajectories can be highly nonlinear, especially in heterogeneous media, complicating the modeling of their travel times and the inversion process. The joint inversion of seismic velocities and source parameters offers a comprehensive approach to understanding subsurface properties and seismic event characteristics [35; 36]. However, this method is notoriously slow and challenging to converge. The complexity arises from the need to simultaneously solve for both the medium's velocity structure and the seismic sources' parameters, a process that significantly increases the computational load and the solution space's dimensionality. The interdependence of velocities and source parameters means that inaccuracies in one can lead to errors in the other, making the process iterative and time-consuming. Achieving convergence requires not only significant computational resources but also clever algorithms and strategies to navigate the vast and complex solution space effectively. Despite these challenges, when successful, joint inversion can provide unparalleled insights into the Earth's subsurface and the dynamics of seismic events. The integration of machine learning (ML) techniques into seismic source relocation and inversion represents a cutting-edge advancement in geophysical sciences, offering new avenues to overcome traditional challenges associated with these processes. Machine learning, with its ability to handle large datasets and uncover complex patterns within them, is well-suited to enhancing the accuracy and efficiency of seismic analyses. Machine learning models, especially those based on deep learning, have shown remarkable success in improving the precision of seismic source relocation [37]. By training on vast arrays of seismic data, these models can learn the intricate relationships between seismic waveforms and their sources' locations.