Have cosmic ray muons or solar neutrinos been used to probe inside the Earth?
In November 2008 neutrino tomography was used to measure Earth's mass. A paper was published in journal Nature. The data was captured by the South Pole’s IceCube Neutrino Observatory.

In November 2013 IceCube announced it had discovered 28 neutrinos that likely originated outside the Solar System.


  The neutrinos that the IceCube detector had “caught” came from different angles because they probed different layers of Earth. By measuring how many neutrinos came from different angles, the scientific team was able to measure the densities of various Earth’s segments, and from that – the total mass of Earth.
  
  The neutrino tomography confirmed the traditional measurements on Earth’s mass, based on gravitational calculations and seismological data. That is especially interesting because neutrino tomography is a conceptually different and independent method – it doesn’t rely on gravity, but purely on weak interactions and the nucleon masses.
  
  While nothing new was discovered, the fact that a new technique has proven the old calculation right is exciting in its own terms.


Also, from the University of Barcelona. 

In 2006 there was a proposal with Harvard University to establish a network of ten detectors to enable tomography of the Earth via antineutrinos.

Not related to the question, but interesting. CERN has a proposal to detect nuclear contraband using cosmic ray muon tomography.