Potential field data have long been used in geophysical exploration for archeological, mineral, and reservoir targets. For all these targets, the increased search of highly detailed three-dimensional subsurface volumes has also promoted the recollection of high-density contrast data sets. While there are several approaches to handle these large-scale inverse problems, most of them rely on either the extensive use of high-performance computing architectures or data-model compression strategies that may sacrifice some level of model resolution. We posit that the superposition and convolutional properties of the potential fields can be easily used to compress the information needed for data inversion and also to reduce significantly redundant mathematical computations. For this, we developed a convolution-based conjugate gradient 3D inversion algorithm for the most common types of potential field data. We demonstrate the performance of the algorithm using a resolution test and a synthetic experiment. We then apply our algorithm to gravity and magnetic data for a geothermal prospect in the Acoculco caldera in Mexico. The resulting three-dimensional model meaningfully determined the distribution of the existent volcanic infill in the caldera as well as the interrelation of various intrusions in the basement of the area. We propose that these intrusive bodies play an important role either as a low-permeability host of the heated fluid or as the heat source for the potential development of an enhanced geothermal system.