We present two solvers for the Hierarchical Poincaré-Steklov (HPS) discretization of 3D variable coefficient Helmholtz problems appearing in geological prospection.  An iterative approach uses a GMRES solver coupled with a leaf-wise block-Jacobi preconditioner. The preconditioner is built using two nested local solvers accelerated by local homogenization. Both the operator and preconditioner are implemented in a matrix-free fashion and with distributed memory. The solver can tackle problems approximately 50 wavelengths in each direction requiring more than a billion unknowns to get approximately 7 digits of accuracy half an hour.  We compare with a the direct solver where matrix compression accelerate the solution and reduce memory footprint.   We test both approaches and their performance with application examples.  This is a work funded by Total Energies and with Adrianna Gillman.

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