The Richter Scale

One of the earlier methods of measuring earthquake magnitude came from the “Richter Scale”, which uses a basic logarithmic formula where every magnitude level is 10 times the previous level. It relied on the amplitude measurements provided by a local seismograph. It’s not widely used anymore due to it’s impracticality for larger magnitude earthquakes and it’s development mainly meant for Southern California geography. \[M_L = log_{10}({A \over A_0})\] where A = amplitude measured by a local seismograph and the \(L\) in \(M_L\) denotes local magnitude scale

Modern Magnitude Formula

The USGS currently uses a moment magnitude formula to measure earthquakes in the US. It accounts for higher magnitude earthquakes and scales accordingly while utilizing the original logarithmic Richter Scale formula. \[M_W = {2\over3}(log_{10}(M_0)-16.1)\] where \(M_0\) is the seismic moment.

Earthquake Magnitude in September 2026

In this graph, we see a map of the continental United States with an overlay of USGS recorded earthquake magnitudes from September 2026. The magnitudes are mapped according to longitude and latitude.

R code used to create graph from previous slide

usmap = ggplot2::map_data("state")

ggplot() +
  geom_polygon(data=usmap, 
               mapping=aes(x=long, y=lat, group=group),
               fill="pink", color="black") +
  geom_point(data=earthquakes, 
             mapping=aes(x=longitude, y=latitude, 
                         size=mag, color=mag)) +
  scale_color_continuous(guide="legend") +
  labs(x="Longitude", y="Latitude", 
       color="Magnitude", size="Magnitude")

Magnitude vs. Depth

The USGS site publishes magnitude data based on size and source of the data. Smaller earthquake data is published using the ml(local richter scale), md(duration), and mb_lg(short-period surface wave) scales. This is common for earthquakes without a measurable moment W-phase(mw, mwr).

R code to create the magnitude vs. depth plot from previous slide

ggplot(earthquakes, aes(x=depth, y=mag, color=magType)) +
  geom_point() +
  labs(x="Depth(km)", y="Magnitude", color="Magnitude Type")

3D Plot of Earthquake Depth

R code to create 3D depth plot from previous slide

xax = list(title="Longitude",
           titlefont=list(family="Modern Computer Roman"))
yax = list(title="Latitude",
           titlefont=list(family="Modern Computer Roman"))
zax = list(title="Depth(km)",
           titlefont=list(family="Modern Computer Roman"))

depth_fig = plot_ly(earthquakes, x=longitude, y=latitude, 
                    z=depth, type="scatter3d", color=depth,
                    mode="markers") %>%
  layout(scene=list(xaxis=xax, yaxis=yax, zaxis=zax)) %>%
  hide_colorbar()

partial_bundle(depth_fig)

References