The propagation of seismic waves is influenced by changes in crustal structure as for example the transition from continental to oceanic crust along the Norwegian margin. We analyzed Lg wave propagation to map lateral crustal changes in Norway and adjacent areas. We used 1369 observations from 279 earthquakes recorded mostly by the Norwegian National Seismic Network between 1990 and 2017. First, we classified Lg wave propagation in terms of efficiency through Lg/Pn ratios and found significant changes between ray paths crossing offshore and onshore areas. Then we derived an average QLg(f) = 529 f0.42 model for Norway, which is in the expected range for a stable tectonic environment. This was used as starting model for a tomographic inversion. We present tomographic models of Lg wave attenuation at frequencies 2 Hz, 4 Hz, and 6 Hz, respectively. We observed the most significant variation between offshore and onshore regions. This can be explained by changes in crustal structure and the occurrence of unconsolidated sediments in the offshore areas.