Surface Wave Magnitude Using Distance to Epicenter

The surface wave magnitude scale is one of the magnitude scales used in seismology to describe the size of an earthquake. It is based on measurements in Rayleigh surface waves that travel primarily along the uppermost layers of the Earth. It is the ground velocity associated with the maximum trace amplitude in the surfacewave train, as recorded on a vertical component seismogram.

The surface wave magnitude is proportional to the logarithm of the product of the angular distance from station to epicenter and the maximum ground velocity.

Formula

QuantityVariable[Subscript["M", "S"], "Unitless"] == 3.3 + 0.7209288399593979*Log[Quantity[1, "AngularDegrees"^(-1)]*QuantityVariable["Δ", "Angle"]] + Log[Quantity[1/(2*Pi), "Seconds"/"Nanometers"]*QuantityVariable[Subscript["V", "max"], "Speed"]]/Log[10]

symbol	description	physical quantity
M_S	surface wave magnitude	"Unitless"
Δ	angular distance from station to epicenter	"Angle"
V_max	maximum ground velocity	"Speed"

Forms

Examples

Open in Wolfram Cloud

Download Example Notebook

Get the resource:

In[1]:=

Out[1]=

Get the formula:

In[2]:=

Out[2]=

Use some values:

In[3]:=

$FormulaData[ ResourceObject[ "Surface Wave Magnitude Using Distance to Epicenter"], \ {QuantityVariable["\[CapitalDelta]","Angle"] -> Quantity[25, "AngularDegrees"]}]$

Out[3]=

Wolfram Formula Repository (Under Development)

Surface Wave Magnitude Using Distance to Epicenter

Formula

Forms

Examples

External Links

Source Metadata

Publisher Information