UTRIP  Final  Report  

 

 

Tidal Triggering of Earthquakes --Case Study of 2011 Tohoku Earthquake

Ta-­‐Wei,  Chang1,  2,  3  Supervisor:  Dr.  Satoshi  Ide1  1)  Dept.  Earth  and  Planetary  Sciences,  School  of  Science,  Univ.  Tokyo,  Tokyo,  Japan  2)  Dept.  Earth  Sciences,  School  of  Earth  Sciences,  National  Central  University,  Taoyuan,  Taiwan  3)  Dept.  Geophysics,  School  of  Earth  and  Space  Sciences,  Peking  University,  Beijing,  China  

         Abstract:  

Following  the  study  of  Tanaka  (2012),  by  looking  at  the  earthquake  sequence  for  10-­‐year  time  span  prior  to  the  2011  Tohoku  earthquake,  we  find  that  there   is  strong   correlation   between   tidal   stress   fluctuation   and   earthquake   occurrence   in  several  regions  close  to  the  epicenter  of  the  Tohoku  earthquake.  In  addition  to  this,  we  also  did  declustering,  and  found  out  that  the  declustered  catalog  showed  far  less  correlation;  which  indicates  that  aftershock  sequences  might  be  the  most  sensitive  to  the  tidal  stress  fluctuation  prior  to  very  large  earthquakes.    Keywords:  Tidal  triggering  of  earthquakes,  declustering,  Tohoku  earthquake    

1. Introduction: 1.1. 2011 Tohoku Earthquake:

The  Tohoku  earthquake  occurred  at  5:46,  Mar.  11,  2011  UTC  in  offshore  Tohoku  region,  

Japan.   This   earthquake,   with   moment   magnitude   ranging   from   9.0   (JMA,   2011)   to   9.1  

(Nettles  et  al.,  2011),  is  the  largest  in  magnitude  ever  recorded  in  Japan  (JMA,  2011),  the  2nd  

largest   in   magnitude   and   the   7th   in   fatalities   in   the   world   since   1990   (USGS,   2015).   A  

devastating   tsunami   was   also   observed   throughout   the   Pacific   Ocean,   especially   around  

near-­‐shore   of   Tohoku   region,   with   maximum   height   of   9.3m   in   Sōma   (JMA,   2012).   This  

earthquake  and  the  induced  tsunami  led  to  a  death  toll  of  19225  (till  3/1/2015)  and  heavily  

damaged  over  500,000  buildings  (Fire  Disaster  Management  Agency  of  Japan,  2015).  

 1.2. Tidal Triggering of Earthquakes:

The  relationship  between  tidal  stress   fluctuation  and  earthquake  occurrence  has  been  

discussed   for   over   a   century.   To   date,   over   a   hundred   studies   have   focused   on   this   topic,  

reaching  almost  opposite  results.  Most  studies,  however,  reached  the  result  that  tidal  stress  

is   not   correlated   with   earthquake;   except   for   special   earthquake   sequences   such   as  

earthquake   swarms,   aftershock   sequences,   earthquakes   in   volcanic   areas   (Tanaka   et   al.,  

2002),  and  tremors  (Ide  et  al.,  2015).  

Of   course,   research   methods   have   improved   gradually   throughout   the   century.   The  

stress   level   was   previously   considered   as   the   stress   on   the   epicenter   at   sea   level,   until  

Heaton  (1975),  who  first  calculated  the  stress  on  the  fault  plane,  providing  a  more  accurate  

estimation   of   stress   either   along   the   slip   direction   or   normal   stress.   In   addition   to   this  

improvement,   the   “tidal   stress”   part   is   also  modified.   There   are   two   parts   of   tides   on   the  

Earth  that  may  lead  to  stress  changes  on  the  fault  plane:  body  tide  and  ocean  tide.  The  body  

tide,  also  the  direct  tide,  is  caused  directly  by  the  gravitational  stress  between  the  Earth  and  

the  Sun,  which  is  easier  to  calculate,  therefore  included  in  most  previous  studies.  The  ocean  

tide,  on  the  other  hand,  is  the  indirect  term,  the  effect  of  ocean  water  loading  fluctuation  that  

is  acted  on  by  the  gravitational  stress  on  the  ocean  water.  This  term  is  the  easiest  to  visualize;  

but   due   to   the   lack   of   oceanic   tidal   data,   is   ignored   in  most   previous   studies   until   Sauck  

(1975)   first   include   this   into   his   calculation.   The   oceanic   tidal  model   is   further   improved  

later  on  the  early  21st  century  by  using  satellite  altimeter  to  calibrate  the  readings,  so  Tanaka  

et   al.   (2012)   can  apply   all   the   improved  methods  and  datasets   to   create   a   comprehensive  

study  of  global  data,  which  showed  very  interesting  results  but  out  of  the  scope  of  this  paper.  

After   the   2011   Tohoku   earthquake,   Tanaka   (2012)   took   advantage   of   all   the  

improvements,   and  applied   the   result   to   the  earthquake  sequence  prior   to   the  mainshock.  

She  found  that  as  the  sampling  time  window  of  3000  days  approaches  the  mainshock  in  time  

steps   of   500   days,   the   correlation   between   tidal   stress   fluctuations   and   earthquake  

occurrence   increases   significantly.   In   fact,   this   kind   of   pattern   can   be   observed   in   several  

large   earthquakes   such   as   the   2004   Sumatra   earthquake   and   the   1982   South   Tonga  

earthquake   (Tanaka,   2012).   As   this   is   rather   interesting,   I’ll  mainly   focus   on   her  method,  

trying  to  reproduce  the  same  result,  and  modify  it  a  little  bit  and  discuss  the  results.  

 

2. Data and Method: 2.1. Tide:

The  “tide”  taken  into  consideration  in  this  study  includes  body  tide  and  ocean  tide.  For  

body  tide,  we  simply  sum  up  the  gravitational  stress  acted  on  Earth  by  the  Sun  and  the  Moon.  

For  ocean  tide,  we  apply  the  SPOTL  software  (Agnew,  2012),  which  convolutes  the  oceanic  

tidal  model  and  the  Green  function  in  PREM  structure  configuration  (Dziewonski  &  Anderson,  

1981).   The   oceanic   tidal  model  we  use   is   developed  by  Matsumoto   et   al.   (2000),  which   is  

calibrated   by   using   TOPEX/POSEIDON   satellite   altimeters.   The   spatial   resolution   of   this  

model  is  0.5°  globally  (NAO.99b  and  NAO.99L),  and  5”  regionally  around  Japan  (NAO.99Jb).  

Tidal  components  included  in  this  study  are:  M2,  S2,  K1,  O1,  N2,  P1,  K2,  Q1,  Mf,  and  Mm,  which  

includes  diurnal,  semidiurnal  and  longer  period  tidal  components  caused  by  effect  of  either  

the  Sun,  the  Moon,  or  both.  

 

2.2. Earthquake: For  the  earthquake  catalog,  we  used  the  Harvard  Global  CMT  catalog  (Dziewonski  et  al.,  

1981)  (Ekström  et  al.,  2012),  which  is  the  most  prestigious  global  earthquake  catalog  in  the  

literature  that  includes  the  fault  plane  geometry  and  slip  direction  data  (including  strike,  dip,  

and   rake).   However,   due   to   the   nature   of   the  matter,  we  would   get   two   fault   planes   that  

produce  the  same  focal  mechanism  solutions.  In  this  study,  we  are  only  focusing  on  the  shear  

stress   along   the   slip  direction;   hence  we   can   actually   just   take   either   one  of   the   two   fault  

planes  and  simply  use   the   rake  data,   since  either  one  of   the   two  rake  data   can  be  applied  

along  with  its  corresponding  fault  plane  geometry,  and  will  give  the  same  result  of  along-­‐slip  

shear  stress.  

 

In   this   study,   I   made   a   change   to   the   study   by   Tanaka   at   2012   —   applying   the  

declustering  technique  to  the  earthquake  catalog,  and  see  if  this  will  change  the  result.  The  

method   I   apply   in   my   study   is   described   in   (Reasenberg,   1985),   which   is   the   standard  

method  regarding  declustering.  The  reason  to  apply  this   is   that   in  previous  studies,  strong  

correlation   is   found   in   aftershock   sequence   but   rarely   elsewhere   (Tanaka   et   al.,   2002).  

Therefore,  if  declustering,  which  is  technically  aftershock  removing  does  changes  the  result,  

this   might   give   us   information   on   either   aftershock   is   more   sensitive   to   tidal   stress  

fluctuation  or  less,  comparing  to  other  “mainshocks”.  In  fact,  Tanaka  et  al.  (2002)  had  done  

this   in   their   comprehensive   study,   reaching   the   result   that   there   is   difference   in   the  

outcomming  readings;  but  the  result  of  correlated  or  not  is  basically  not  changed.  

 

2.3. Stress: For  each  earthquake,  we  calculate  the  tidal  stress  tensor  resulting  from  both  body  tide  

and   ocean   tide.   We   do   this   calculation   for   a   24-­‐hour   time   span,   centering   at   the   time   of  

mainshock.  The  time  resolution  is  4  minutes,  creating  360  sampling  points  in  a  day.  The  360  

sampling  points  in  24  hours  is  able  to  create  a  1°  phase  resolution  as  mentioned  in  the  next  

section.  From  the  stress  tensor,  we  get  the  traction  vector  on  the  fault  plane  by  multiplying  

the  stress  tensor  by  the  normal  vector  of  the  fault  plane  specified  by  the  fault  geometry  and  

rake  information  in  the  earthquake  catalog.  After  that,  we  project  the  traction  onto  the  fault  

plane  in  the  coordinate  of  normal  to  fault  plane,  rake,  and  the  direction  on  the  fault  plane  that  

is  orthogonal  to  both.  This  allows  us  to  acquire  the  shear  stress  along  the  slip  direction,  as  is  

my  main  focus  in  this  study.   In  Tanaka’s  study,  the  trace  of  stress  tensor,  which  represents  

the  confining  stress,  is  also  evaluated  in  addition  to  the  shear  stress  along  the  slip  direction  

with  very  different  results  (Tanaka  et  al.,  2002),  but  is  out  of  scope  here.  

 

2.4. Statistical Analysis From  the  previous  step,  we  have  already  acquired  the  fluctuation  of  shear  stress  along  

the   slip   direction   in   a   timespan   of   24   hours.   From   that,   we   apply   the   Schuster   test,   the  

standard  method   to   evaluate   the  phase   angle   of   occurrence   of   earthquakes   that   is   used   in  

(Tanaka  et  al.,  2002)  and  many  other  previous  studies.  First,  we  define   the  phase  angle  as  

follows:  0°  is  the  closest  maximum  of  stress  to  the  earthquake;  180°  is  the  minimum  directly  

following   the   maximum,   and   -­‐180°   represents   the   first   minimum   directly   before   the  

maximum,   as   shown   in   figure   1.   From   this   definition,   we   could   get   the   phase   angle   of   all  

earthquakes  we’d  like  to  study.  

 

 

 

 

 

 

 

 

 

 

 

 

 

After  getting  the  phase  of  each  event,  we  then  calculate  the  p-­‐value  given  as  follows:  

                                                        𝑝 = 𝑒(!!!

! )  

where            𝐷2 = 𝑐𝑜𝑠𝜃𝑖𝑁

𝑖=1

2

+ 𝑠𝑖𝑛𝜃𝑖𝑁

𝑖=1

2

 

In  the  above  equations,  N  is  the  total  amount  of  earthquake  in  question,  and   𝜃!   is  the  

phase   angle   of   any   particular   earthquake.   In   statistics,   the   p-­‐value   is   the   confidence   in  

rejecting   the  null   hypothesis;   higher   p-­‐value   indicates   less   confidence  while   small   p-­‐value  

indicates  strong  confidence  in  rejecting  the  null  hypothesis.  In  this  study,  the  null  hypothesis  

is   that   earthquake   occurrence   is   not   correlated   with   tidal   stress   fluctuation.   Hence,   very  

small   p-­‐value   indicates   that   earthquakes   tend   to   occur   at   around   phase   angle   0°,   which  

means  the  peak  tidal  stress;  and  p=1  indicates  that  there  is  no  correlation  between  the  two,  

i.e.,  the  phase  angle  of  earthquakes  is  evenly  distributed.  

From   all   the   aforementioned,   we   could   now   start   to   find   the   relation.   First,   select   a  

region   or   apply   any   criteria   of   interest   (i.e.  magnitude,   depth,   location,   rupture   type,   etc),  

calculate  the  phase  of  all  the  earthquakes  in  it,  acquire  the  p-­‐value  of  that  area,  and  then  we  

could  judge  if  tidal  stress  fluctuation  is  correlated  with  earthquake  occurrence  in  the  region.  

The  entire  procedure  is  summarized  and  visualized  as  in  figure  2:  

 

0° 180°

 

90°

-­‐180°

Shear  stress  along  

slip  direction

Figure  1:  Schematic  figure  of  the  definition  of  phase.  For  all  other  phase  angle,  we  

simply  divide  the  time  interval  linearly.  The  resolution  of  angle  is  1°.  

 

3. Results: 3.1. Study Area and Criterions:

In   this   study,   since   tidal   stress   has   stronger   effect   on   shallower   earthquakes,  we   only  

used  earthquakes  of  depth  within  70  km,  which  is  by  the  definition  of  shallow  earthquakes.  

In   addition,   since   the   research   area   of   this   study   is   mainly   offshore,   to   ensure   the  

completeness  of  earthquake  events,  we  apply  the  cutoff  magnitude  of  MW  5.0.  Furthermore,  

since  one  of   the  main   focuses  of   this   study   is   to   reproduce   the   result  of   (Tanaka,  2012),   I  

choose  to  include  the  earthquake  within  10  years  prior  to  the  Tohoku  earthquake,  which  is  

close  to  but  slightly  longer  than  the  3000-­‐day  period  she  applied.  

Similar  to  (Tanaka,  2012),  the  study  area  is  chosen  to  be  region  close  to  the  epicenter  of  

Tohoku   earthquake.   For   comparison,   I   did   the   same   calculation   in   15   regions   around   the  

region   for   area   of   200×200  𝑘𝑚! ,   with   each   center   of   region   expressed   in   figure   3   as  

50×50  𝑘𝑚!,  since  these  regions  are  moved  around  in  steps  of  50  km.  As  an  example,  Figure  4  

Determine  the  correlation!  

Earthquake  catalog

Stress  components  on  fault  plane

Phase  of  each  earthquake

P-­‐value  of  earthquakes  of  interest  

Tidal  stress  tensor  at  focus

Earth  and  body  tide  data

Focal  mechanism  and  rake  

Figure  2:  The  basic  flow  chart  of  this  study  

expresses   the  actual   region  of   200×200  𝑘𝑚!   with   its  center   is   indicated   in   figure  3  as   the  

blue  patch.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

For   each   area,   I   plotted   a   histogram   that   shows   the   distribution   of   phases   as  well   as  

calculate   the   p-­‐value   for   each   region.   For   easier   reading,   the   bin   color   of   the   histogram  

represents  the  p-­‐value  of  each  area:  Deep  blue  indicates  a  <0.05  p-­‐value,  which  represents  

high   correlation;   turquoise   indicates   p-­‐value   within   0.1~0.05;   and   red   represents   p>0.1,  

which  indicates  that  the  correlation  is  weak  between  the  two.  

 

3.2. Result: Following   is   the   result   for   all   15   regions   as   15   histograms   in   figure   5,   as  well   as   the  

result  for  the  declustered  catalog  in  figure  6.  The  regions  the  histograms  indicate  are  located  

as  in  the  order  of  the  15  patches  in  figure  3.  

 

140˚

140˚

142˚

142˚

144˚

144˚

146˚

146˚

34˚ 34˚

36˚ 36˚

38˚ 38˚

40˚ 40˚

42˚ 42˚

Figure  3:  The  “centers”  of  the  15  study  

areas.  The  actual  area  of  the  blue  patch  

is  indicated  in  figure  4.  The  red  star  is  

the  Tohoku  earthquake  mainshock.  

Figure  4:  The  square  represents  the  

patch  in  blue  in  figure  3;  the  small  

dots  are  all  the  earthquakes  in  the  

catalog  used  in  the  study.  

140˚

140˚

142˚

142˚

144˚

144˚

146˚

146˚

34˚ 34˚

36˚ 36˚

38˚ 38˚

40˚ 40˚

42˚ 42˚

3.2.1. Not Declustered:

Figure  5:  The  result  for  the  un-­‐declustered  catalog.  We  can  clearly  see  that  for  the  northern  

region,  a  higher  correlation  is  found;  some  could  even  reach  quite  significant  p-­‐value.  

3.2.2. Declustered:

Figure  6:  The  result  for  the  declustered  catalog.  Comparison  with  the  previous  

result  clearly  indicates  that  there’s  now  no  correlation  in  all  of  the  regions.  

4. Discussion: From   figure   5,   we   can   observe   that   for   the   earthquake   sequence   10   years   prior   to   the  

Tohoku  earthquake  mainshock,   there   is   strong  correlation  between   tidal   stress   fluctuation  and  

earthquake  occurrence  in  some  regions  to  the  north  of  the  mainshock.  The  lowest  p-­‐value,  as  can  

be   seen   in   figure   5,   reaches   as   low   as   0.019.   However,   as   for   figure   6,  we   can   see   that   in   the  

declustered  catalog,  no  correlation  is  found  in  all  regions,  however  how  well  they  are  correlated  

in  the  region  before  applying  declustering.  

Comparing   the   above   two   figures,   we   can   clearly   see   that   there   is   significant   difference  

between  declustering  or  not.  Since  declustering  is  basically  removing  the  aftershocks,  we  can  see  

that  after  removing  the  aftershocks,  there  is  now  no  correlation.  From  that,  we  can  say  that  the  

aftershocks   we   have   removed   are   the   most   sensitive   earthquakes   regarding   the   tidal   stress  

fluctuation.   This   is   basically   the   same   conclusions   as  many  previous   studies   as   summarized   in  

Tanaka  et  al.,  (2002);  yet  the  opposite  from  the  declustering  they  did  in  the  same  study.  

Comparison  with  previous  studies,  especially  (Tanaka,  2012),  we  found  very  similar  results,  

either  the  pattern  of  the  histogram  or  the  regions  with  low  p-­‐values.  However,  the  lowest  p-­‐value  

in  her  study  is  0.0034,  which  is  about  5.5  times  smaller  than  mine.  This  may  be  resulting  from  the  

fact  that  the  region  and  sampling  time  is  slightly  different  from  hers.  Note  here  that  the  program  

used  in  calculating  the  tidal  stress  in  this  study  is  different  from  hers.  The  program  she  used  is  

derived  from  GOTIC2  (Matsumoto  et  al.,  2001);  while  the  one  I  applied  is  SPOTL  (Agnew,  2012).  

However,  Yabe  Suguru  of  Dept.  EPS,  Univ.  Tokyo  had  confirmed  the  consistency  between  the  two  

programs,  hence  this  difference  is  quite  unlikely  to  be  the  causation  of  the  difference  in  result.  

As   for   the   declustering   part,   Tanaka   et   al.   (2002)   found   that   removing   the   aftershocks   in  

global  catalog  doesn’t  change  the  conclusion  of  either  correlated  or  not,  even  though  the  readings  

changed  a  bit.  However,  I  reached  a  dramatically  different  result,  saying  that  the  aftershocks  are  

rather  sensitive  to  the  tidal  stress  fluctuation,  which  is  quite  similar  to  the  many  previous  studies  

listed  in  Tanaka  et  al.  (2002).  The  observation  that  aftershocks  of  earthquakes  before  the  Tohoku  

mainshock  are  sensitive  to  tidal  stress,  together  with  the  fact  that  there  are  more  correlation  in  

the   earthquake   sequence   prior   to   the   Tohoku  mainshock   comparing   to   all   earthquakes   in   the  

study  by  Tanaka  et  al.,  (2002),  we  can  gather  that  these  are  special  effects  of  either  the  Tohoku  

earthquake,  or  any  earthquakes  with  very  large  magnitude.  

 

 

 

5. Conclusion: By   calculating   tidal   shear   stress   by   ocean   tide   and   body   tide   in   slip   direction   on   the   fault  

plane  of  earthquakes   in  10  years  prior   to   the  Tohoku  earthquake,  we   found  strong  correlation  

between  tidal  stress  fluctuation  and  earthquake  occurrence  in  some  region  close  to  the  location  

of  the  Tohoku  earthquake,  confirming  the  result  of  Tanaka  (2012).  Applying  decluster  showed  no  

correlation  in  all  region,  indicating  that  aftershocks  of  mainshocks  before  the  Tohoku  earthquake  

are  very  sensitive  to  the  tidal  stress  fluctuation.  

 

6. Acknowledgement: The  author  thanks  Tomoaki  Nishikawa  and  Suguru  Yabe  for  offering  all  the  help  in  his  stay  in  

Univ.   Tokyo.   In   addition,   the   author   is   grateful   to   the   International   Liaison  Office   of   School   of  

Science,  UTokyo  for  all  the  help  in  all  the  administrative  work.  Helpful  comments  and  suggestions  

by   Dr.   Satoshi   Ide   during   the   study   such   as   to   apply   declustering   are   highly   appreciated.  

Discussion   with   the   Ide   lab,   together   with   Kate   Huihsuan   Tsai,   is   very   helpful.   The   code   of  

calculating  tidal  stress  is  developed  by  Suguru  Yabe,  which  combined  SPOTL  program  by  Agnew  

and  tidal  model  by  Matsumoto  et  al.  Figures  3  and  4  are  plotted  using  GMT  software  by  (Wessel  &  

Smith,   1991).   A.   Allmann   writes   the   declustering   program   in   the   ZMAP   software   package  

(Wiemer,  2001).  Comments  on  the  manuscript  by  Dr.  Satoshi  Ide  are  highly  beneficial.  The  UTRIP  

program  is  funded  by  the  GSS-­‐UTRIP  Scholarship.    

 

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