Analyze the Frequency and Magnitude of Earthquakes

Explore earthquake records by examining magnitude patterns and using statistical models to summarize seismic activity

Earthquake records provide information on how often seismic events occur and how strong they are. Distribution models can be used to summarize patterns in seismic activity and estimate probabilities of extreme events.

Load earthquake magnitude data for the year 2013 for earthquakes with magnitude at least 3.5 as an event series:

In[1]:=

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

EarthquakeData

:Earthquakes returned with duplicate dates; values may be combined.

⌚

26.6814

Visualize a sample of earthquake magnitudes over time:

In[2]:=

DateListPloted,FillingAxis,PlotRange

Tue 1 Jan 2013

Tue 15 Jan 2013

,Automatic

Out[2]=

Out[80]=

Extract magnitude values from the event series:

In[3]:=

magnitudes=Values[ed];

Display a probability-density histogram of earthquake magnitudes:

In[4]:=

Histogram[magnitudes,20,"ProbabilityDensity"]

Out[4]=

Determine the largest magnitude registered within the time period:

In[5]:=

Max[ed]

Out[5]=

8.3

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

In[6]:=

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

Out[6]=

Fit a two-component normal mixture to approximate the magnitude distribution:

In[7]:=

distMagnitudes=EstimatedDistribution[magnitudes,MixtureDistribution[{p,1-p},{NormalDistribution[a,b],NormalDistribution[c,d]}]]

NMaximize

:Failed to converge to the requested accuracy or precision within 100 iterations.

Out[7]=

MixtureDistribution[{0.,1.},{NormalDistribution[-32.8947,1.68347],NormalDistribution[4.67701,0.546803]}]

Overlay the fitted mixture density on the empirical histogram:

In[8]:=

Show[Histogram[magnitudes,20,"ProbabilityDensity"],Plot[PDF[distMagnitudes,x],{x,Min[magnitudes],Max[magnitudes]},PlotStyleThick,PlotRangeAll]]

Out[8]=

Estimate the probability that a given earthquake will be of a magnitude 7 or larger:

In[9]:=

Probability[x≥7,xdistMagnitudes]

Out[9]=

0.0000107694

Simulate magnitudes for hypothetical future earthquakes:

In[10]:=

ListPlot[RandomVariate[distMagnitudes,30],FillingAxis]

Out[10]=

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Analyze the Frequency and Magnitude of Earthquakes

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Analyze the Frequency and Magnitude of Earthquakes

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