EarthquakeData
EventSeries
TimeSeries
Fit
Histogram
HistogramList
ListLogLogPlot
DateListPlot
Partition
MaximalBy
Max

Geography
Data Science

Analyze the Frequency and Magnitude of Earthquakes

Explore the distribution of earthquake magnitudes recorded over a period of time

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Use

EarthquakeData

to obtain the magnitudes of earthquakes recorded in 2013 with magnitude at least 3.5:

In[1]:=

ed=Quiet[EarthquakeData[All,3.5,{{2013,1,1},{2013,12,31}},"Magnitude"]]

Out[1]=

EventSeries

Time: 01 Jan 2013 GMT -5 to 31 Dec 2013 GMT -5
Data points: 6518



Visualize the data over time:

In[2]:=

DateListPloted,



Out[2]=

Determine the largest magnitude registered within the time period:

In[3]:=

Max[ed]

Out[3]=

8.3

Show the frequency of the selected earthquakes as a function of their magnitude:

In[4]:=

Histogram[ed,{3.5,8.5,0.5},ScalingFunctions"Log",LabelingFunctionTop,ImageSize300]

Out[4]=

Use

HistogramList

to generate a list of bin delimiters and counts for the data:

In[5]:=

{bins,counts}=HistogramList[ed,{3.5,8.5,0.5}]

Out[5]=

{{3.5,4.,4.5,5.,5.5,6.,6.5,7.,7.5,8.,8.5},{529,1519,2965,1087,277,81,39,15,4,2}}

Find the most frequent magnitude bin:

In[6]:=

MaximalBy



{Partition[bins,2,1],counts}

,Last

Out[6]=

{{{4.5,5.},2965}}

Explore the distribution of earthquake magnitudes from high to low:

In[7]:=

ListLogLogPlot[Reverse@Sort[Values[ed]]]

Out[7]=

Take the linear section of the data:

In[8]:=

data=Reverse[Sort[Values[ed]]]〚100;;2000〛;

Fit a curve to it:

In[9]:=

sol=Fit[data,{1,x,x^2,x^3},x]

Out[9]=

5.94653-0.00176614x+1.13915×

-6

-2.70317×

-10

Show the curve with the data:

In[10]:=

Show[LogLogPlot[sol,{x,1,Length[data]}],ListLogLogPlot[data]]

Out[10]=

Related Symbols

EarthquakeData
EventSeries
TimeSeries
Fit
Histogram
HistogramList
ListLogLogPlot
DateListPlot
Partition
MaximalBy
Max

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Contributed by: Wolfram Staff

Wolfram Language Example Repository

Analyze the Frequency and Magnitude of Earthquakes

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Publisher Information