# Energy and Magnitude: A Historical Perspective

## Abstract

We present a detailed historical review of early attempts to quantify seismic sources through a measure of the energy radiated into seismic waves, in connection with the parallel development of the concept of magnitude. In particular, we explore the derivation of the widely quoted “Gutenberg–Richter energy–magnitude relationship” (

$$\begin{aligned} \log _{10} E = 1.5 M_{\mathrm{s}} + 11.8 \end{aligned}$$

(1)

*E*in ergs), and especially the origin of the value 1.5 for the slope. By examining all of the relevant papers by Gutenberg and Richter, we note that estimates of this slope kept decreasing for more than 20 years before Gutenberg’s sudden death, and that the value 1.5 was obtained through the complex computation of an estimate of the energy flux above the hypocenter, based on a number of assumptions and models lacking robustness in the context of modern seismological theory. We emphasize that the scaling laws underlying this derivation, as well as previous relations with generally higher values of the slope, suffer violations by several classes of earthquakes, and we stress the significant scientific value of reporting radiated seismic energy independently of seismic moment (or of reporting several types of magnitude), in order to fully document the rich diversity of seismic sources.## Keywords

Radiated seismic energy earthquake magnitudes historical seismicity seismic scaling laws## Notes

### Acknowledgements

I am grateful to Alexandr Rabinovich, Alexei Ivashchenko, and Igor Medvedev for providing copies of critical Russian references, and to the staff of the interlibrary loan desk at Northwestern University for their exceptional professionalism over the years. The paper was significantly improved by the comments of three anonymous reviewers. Discussions with Johannes Schweitzer are also acknowledged.

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