We have made a statistical study of the spatial distribution of low frequency waves (~0.01--0.1 Hz) in the region upstream of the pre-dawn to dawn side bow shock (-50 Re<X<15 Re) using both GEOTAIL and ISEE-3 magnetometer data. We have found that the wave amplitude dependence on D and Xs, where D is the distance from the bow shock and Xs the x-coordinate position of shock foot point of the IMF, can be described by a functional form of A exp(Xs/LX-D/LD), with the characteristic attenuation distances, LX=62¿12 Re and LD=59¿38 Re. ¿ American Geophysical Union 1995