We present a novel inversion scheme for decomposing upgoing and downgoing wavefields from vertical particle velocity recordings in downhole arrays at multiple depth levels. Our method requires no knowledge of the subsurface medium parameters as the required operators are obtained directly from the data by direct-wave interferometry. As we demonstrate, the method can be applied with as few as two receiver arrays, as long as their vertical spacing is sufficiently small. Additional depth levels can be used to improve the stability of the inversion.