(guebin) Eearthquake
import tqdm
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import plotly.express as px
import warnings
warnings.simplefilter("ignore", np.ComplexWarning)
from haversine import haversine
from IPython.display import HTML
- load
df= pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/earthquakes-23k.csv')
df
- cleaning
df.Date[df.Date == '1975-02-23T02:58:41.000Z']
df.iloc[3378,0] = '02/03/1975'
df.Date[df.Date == '1985-04-28T02:53:41.530Z']
df.iloc[7512,0] = '04/28/1985'
df.Date[df.Date == '2011-03-13T02:23:34.520Z']
df.iloc[20650,0] = '03/13/2011'
df= df.assign(Year=list(map(lambda x: x.split('/')[-1], df.Date))).iloc[:,1:]
df
df.Year = df.Year.astype(np.float64)
class MooYaHo:
def __init__(self,df):
self.df = df
self.f = df.Magnitude.to_numpy()
self.year = df.Year.to_numpy()
self.lat = df.Latitude.to_numpy()
self.long = df.Longitude.to_numpy()
self.n = len(self.f)
self.theta= None
def get_distance(self):
self.D = np.zeros([self.n,self.n])
locations = np.stack([self.lat, self.long],axis=1)
for i in tqdm.tqdm(range(self.n)):
for j in range(i,self.n):
self.D[i,j]=haversine(locations[i],locations[j])
self.D = self.D+self.D.T
def get_weightmatrix(self,theta=1,beta=0.5,kappa=4000):
self.theta = theta
dist = np.where(self.D<kappa,self.D,0)
self.W = np.exp(-(dist/self.theta)**2)
# nlst = self.df.groupby('Year').aggregate(len).Latitude.tolist()
# nlst = [0]+np.cumsum(nlst).tolist()
# beta_matrix = np.zeros([self.n,self.n])
# for i in range(len(nlst)-1):
# beta_matrix[nlst[i]:nlst[i+1],nlst[i]:nlst[i+1]] = beta
# self.W = self.W * beta_matrix
# def _get_laplacian(self):
# self.L = np.diag(1/np.sqrt(d)) @ (D-self.W) @ np.diag(1/np.sqrt(d))
# self.lamb, self.Psi = np.linalg.eigh(self.L)
# self.Lamb = np.diag(self.lamb)
def _eigen(self):
d= self.W.sum(axis=1)
D= np.diag(d)
self.L = np.diag(1/np.sqrt(d)) @ (D-self.W) @ np.diag(1/np.sqrt(d))
self.lamb, self.Psi = np.linalg.eigh(self.L)
self.Lamb = np.diag(self.lamb)
def fit(self,m):
self._eigen()
self.fhat = self.Psi[:,0:m]@self.Psi[:,0:m].T@self.f
self.df = self.df.assign(MagnitudeHat = self.fhat)
self.df = self.df.assign(Residual = self.df.Magnitude- self.df.MagnitudeHat)
plt.plot(self.f,'.')
plt.plot(self.fhat,'x')
def vis(self,MagThresh=7,ResThresh=1):
fig = px.density_mapbox(self.df,
lat='Latitude',
lon='Longitude',
z='Magnitude',
radius=15,
center=dict(lat=37, lon=160),
zoom=1.5,
height=900,
opacity = 0.3,
mapbox_style="stamen-terrain")
fig.update_layout(margin={"r":0,"t":0,"l":0,"b":0})
fig.add_scattermapbox(lat = self.df.query('Magnitude > @MagThresh')['Latitude'],
lon = self.df.query('Magnitude > @MagThresh')['Longitude'],
marker_size= 8,
marker_color= 'red',
opacity = 1
)
fig.add_scattermapbox(lat = self.df.query('Residual**2 > @ResThresh')['Latitude'],
lon = self.df.query('Residual**2 > @ResThresh')['Longitude'],
marker_size= 8,
marker_color= 'blue',
opacity = 1
)
return HTML(fig.to_html(include_mathjax=False, config=dict({'scrollZoom':False})))
- make instance for analysis
moo=MooYaHo(df.query("Year == 2016"))
- 테스트용으로 2016년 자료만 수집
- get distance
moo.get_distance()
moo.D[moo.D>0].mean()
- 0이 아닌 거리의 평균은 8600정도?
plt.hist(moo.D[moo.D>0])
- 히스토그램결과 -> 2500보다 거리가 작으면 거의 같은 지역이라고 봐도 무방할듯
- weight matrix
moo.get_weightmatrix(theta=(8647.92),kappa=2500)
- 평균적으로 노드는
np.exp(-(dist/8647)**2)=np.exp(-1)=0.36787944117144233정도의 연결강도를 가진다. - 거리가 2500이하이면 weight를 1로 설정한다.
- fit
moo.fit(m=150)
moo.df
moo.df.query('Magnitude>7')
plt.plot((moo.df.Residual)**2)
- vis
#moo.vis(MagThresh=7,ResThresh=1) # <- 실행해봐요
- 전체자료는 underlying에 위치
- 지진강도가 MagThresh 이상인 자료는 붉은점으로 시각화함
- 이상치정도(우리가 제안하는 새로운 메져) ResThresh 이상인 자료는 파란점으로 시각화함
- 시간효과를 따로 모형화하지는 않음