Modelos de fuente sismica finita. Modelo de falla circular. Modele de Haskell

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1 Modelos de fuente sismica finita Modelo de falla circular Modele de Haskell

2 Nacimiento de la dinamica de la fuente A principios de los años 1970 : Aki (1967) Scaling law of earthquake spectra Kostrov (1964, 1966) Circular crack, 2D crack, Energy Brune (1970) Circular crack body wave spectrum Madariaga (1976) put together all this. R 2 Parametros: Mo R No definen la velocidad de ruptura

3 Ley de escalamiento de Aki Size Hay una sola escala de longitud: Radio R o L Mo σ R 3

4 Ley de escala de los terremotos Magnitude (M w ) Moment (Nm) Longueur (km) Durée (s) Glissement (m) ? 300? 100?

5 n Slip of a circular crack stress D 24 Δσ 7π μ 2 2 ( ) R r r = Average slip R D = 16 Δσ 7π μ R

6 Deslizamiento u Modelo de ruptura sismica circular (3D) 2R L (x o -x) 1/2 Distribution de deslizamiento eliptica Esfuerz o 1/(x-x o ) 1/2 Concentration de esfuerzos Augmentation de contrainte x x o L chute de contrainte constant Caida de esfuerzo D 24 Δσ 7π μ 2 2 ( r) = R r

7 Modelo de fisura circular estática Deslizamiento D r) 24 Δσ 7π μ 2 2 ( R r = Deslizamiento medio D = 16 Δσ 7π μ R Momento sísmico 3 M 0 = 16 Δσ 7 R Energia de deformacion W = 8 7 Δσ μ 2 R 3

8 Fundamentals of earthquake scaling Surface Μ 0 = σ R 3 Signal R R σ R 2 R 0 Mo R 2 0 t R 2 Spectrum R 3 R -1 f R 0 3 R 0-1

9 Fundamentals of earthquake scaling Surface R Displacement Signal R 2 Velocity Signal R t R R 2 Acceleration Signal 1 Spectrum R 3 R -1 f

10 Modelo de escalamiento de la fuente Deslizamiento medio D = 16 Δσ 7π μ R Momento sísmico M 0 = 16 7 Δσ R 3 Frecuencia esquina f c = 0.37 β R Momento vs. frecuencia M 0 3 fc

11 Escalamiento de momento y corner frequency Momento sismico Mw Corner frequency f c M 0 3 fc Frecuencia f

12 Modern test of earthquake scaling law Prieto, Shearer and Vernon, JGR, 2004

13 Spectral analysis of California earthquakes P wave S wave

14 Modern tests of earthquake scaling law individual collapsed Test by Prieto et al JGR, 2004 f p / =1.6 f p f s Circular crack model / =1.7 f p f s f s ( Madariaga, 76)

2,5 10 20 Nm From Peyrat et al (GJI 2010) Inverted

15 The Tocopilla Earthquake of 21 November 2007 A double event at the bottom of the plate interface Mw=7,8 Mo = 2, Nm From Peyrat et al (GJI 2010) Inverted triangles accelerograms In red PBO stations used for this study

16 The Tocopilla earthquake sequence in Northern Chile Main event Mw 7.7 on 14 November 2007 Two main aftershocks on 15 November 2007 Deep slab push aftershock 16 December 2007

17 Spectral stack of a set Tocopilla aftershocks Q From Lancieri et al (GJI 2012)

18 Acccelerograms of the main Tocopilla earthquake 4 PBO (GFZ) stations

19 Espectro de desplazamiento del Terremoto de Tocopilla de 2007 observado en 4 estaciones de la red PBO Omega -1 Stations PB04 PB03 PB05 PB07 Moment rate 25 s From Lancieri et al (GJI 2012) and Peyrat et al (GJI 2010)

20 How to model an earthquake: Maule 27 Febrero 2010 Constitución, 19 de Marzo de 2010 Ch. Vigny

Central Chile Seismicity since 1906 2015 Mw 8.

21 Central Chile Seismicity since Mw 8.3 Central Chile Mw>7.8 From Campos et al, 2002

Preseismic deformation from GPS «We would then conclude that the southern part of the Concepción Constitución gap has accumulated a slip deficit that is large enough to produce a

22 Preseismic deformation from GPS «We would then conclude that the southern part of the Concepción Constitución gap has accumulated a slip deficit that is large enough to produce a very large earthquake of about Mw= » This is of course a worst case scenario that needs to be refined by additional work. (Campos, Ruegg, Vigny, R.M. et al, 2002, 2003, 2009 )

23 Ground displacement from GPS stations for themaule earthquake of 2010

24 Static GPS observation of the Maule 2010 earthquake Rupture zone 400 km Vigny et al, Science, 2011 Moreno et al, EPSL, 2012

25 Vertical displacements measured by GPS Hinge line Color diamonds Vertical displacement of biological markers (Farias et al, 2010) From Vigny et al, 2011

26 Inversion of Geodetic slip distribution Moreno et al 2012 Vigny et al 2012

27 Modelling the near field GPS data for the Mw 8.8 Maule 2010 earthquake From Vigny et al Science (2011)

28 Maule 2010: geodetic versus Far field BW inversion Slip inverted from GPS Slip Inverted from Far field body waves Mw = 8.8 Moreno et al (EPSL, 2012) Pro, Buforn, Madariaga (EGU 2013)

29 Maule 2010: Far field Body wave inversion

30 Ground velocity inversion from cgps Uses AXITRA for synthetics Ruiz Madariaga, Ruiz unpublished et al, Earthquake Spectra, 2012

31 Postseismic deformation after Maule E. Klein et al, 2015, Ruiz et al, 2015

32 Use of stacking and backprojection for modelling High frequency features

33 Low and High Frequency features of Maule 2010 Uses Backprojection 25/03/2012 Kieser and Ishii, 2011 From Ruiz et al, 2012

34 Use of seismic antennaes for stacking Source Receiver Antenna Mantle ray trajectories Rayos Frente de ondas

35 Use of a seismic receiver antenna Example of Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion From SPUD in IRIS Data Center

36 Ruiz et al, EPSL 2013 Example of Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion Near field Accelerogram Seismic source

37 Example of Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion Far field body wave modellig

38 SH

39 Example of Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion Observed and synthetic interferogram

40 Available data from the IRIS data center Wilber III applicat Red US array 25 Marzo 2012 Constitucion EQ

41 Displacement record «section» Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion Traces were aligned by Cross correlation

42 Displacement record «section» Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion Signal Ocean reverberations Michigan precursor Texas P sp

43 Displacement record «filter» AAM (Michigan) Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion Original BB Band pass Hz Hz Hz

44 Velocity record «section» Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion

45 Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion 5 velocity seismograms of the US array P sp Michigan precursor Texas

46 Velocity record «filter» AAM (Michigan) Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion Original BB Band pass Hz Hz Hz

47 precursor P s P Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion Sum the stack at different points on the source area This is a constant latitude (-35.1) section

48 Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion Sum the stack at different points on the source area This is a constant longitude (-72.03) section

49 Maule aftershock Mw 7.1 of 25/3/2012 near Constitucion This figure shows the projection (energy sum) Of the stacked seismograms

50 Use of a receiver antenna Example of Maule aftershock Mw 6.7 of 14/2/2011 near Constitucion Example of stack at different frequencies

51 Example of Maule aftershock Mw 6.7 of 14/2/2011 near Constitucion source reverberationsreve

52 Example of Maule aftershock Mw 6.7 of 14/2/2011 near Constitucion

53 There are several ways to obtain The stacked source area. Most of them are cosmetic Because at high frequency signals are coherent

54 Back Projection of Maule earthquake : Data US Array Hz Satriano et al., in progress Hz Travel time residuals corrected by multichannel cross correlation --> station corrections POLENET Array

55 Back Projection: results US Array Hz POLENET Array Hz Satriano et al., in progress

56 Teleseismic Kinematic Inversion and Back Projection US array 0-45 s s s US array POLENET array POLENET array 0-45 s s s Satriano, Donicio et al, in preparation

57 The end

Earthquake Source Dynamics and seismic radiation From large Chilean earthquakes

. Earthquake Source Dynamics and seismic radiation From large Chilean earthquakes R. Madariaga 1,2, S. Ruiz 2, F. Leyton 3, J.C. Baez 3 École Normale Supérieure de Paris, France; Centro Sismologico Nacional