Acoustic data is collected on the sphere. Several sensors on the sphere detect sound in an essentially continuous manner. A sound is created at a location on the sphere and travels through the material of the hollow sphere eventually arriving at the sensor location where the sound intensity and time of arrival is recorded. This information is used to determine the speed of sound at locations on the surface of the sphere. The speed of sound is modeled using a spline on the sphere. This experimental endeavor is called the calibration phase of the methodology. After the calibration phase, in the estimation phase of the experiment, a sound is created at an arbitrary location on the surface of the sphere. Using the calibration phase speed of sound model and the new sensor information about the arbitrary sound arrival time the arbitrary sound location on the sphere and time of the arbitrary sound initiation is estimated. Various extensions of this methodology, including location and initiation time estimation confidence region determination and possible in-homogeneous or non-continuous speed of sound extensions, are provided.