We have compiled bathymetry and earthquake data of the Sunda Shelf to study the

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2 Abstract We have compiled bathymetry and earthquake data of the Sunda Shelf to study the flexural stresses in the Malay Basin which are due to the post last-deglaciation sea level rise of about 120 m. The data were inserted into Matlab coding to create 3-D flexural stress model and to see the distribution of shallow earthquakes. The 3-D model shows that the plate offshore west of the Thailand Peninsular has been subsided while the coast along the west of the peninsular has been uplifted. The Malay Basin area consists of complicated variations of flexural stresses due to variations in the geometry of the water load. The bathymetry of the Malay Basin area varies causing the water load thickness to be varied. The distribution of the shallow earthquakes shows a good correlation between crustal deformations and stress concentrations. In the Malay Basin area, shallow earthquakes occurred in stress concentrated areas, in the shallow sea south of Vietnam and in the shallow sea east of Thailand Peninsular. In addition to shallow earthquakes, there is a normal in the shallow sea east of Thailand Peninsular and a strike-slip fault in the shallow sea south of Vietnam. As a result of uplift due to flexure, two passive margin volcanoes were formed in the stress concentrated area in the shallow sea south of Vietnam. The extension of the uplift gave less resistant for magma to be pushed up and out of the plate. 1

3 1. Introduction Since about 20,000 to 8,000 years ago, after the Last Glacial Maximum, approximately 120 m of water has been placed on top of the Sunda Shelf (Hanebuth et al., 2008). In Figure 1, the plot of post-glacial sea level rise, most of the data of Sunda/Vietnam Shelf fall in the region of 120 m of sea level rise. This amount of water created a large weight on the lithosphere of the basins which leads the lithosphere to bend. The lithospheric flexure has created considerable stresses which vary throughout the region of the Sunda Shelf. In this study, the investigated regions are the basins from the west of Sumatra to the east of Malaysian Peninsular. A similar study by Grollimund and Zoback, 2000 investigated the effect of glaciation on the lithosphere in the northern North Sea. This investigation of the stresses of Sunda Shelf is based on the bathymetry data, calculations from Watts (2001), and occurrences of shallow earthquakes. The objectives of this study are to construct 3-D flexural and stress models of the studied area of Sunda Shelf, to investigate whether the sea level rise has caused the flexural which then caused stress changes, and to correlate the flexural and stress changes with shallow earthquake occurrences. The flexure of the lithosphere has created small scale deformations in many spots in this region especially where stresses are concentrated as shown in the World Stress Map project (Zoback, 1992). The spots with high tensional stress concentration have tendencies to form normal faults. When these faults fail, low magnitude and shallow earthquakes are created. Data of shallow earthquake events are collected from the Incorporated Research Institutions for Seismology (IRIS) which scatter around the area. The data from IRIS show that there have been many earthquake occurrences in the 2

4 studied area which have hit areas with low stress concentration. In compensating this matter, the elastic thickness of the plate and the depth at which flexural stresses are measured need to be taken into account. The elastic thickness of the plate is set to be low, as low as 5 km, based on previous studies. However, the thickness of 5 km does not mean that below that depth, the rocks are ductile. Figure 2 shows the map of the Southeast Asia. Malay Basin is located east of the Malaysian Peninsular. The plate boundary between the Indo-Australian plate and the Eurasian plate is located west of Sumatra extending towards the north and along the offshore of Java in which the Indo-Australian plate is subducting beneath the Eurasian plate. Subduction zone volcanoes have been formed along the plate boundary. However, there are some passive margin volcanoes have been formed in south Vietnam and in the shallow sea south of Vietnam. 2. Elastic Plate Flexure due to the Sea Level Rise Lithospheric plates sit on top of highly viscous asthenosphere. Due to their characteristic of being rigid, lithospheric plates can be subsided and uplifted. As a plate subsides, it pushes the asthenosphere around creating uplifts. Figure 3 shows an unflexed lithosphere being loaded by a weight of water. Due to the loading, the lithosphere is flexed creating a bend with curvatures. The curvatures consist of compressional region, neutral surface, and extensional region. Neutral surface is the center surface of a plate in which there are no compression and extension meaning that there are no stresses. As a plate subsides, the upper part of the plate undergoes compression and the lower part undergoes extension. As a plate uplifts, the upper part of the plate undergoes extension and the lower part undergoes compression. One important parameter which affects the 3

5 amount of flexure is elastic thickness, T e. Larger elastic thickness results in stronger crust and harder to bend. 4

6 3. Methods 3.1. Data preparation Bathymetry data were collected from the National Geophysical Data Center website. Custom grid was set to 1-minute grid cell size with the resolution of 1.85 km from the latitude of 0 to 16 N and longitude of 88 E to 116 E. The 1-minute grid cell size is called ETOPO1 data. This data format is very detailed due to the sharp resolution. Other alternative is the ETOPO2 data with 2-minute grid cell size but this type of data has lower resolution which would result in less details of the bathymetry of the studied basins. Seismicity and earthquake data were obtained from the Incorporated Research Institutions for Seismology website. The magnitudes of earthquake were set at 0 to 9 and the depths were set at 0.1 to 30 km. It is important to put focus on shallow earthquakes because lithospheric flexure can result in shallow earthquakes and deformations. Deep earthquakes are mostly formed by plate tectonics especially in convergent boundaries where plate failures can occur deep in subduction zones D flexural stress modelling To model the flexural stresses of Malay Basin and other Sunda regions due to the 120 m sea level rise, the equations and calculation methods from Watts (2001) were used. The calculations and modelling were done using Matlab. This model calculates the elastic part of the lithosphere. Therefore, the value of effective elastic thickness, T e, affects the resulting flexural stresses. In this study, the effective elastic thickness was set to 5 km based on previous studies (Hutchison, 2004; Madon and Watts, 1998; Wheeler and White, 2000; Wheeler and White, 2002;). Hutchison (2004) suggests the effective elastic 5

7 thickness of 8 to 10 km due to rifting. Madon and Watts (1998) suggest the elastic thickness of Malay Basin is virtually zero to compensate locally sediment loading by Airy isostasy. Wheeler and White (2000) suggest that the elastic thickness cannot be greater than 2 km indicated by their optimization calculated using values of constants. In their paper in 2002, Wheeler and White suggest low elastic thickness as a characteristic of stretched continental crust. Based on these studies, I set the effective elastic thickness to be 5 km by averaging the values from these studies. This model assumes the lithosphere to be an infinite beam which responses to the loading of the water mass. The flexural response results in topographic changes of the basins. The spatial flexural deflection of lithosphere is determined by the load, flexural response, and Airy response. The spatial flexural deflection, w(k) is expressed in this equation: w(k) = L(k).Φ(k).A(k) (1) L(k) is the load acting on the lithosphere, Φ(k) is the flexural response of the plate, and A(k) is the Airy response which is the readjustment of the isostasy of the lithosphere and asthenosphere. k is the wave number which indicates the distribution of the load. Flexural response function, Φ(k), is the function of flexural rigidity and wave number of the load. The expression of Φ(k) is: Φ(k) = (2) 6

8 D is the flexural rigidity which indicates the strength of the plate; g is the gravitational acceleration, which is 9.81 m/s 2 ; and ρ plate is the density of the lithospheric plate. Flexural rigidity, D, is the function of elastic thickness of the lithosphere and is described as: (3) The parameter E is the Young's modulus which is 5.60 x Pa, T e is the effective elastic thickness which is 5 km, and ν is the Poisson's ratio which is Lithospheric flexure creates stresses in the plate. Stress generated, σ, is the function of the curvature of the plate and is expressed in this equation: σ x = (4) is the curvature of the flexural response and is the distance to a particular horizontal fibre in the beam. The Matlab coding was made by Dr. Bice (attached in the Appendix). In constructing flexure and flexural stress 3-D models using Matlab, first the spatial data from Equation 1 were converted to Fourier transform. Then the Fourier transform data were inverted back to spatial. The bathymetry data are crucial in the calculation of the stresses as they determine the water loading thickness due to the sea level rise. The general sea level rise in the studied area is 120 m, however, at regions with lower bathymetry, lower water thicknesses were loaded on top of them. 7

9 4. Results The first part of the Matlab coding utilizes the ETOPO1 bathymetric data set to create a topographic and bathymetric map of the studied area (Figure 4). Figure 4 illustrates the terrain elevation in meters relative to sea level shown by the color bar. Blue covers deep oceans which go down to 5000 m deep and yellow covers shallow sea areas with depths of 100 to 200 m. Dark yellow and red indicate landmasses and mountains respectively. The mountains reach up to 2000 m elevation. Detailed depth variations are observed in the Malay Basin area, seafloor in the Strait of Malacca (between Sumatra and Malaysian Peninsular), and along the coasts of Thailand Peninsular. The region west of Thailand Peninsular also shows interesting deep to shallow depth variations. As this study is to investigate the effects of sea level rise on the seafloor, we used Matlab to calculate the total water load on the seafloor of the studied area. Figure 5 shows the total water load thickness in meters indicated by the color bar on the right side of the figure. The vast blue color area with 0 m water depth indicates landmasses with no sea level rise. From Figure 5, observed are variations of sea level rise in the South China Sea area where the Malay Basin is. Variations of sea level rise are also observed in the Strait of Malacca which is in between Sumatra and the Malaysian Peninsular. High sea level rise up to 120 m covers most of the deeper ocean which is shown by the red color. Figure 6 shows the total water depth in meters of the area. Landmasses are covered in red. Figure 6 only shows the water depth and disregards the elevations above sea level. The observed 3-D flexural shows similar patterns to the distribution of the water load (Figure 7). Areas with larger water loads hold bigger flexures. It is important to ignore the edge-effect which occurs at the edges of the studied area. The areas east of the 8

10 Malaysian Peninsular and in between Sumatra and the Malaysian Peninsular show variations of seafloor flexures. There are series of uplift and subsidence in these regions. Dark red means small uplift of 1 to 3 m. Small uplifts are observed along the coasts of eastern and western parts of Malaysian Peninsular, western part of Thailand Peninsular, east coast of Vietnam, and northern coast of Sumatra. Light red to blue indicate subsidence. Figure 8 and 9 show the flexural stress map of the studied area at lithospheric depth of 4.5 km. Since we set the elastic thickness to be at 5 km, the lithospheric depth of 4.5 km means the flexural stresses are located below the neutral line where no compression and extension have occurred. Basically, Figure 8 and 9 show the flexural stresses in the lower part of the lithosphere. Red indicates extension while blue indicates compression. The flexural stresses range from -10 MPa to 8 Mpa in the studied area. These are large stresses. The coast along the west of Malaysian and Thailand peninsular experiences uplift while further away from the coast towards the shallow sea, the lithosphere experiences subsidence. Moving away from this region towards the west, there is a vast area of no flexural stress until there is another curvature. The Malay Basin area east of the Malaysian Peninsular consists of inconsistent distribution of flexural stress. More uplifts and subsidences are present in the area. Again the edge-effect needs to be ignored in Figure 8 and 9. There have been many recent shallow earthquake occurrences in the studied area (Figure 10). These earthquakes are 0.1 to 10 km in depth. Most of the earthquakes occurred in stress concentrated spots. Figure 11 shows the earthquake occurrences in the shallow sea south of Vietnam. The earthquakes occurred around a plate uplift. Figure 12 shows some earthquakes offshore east of Thailand Peninsular which cluster in a small 9

11 subsidence region. Figure 14 and 15 show more earthquakes which cluster in many stress concentrated areas. 10

12 5. Discussion 5.1. Elastic thicknesses In this study, the elastic thickness used is 5 km. This is considered a very thin elastic thickness which indicates that the lithosphere is very weak and easily bended. Lower elastic thickness results in higher curvature. As mentioned in the methods section, stress is the function of curvature, (Equation 4). Larger curvature results in larger stress. In general, the low elastic thickness of the lithosphere leads to large induced stresses which range from -10 to 8 MPa. The Malay Basin has a very low elastic thickness due to the filling of 12 km of sediment mostly within a very narrow area (Madon and Watts, 1998). Madon and Watts explain that the plate of the Malay Basin is greatly curved in the vertical plane because of strong sediment loading which then results in high flexural stress. The low elastic thickness also might due to the flexural stress exceeding the failure criterion causing the lower part of the lithosphere to decouple from the upper brittle part thus reducing the elastic thickness (McNutt et al., 1988). One other explanation for the low elastic thickness is due to major strike-slip faults in the brittle crust in this region which can weaken the lithosphere (Turcotte and Schubert, 1982). Figure 16 shows how the flexural stresses distribution would look like with elastic thickness of 15 km. With 15 km elastic thickness, the magnitude of the stresses is lower which ranges from -5 to 4 MPa. The pattern of the distribution of the flexural stresses is similar but the distribution is wider, smoother, and less detailed. The whole Thailand Peninsular and northern Sumatra experience small uplift. In the flexural stress map of elastic thickness of 5 km, much of the Thailand Peninsular and northern Sumatra experience no stress change. 11

13 5.2. Flexural and induced stresses Due to complicated variations of elevations in the Malay Basin area and along the coast of Malaysian and Thailand peninsular, the resulting geometry of water load on these two areas is complicated (Figure 5). The varied geometry of water load leads to differences in flexural responses in which it has caused the two areas to form spots of uplift and subsidence. The spots with thicker water load has been pushed down and forcing spots with thinner water load to be uplifted Shallow earthquakes, volcanoes, and stress concentrations Based on the flexural stress map and the occurrences of shallow earthquakes, we were able to correlate stress concentrations with shallow earthquakes. There have been shallow earthquakes which occurred in passive margins further away from the subduction zone (examples are in Figure 11 and 12). Due to being far away from any convergent boundary, the earthquakes must have occurred due to shallow deformations. Lithospheric flexure is the best explanation forming the earthquakes. Uplifted and subsided plates are prone to form normal and strike-slip faults. In Figure 11, the earthquakes occurred in a stress concentrated area. Red color indicates subsidence and blue color indicates uplift. Most of the earthquakes in Figure 11 occurred close to the uplift spot. Passive margin volcanoes are also present in the shallow sea south of Vietnam. Figure 2 marks two volcanoes in the shallow sea area south of Vietnam. In Figure 11, the area where the two volcanoes are located in the blue region which indicates uplift. The lower part of the plate had experienced compression while the upper part was experiencing extension. This had caused the plate to flexure upward or uplift. One 12

14 plausible explanation is that as the plate was flexed upward, it gave less resistant for magma to be pushed upward and out of the plate to form volcano. 13

15 6. Conclusions In conclusion, from the 3-D flexural stress of the Malay Basin area, the sea level rise of about 120 m in the area has caused large induced stresses. The stresses range from -10 to 8 MPa which are very large stresses. These large stresses are due to the small effective elastic thickness of 5 km. Small elastic thickness results in weaker flexural rigidity which in turn makes it easier to bend the plate. 120 m of water thickness is a very large weight load. Regarding the crustal deformation, as shallow earthquakes in the studied area mostly occurred in stress concentrated areas with the addition of passive margin volcano formations in the uplift regions south of Vietnam, it is plausible to correlate stress concentration with crustal deformation and volcano formation due to the distances of the earthquakes being far from convergent boundaries. The extension of the plate had reduced the resistant for the magma to be pushed out of the plate. The concentrated stresses have formed multiple faults in the area south of Vietnam. 14

16 Acknowledgement I would like to thank my thesis advisor, Geosciences Professor at The Pennsylvania State University, Dr. David Bice, for his supervision, guidance, and advice in completing this senior thesis project. 15

17 References Bice, D., personal communication. Grollimund, B., and Zoback, M., 2000, Post glacial lithospheric flexure and induced stresses and pore pressure changes in the northern North Sea. Tectonophysics, v. 327, no. 1-2, p Hanebuth, T.J.J., Stattegger, K., and Bojanowski, A., 2008, Termination of the Last Glacial Maximum sea-level lowstand: The Sunda-Shelf data revisited. Global and Planetary Change, v. 66, p Hanebuth, T.J.J., Stattegger, K., and Grootes, P., 2000, Rapid Flooding of the Sunda Shelf: A Late-Glacial Sea-Level Record. Science, v. 288, p Hutchison, C. S., 2004, Marginal basin evolution: the southern South China Sea. Marine and Petroleum Geology, v. 21, p Lindholm, C.D. et al., 1995, Crustal Stress in the northern North Sea as inferred from borehole breakouts and earthquake focal mechanisms. Terra Nova, v. 7, p Madon, M., and Watts, A. B., 1998, Gravity anomalies, subsidence history and the tectonic evolution of the Malay and Penyu Basins (offshore Peninsular Malaysia). Basin Research, v. 10, p Watts, A. B., 2001, Isostasy and Flexure of the Lithosphere. Cambridge University Press, 458 p. Turcotte, D. L., and Schubert, G., 1982, Geodynamics: Applications of Continuum Mechanics to Geological Problems. Wheeler, P., and White, N., 2000, Quest for dynamic topography: Observations from Southeast Asia. Geology, v. 28, p Wheeler, P., and White, N., 2002, Measuring dynamic topography: An analysis of Southeast Asia. Tectonics, v. 21, no. 5, p Zoback, M., 1992, First- and Second-Order Patterns of Stress in the Lithosphere: The World Stress Map Project. Journal of Geophysical Research, v. 97, no. B8, p. 11,703-11,728. The Incorporated Research Institutions for Seismology website. The National Geophysical Data Center website. UNAVCO website. 16

18 Figures Figure 1: The post-glacial sea level rise with years ago (thousands) on the x-axis and sea level change (m) on the y axis. The Last Glacial Maximum started around 21,000 years ago and since then, sea level has been risen up. Most of the Sunda/Vietnam Shelf symbols fall in the region of approximately 120 m sea level rise. 17

19 Figure 2: The studied area of this study. The Malay Basin is east of the Malaysian Peninsular. Shallow seas and deep oceans are distinguished in this figure. Plate boundary or convergent boundary between the Indo-Australian plate and Eurasian plate extends along the offshore west of Sumatra towards the north and offshore south of Java. The Indo-Australian plate is subducting beneath the Eurasian plate. The red triangle symbols indicate volcanoes. Subduction zone volcanoes formed along the plate boundary and passive margin volcanoes are present in Vietnam and in shallow sea south of Vietnam. The figure was contructed from the UNAVCO website. 18

20 Figure 3: Flexural and stress diagram. As water is loaded, the unflexed lithosphere flexures creating curvatures which undergo compression and extension. The neutral surface sits at the center of the plate where no stresses are induced meaning there are no compression and extension in that surface. Elastic thickness, T e, plays a crucial role in the strength of the plate. 19

21 Figure 4: Bathymetric and topographic map of the studied area with distance in km on x- and y-axes. The color bar indicated elevation relative to the sea level. Dark blue indicates deep ocean and dark red indicate high elevation. The Malay Basin consists of complicated ranges of bathymetry. 20

22 Figure 5: Water load thickness with distance in km on the x- and y-axes. The color bar indicates the thickness of the water load in meters. The vast blue regions are landmasses and the red regions are deep oceans. In the Malay Basin, there are variations of water load thickness due to variations in the bathymetry. 21

23 Figure 6: Total water depth in meters with distance in km on the x- and y-axes. The color bar indicates total water depth in meters. Landmasses are covered by dark red color. Deep oceans reach the depths down to 5000 m. 22

24 Figure 7: 3-D flexural map in meters at the elastic thickness of 5 km. x- and y-axes are distance in km. The color bar indicates flexure of the plate in meters. Dark red indicates small uplift of up to 3 m and light red to dark blue indicate subsidence. 23

25 Figure 8: 3-D flexural stress map at lithospheric depth of 4.5 km. x-,y-, and z-axes are distance in km and color bar indicates flexural stress in MPa. 24

26 Figure 9: Plane view of the flexural stress map at lithospheric depth of 4.5 km. x- and y- axes are distance in km and the color bar indicates flexural stress in MPa. 25

27 Figure 10: Distribution of shallow earthquakes on the flexural stress map. '+' symbols indicate earthquakes at depths of 0.1 to 5 km and 'x' symbols indicate earthquakes at depths of 5 to 10 km. 26

28 Figure 11: Shallow earthquake occurrences in the shallow sea south of Vietnam. The earthquakes occurred in a stress concentrated area. 27

29 Figure 12: Shallow earthquakes occurrences in the shallow sea east of Thailand Peninsular. The earthquakes occurred in an area of plate which has been subsided. 28

30 Figure 13: Shallow earthquake occurrences in Sumatra. 29

31 Figure 14: Shallow earthquake occurrences west of Thailand Peninsular. 30

32 Figure 15: Shallow earthquake occurrences north of Sumatra. 31

33 Figure 16: 3-D flexural stress map at the elastic thickness of 15 km and at lithospheric depth of 13 km. x-, y-, and z-axes are distance in km and the color bar indicates flexural stress in MPa. 32

34 Figure 17: World Stress Map of the studied area. 33

35 Appendix [Matlab coding] clear,clc % Govers Med Miocene Reconstruction clear all; load basin1.xyz; % The ETOPO1 data long=basin1(:,1); lat=basin1(:,2); elev=basin1(:,3); y=lat*111; x=long.*(2*pi*6371*cosd(lat))/360; gx1=linspace(min(x),max(x),512); gy=linspace(min(y),max(y),512); [XI,YI]=meshgrid(gx1,gy); ZI0=griddata(x,y,elev,XI,YI); a=isnan(zi0); ZI0(a)=0; gx=gx1(60:426); ZIc=ZI0(:,60:426); XI=XI(:,60:426); YI=YI(:,60:426); gx2=linspace(min(gx),max(gx),512); [XI2,YI2]=meshgrid(gx2,gy); ZI=interp2(XI,YI,ZIc,XI2,YI2); figure(2); pcolor(gx2,gy,zi); shading interp; colorbar; hold on; v=[0]; % these are the contour lines contour(gx2,gy,zi,[0 0],'k'); hold off; xlabel('km') ylabel('km') gx=gx2; %% % just water ZI2=ZI; l=zi2>0; ZI2(l)=0; 34

36 figure(3);pcolor(gx,gy,zi2); shading interp; colorbar; title('total Water depth in meters') %% % just upper 130 m ZI3=ZI2; w=zi3<=-130; ZI3(w)=-130; ZI3=-ZI3; figure(31);pcolor(gx,gy,zi3); shading interp; colorbar; title('water Load thickness in meters') %% flexure %============================== Te=5e3; % m elastic thickness g=9.81; % gravity v=0.25; %Poisson's ratio E=56e10; %Young's modulus npts=512; D=E*Te^3/(12*(1-v^2)); % flexural parameter thick=30e3; % m crust thickness rho_load = 2700; rho_infill = 2500; rho_water = 1030; rho_mantle = 3300; hk_sea = fft2(zi3); dy=1e3*(gy(2)-gy(1)); dx=1e3*(gx(2)-gx(1)); ty = 2*pi/dy*(0:1:256)/512; tx = 2*pi/dx*(0:1:256)/512; ty = [ty fliplr(ty(2:256))]; tx = [tx fliplr(tx(2:256))]; %equations from p. 180 in watt's book [kx,ky]=meshgrid(tx,ty); kk = sqrt(kx.^2+ky.^2); 35

37 D=E*Te^3/(12*(1-v^2)); % flexural parameter wk_sea = (rho_water).*(g./(kk.^4.*d+(rho_mantle)*g)).*hk_sea; w1 = -real(ifft2(wk_sea)); figure(4); surf(gx,gy,w1); shading interp; colorbar title(['flexure in meters',' EET = ',num2str(te/1e3),'km']) %% stresses stress_depth=4.5e3; Yf=(-.5*Te)+stress_depth; % this sets the depth below the surface where the stress is calculated dw2=del2(w1,dx,dy); Sigma=(1e-6*E*Yf/(1-v^2)).*dw2; figure(5); surf(gx2,gy,sigma); shading interp; colorbar title(['flexural Stress (MPa) at depth (km) = ',num2str(stress_depth/1000)]) figure(6); [px,py] = gradient(sigma,dx,dy); pcolor(gx,gy,sigma); shading interp; colorbar; hold on; quiver(gx,gy,px,py); hold off; title(['flexural Stress (MPa) at ', num2str(stress_depth/1e3),' km depth']) Sigma2=interp2(Sigma,.1); qx=linspace(min(gx),max(gx),128); dqx=gx(2)-gx(1); qy=linspace(min(gy),max(gy),128);dqy=gy(2)-gy(1); [px2,py2] = gradient(sigma2,dqx,dqy); 36

38 %% EARTHQUAKE DATA %Data are from IRIS EQ1=xlsread('earthquakedata.xlsx', 'EQ1'); %Earthquakes with depths 0.1-5km EQ2=xlsread('earthquakedata.xlsx', 'EQ2'); %Earthquakes with depths 5-10km elat1=eq1(:,1); elong1=eq1(:,2); ey1=elat1*111; ex1=elong1.*(2*pi*6371*cosd(elat1))/360; elat2=eq2(:,1); elong2=eq2(:,2); ey2=elat2*111; ex2=elong2.*(2*pi*6371*cosd(elat2))/360; figure(8); pcolor(gx2,gy,sigma); shading interp; colorbar; hold on; v=[0]; % these are the contour lines contour(gx2,gy,zi,[0 0],'k'); hold off; title(['flexural Stress (MPa) at ', num2str(stress_depth/1e3),' km depth']) figure(9); pcolor(gx2,gy,sigma); shading interp; colorbar; hold on; v=[0]; % these are the contour lines contour(gx2,gy,zi,[0 0],'k'); plot(ex1,ey1,'k+'); plot(ex2,ey2,'kx'); hold off; title(['flexural Stress (MPa, red=extension) with EQ at ', num2str(stress_depth/1e3),' km depth']) 37