Ben-Avraham Z. , Lyakhovsky V.

1. The Dr. Moses Strauss Department of Marine Geosciences, Leon H.Charney School of marine

sciences. Haifa University, Mt. Carmel, Haifa 31905, Israel.

2. Department of Geophysics and Planetary Sciences, Tel Aviv University, Tel Aviv 69978.

3. Geological Survey of Israel, 30 Malkhe Israel, Jerusalem 95501.

Coulomb failure stress

change in heterogeneous

crust; case study for the

7.2 Mw Nuweiba

earthquake

Mariana Kukuliev-Belferan(1)(2)

(1)(2) (3)

Contents

Introduction1

Preliminary simulation2

Motivation3

Input parameters4

Simulation5

Results and discussion6

Conclusions7

Introduction

� Coulomb Failure stress change

∆�� = ∆�� + �′∆�when: �� - failure stress, � - shear stress, �� - normal stress and �′ - effective

friction coefficient.

�� =�

��� + �� −

�

��� − �� �����

� =�

��� − �� �����

when: failure plane is orientated at � to the �� axis.

(King G. et al 1994)

Δσf > 0

Δσf ≤ 0

Introduction

� Nuweiba earthquake

� Date: 22/11/95

� Moment Magnitude: 7.2 Mw

� Place: Gulf of Elat

� Pre-seismic period:

1983, 1990, 1993.

� Post –seismic period:

6 months.

Earthquake location system of Geophysical Institute of Israel (gii.co.il)

Introduction

� Aftershocks

Earthquake location system of Geophysical Institute of Israel (gii.co.il)

2.0 < Md < 3.0

3.0 < Md < 4.0

4.0 < Md < 5.0

5.0 < Md < 6.0

6.0 < Md

Latitude

(Nº)

Longitude (Eº)

Mw

28.45 34.75 5.1

29.17 34.78 4.6

28.55 34.72 5.2

29.33 34.75 5.6

29.20 34.86 5.2

28.89 34.61 4.5

28.68 34.72 4.5

28.86 34.71 5.2

28.98 34.64 4.8

Dynamic source parameters of first 9 aftershocks with

magnitude more than 4.5Mw (Hofstetter et al. 2003)

Introduction

� Previous works

Source parameters of the Nuweiba earthquake determined by previous studies (Baer et al. 2008)

Notes: Reference 1 : Kikuchi (1995) and Shamir (1996); 2: Pinar & Turkelli (1997); 3: Klinger et al. (1999); 4: Hoffstetter et al.

(2003); 5:Baer et al. (1999, 2001); 6: Klinger et al. (2000); 7: Shamir et al. (2003) and 8: Baer et al. 2008. (v): variable slip; (T):

total; depth, length and width are in kilometers. NA: non available. a-Centre of fault trace. b-Defined differently in each of the

previous studies; in this study—centroid depth (average depth weighted by the fault slip).c-x10^26 Dyn-cm.

Preliminary simulation

� Coulomb-3

� Homogeneous halfspace

� Mechanism- Finite rectangular source (Okada, 1992)

� Method- analytical solution

� Calculation – directly from the co-seismic slip data

Preliminary simulation

� CFS change distribution

Latitude

(Nº)

Longitude (Eº)

Mw

28.45 34.75 5.1

29.17 34.78 4.6

28.55 34.72 5.2

29.33 34.75 5.6

29.20 34.86 5.2

28.89 34.61 4.5

28.68 34.72 4.5

28.86 34.71 5.2

28.98 34.64 4.8

Dynamic source parameters of first 9 aftershocks with magnitude more

than 4.5Mw (Hofstetter et al. 2003)

Objective

How the Coulomb failure stress

distribution is affected by the

crustal structure heterogeneity?

Motivation

� Gulf of Elat Crustal structure

Ben-Avraham et al. 1979, Ben-Avraham 1985

Ben-Avraham 1985

Model from profile 3

Model from profile 2

Model from profile 4

Motivation

� Arava Valley Crustal structure

Makris et al. 1983

Desert Project 2004

Ginzburg et al. 1979

El-Isa et al. 1987

DESERT Project 2004

The Simulation

� COMSOL Multiphysics

� 3D Structural/Geometry model

� Mechanism- Finite rectangular source (Okada, 1992)

� Method- finite element

� Calculation – whole stress tensor => Coulomb failure stress

change

Input parameters

� Algorithmic Scheme

Input parameters

� Failure Geometry and Displacement

Baer G. et. al 2008

Input parameters

� Interpolated depth maps

The depth maps of (a) Basement and (b) Mantle obtained of profile (Ginzburg, and Makris, 1979; Makris, et al.,

1983; EL-ISA, et al., 1987; Weber, 2004) integration using kriging interpolation method. The research area

contoured by double white circle and the white lines show the geography.

a b

Input parameters

� Model Structural Components

Layers that composes the structural model (a) Top of Basement and (c) Top of Mantle elevation [km]. Because of

the relative (to the basement) small topography changes, the topography chosen be as a flat layer. The north

direction is on the negative ‘y’ direction of the coordinate system presented on this figures and the east direction

is on negative ’x’ direction.

a

N

S

b

S

N

Simulation

� Using COMSOL – by three steps

Step 1: Benchmarking 3D simulation of homogeneous

crust.

Results

� CFSΔ in homogeneous crust

This figure present CFS∆ distribution on the pie composed of two pieces that simulate the homogeneous soil. The

simulation was carried out by finite element method using COMSOL software. The red area preset the height

failure probability zone. The color bar present CFS∆ at range of ±5 [bar]. The coordinate system is in rang of at Z

direction and at X,Y directions.

Coulo

mb-3

CO

MS

OL

This figure present comparison between results of two homogeneous models. (a) CFS∆ distribution on

homogeneous media using coulomb-3 software. The red area preset the height failure probability zone, the red

and green lines in the center of the model present the fault lengths. The color bar present CFS∆ at range of ±5

[bar]. (b) CFS∆ distribution on homogeneous media by finite element method using COMSOL software. The red

area preset the height failure probability zone. The color bar present CFS∆ at range of ±5 [bar].

Results

� Comparison – different methods

Geological Units

Depth (km)

Vp(km/s)

Vs (km/s) Density (kg/m^3)

Basement 1-7.2 5.5 3.1 2600

Lower crust 7.2-21.64 6.25 3.6 2800

Upper mental 21.64-30 7.95 4.45 3200

Step 2: Three Dimensional flat layered model

Simulation

� Using COMSOL – by three steps

Step 1: Benchmarking 3D simulation of homogeneous

crust.

Velocity structure (Faigin and Shapira, 1994)

This figure present simulation results of ∆CFS followed to Nuweiba 7.5Mw earthquake in flat layered media consist of three

layers: sediments, lower crust and the upper mantle. The simulation carried out by FEM using COMSOL 4.2 software. The

red area represent the high failure probability zone, the color bar at range of ±5 [bar] of ∆CFS.

Results

� CFSΔ in flat layered model

These figures present the difference between the results of homogeneous and flat layered simulations. The difference presented on

the plane of the model surface (at the depth equals 0). The areas with no change in positive value of the ∆CFS filled with blue and

with greater of change the color scale closer to the red with the maximal value of change around the 1.2 [bar].

Results

� Comparison – top of the model

These figures present the difference between the results of homogeneous and flat layered simulations at the depth of 7.2 km. The

areas with no change in the positive value of ∆CFS filled with blue and with greater of change the color scale closer to the red with

the maximal value of change around the 2.4 [bar].

Results

� Comparison - depth of 7.2 km

These figures present the difference between the results of homogeneous and flat layered simulations at the depth of 21.64 km. The

areas with no change in the positive value of ∆CFS filled with blue and with greater of change the color scale closer to the red with

the maximal value of change around the 2.4 [bar].

Results

� Comparison - depth of 21.64 km

Step 3: Three Dimensional structural model

Geological Units

Depth (km)

Vp(km/s)

Vs (km/s) Density (kg/m^3)

Basement 1-7.2 5.5 3.1 2600

Lower crust 7.2-21.64 6.25 3.6 2800

Upper mental 21.64-30 7.95 4.45 3200

Step 2: Three Dimensional flat layered model

Simulation

� Using COMSOL – by three steps

Step 1: Benchmarking 3D simulation of homogeneous

crust.

Velocity structure (Faigin and Shapira, 1994)

This figure represent simulation results of ∆CFS followed to Nuweiba 7.2Mw earthquake in structural model of

research area consist of: the Gulf of Elat filled with the sediments, the seismic basement and the upper mantle.

The simulation carried out by FEM using COMSOL software. The red area represent the high failure probability

zone, the color bar at range of ±5 [bar] of ∆CFS.

Results

� CFSΔ in Structural model

The figure presents the difference of ∆CFS between the (b) homogeneous and the (a) heterogeneous simulations on the models

surface. At the figure that present the difference (c) the areas with no change in positive value of ∆CFS filled with blue and with

greater of change the color scale closer to the red with the maximal value of change 10 [bar].

Results

� Comparison – top of the model

The figure presents the difference of ∆CFS between the (b) homogeneous and the (a) heterogeneous simulations on the depth of

7.2 [km]. At the figure that present the difference (c) the areas with no change in positive value of ∆CFS filled with blue and with

greater of change the color scale closer to the red with the maximal value of change 10 [bar

Results

� Comparison – depth of 7.2 km

The figure presents the difference of ∆CFS between the (b) homogeneous and the (a) heterogeneous simulations on the depth of

21.64 [km]. At the figure that present the difference (c) the areas with no change in positive value of ∆CFS filled with blue and with

greater of change the color scale closer to the red with the maximal value of change 10 [bar].

Results

� Comparison – depth of 21.64 km

Hook's

low

equation:

∆σ=D·∆ε

Discussion

Discussion

Latitude

(Nº)

Longitude (Eº)

Mw

28.45 34.75 5.1

29.17 34.78 4.6

28.55 34.72 5.2

29.33 34.75 5.6

29.20 34.86 5.2

28.89 34.61 4.5

28.68 34.72 4.5

28.86 34.71 5.2

28.98 34.64 4.8

Dynamic source parameters of first 9 aftershocks with magnitude more

than 4.5Mw (Hofstetter et al. 2003)

Discussion

Latitude

(Nº)

Longitude (Eº)

Mw

28.89 34.61 4.5

28.86 34.71 5.2

28.98 34.64 4.8

Depth

(Km)

12

18

9

� The Coulomb stress distribution is significantly

influenced by the heterogeneity of the crust

therefore, it is suggested to include this parameter

in future modeling.

� The structural model simulation indicates differences

in ∆CFS at the scale of 10[bar].

� The flat layered model simulations present

differences in ∆CFS at the scale of 1.2[bar], which

increases with depth to 10[bar].

Conclusions