Following the idea introduced by Wiemer and Wyss [1997>, here is an attempt to map the seismic hazard, in terms of the b value in the frequency-magnitude distribution, in a region with moderate seismic activity (B¿arn region, French Pyrenees). In this area, the complexity of the geology makes it necessary to perform a 3-D mapping, b values are computed within 5 km radius spherical volumes, that contain an average of 140 events. Strong lateral variations, between 0.45 and 1.8, are observed at short scales in the whole investigated volume. The minimum of the b value is clearly correlated with a historically active zone, which last ruptured in 1980 (Mb=5.1). Interpretating low b values in terms of high stresses may lead us to consider this minimum-b patch as a 5 km radius asperity. This study allows to define its location and dimensions. ¿ 1999 American Geophysical Union