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Measurement of the sound intensity vector distribution is a useful way to identify noise sources in a vehicle especially at low frequencies. Due to the effect of standing waves, it is difficult to identify the source location from the sound pressure measurement at the driver's ear position. Direct measurements, such as scanning the entire vehicle cabin with a three-dimensional sound intensity probe is very time consuming, and is not able to track temporal and spatial changes in the sources. In this paper, an approach is presented that provides a prediction of the vector sound intensity field throughout a volume exterior to a rigid spherical measurement array consisting of flush mounted microphones.