The body-wave magnitude m_b: An attempt to rationalize the distance-depth correction q(Δ, h)

We explore the possible theoretical origin of the distance-depth correction q(Δ, h) introduced 75 yr ago by B. Gutenberg for the computation of the body-wave magnitude mb, and still in use today. We synthesize a large data set of seismograms using a modern model of P-wave velocity and attenuation, and process them through the exact algorithm mandated under present-day seismological practice, to build our own version, qSO, of the correction, and compare it to the original ones, q45 and q56, proposed by B. Gutenberg and C.F. Richter. While we can reproduce some of the large scale variations in their corrections, we cannot understand their small scale details. We discuss a number of possible sources of bias in the data sets used at the time, and suggest the need for a complete revision of existing mb catalogues.