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3D Structure and Animation

As the cold Pacific plate subducts beneath NE Japan, high-temperature magma is produced and causes an eruption of an island arc volcano. Many observed seismic activities, either large- or microearthquakes, have led seismologists to determine the detailed velocity structure beneath Japan [2, 4]. For example, Zhao and others [4] analyzed 14,045 arrival times including both P and S waves. Complex seismic velocity discontinuities (the Moho discontinuity and the upper plane of the subducting Pacific plate) are taken into account in their 3D velocity inversion. Their results have shown low-velocity zones in the crust beneath the volcanoes and in the central part of the mantle wedge, and up to 6 percent higher velocity in the Pacific plate. Their tomography results, given in FORTRAN code, yield a value of velocity perturbation in percentages at any point of the upper mantle beneath NE Japan. For a 3D animation, here we use their 3D P wave velocity structure.

Figures 1 (a) to (e) show a 3D mapping of the Earth's interior to 120 km depth beneath NE Japan (lat. 36.5-41.6 N, long. 138.5-142.5 E) based on the P wave seismic tomography by Zhao and others [4]. In this figure, the vertical scale is exaggerated 3.2 times so that the details of the internal structure can be seen clearly. Programs are given in Listings 1 to 3 for 3D views and animations. Even simple Mathematica code yields 3D Earth structure in considerable detail. At the top of the figures (the Earth's surface), the location of active volcanoes (red circles) and the map of NE Japan are shown. To be transparent, the Moho discontinuity and the surface of -3% velocity perturbation are described, not by planes, but by green and pink points, respectively. The Moho discontinuity is a boundary between the crust and the mantle. The upper plane of the subducted Pacific plate is shown by a combination of ten light blue rectangles. In Listings 1 to 3, dv-3 is a set of points of -3% velocity perturbation, while dv-4 and dv-5 consist of the data tracing outlines of the north-south cross sections of -4% and -5% velocity perturbations. These low-velocity regions are shown in polygons (yellow and orange, respectively) with contour lines that reduce the data quite a lot (compared with points) and help to save memory. Within the yellow and orange polygons, velocity perturbations are less than -4% and -5%, respectively. The contour lines (light purple, the data file dv-4c) trace outlines of -4% velocity perturbation at every 1 km depth. These low-velocity data can be shown in dots, too; however, the memory needed for 3D views and animations becomes quite large.

(a)

(b)

(c)

(d)

(e)

Figure 1. Three-dimensional mapping of low-velocity zones and seismic activities in northeastern Japan as viewed from (a) above and (b) below from southwest direction, from (c) above and (d) below from northwest direction, and from (e) below from west (symbols are described in (e)). Vertical scale is exaggerated 3.2 times. It is observed that fairly low-velocity zones exist locally beneath the sites of volcanoes and downwards to the west. The high temperature regions (regions of less than velocity perturbation) appear to extend to greater depths in the mantle wedge, suggesting a plume-like uprising of hot mantle rocks. In between the volcanoes and the low-velocity zones, S wave reflectors exist and low-frequency microearthquakes occur. Two major low-velocity zones are observed below 60 km depth and branch off at the uppermost mantle, and eventually underplate the Moho right beneath the volcanoes.

dv1={PointSize[0.001],RGBColor[0.9,0.4,1],Map[Point,<<dv-3]}
dv2={EdgeForm[],FaceForm[RGBColor[0.9,0.8,0],
RGBColor[0.9,0.8,0]],Map[Polygon,<<dv-4]}
dv3={EdgeForm[],FaceForm[RGBColor[0.9,0.5,0],
RGBColor[0.9,0.5,0]],Map[Polygon,<<dv-5]}
dvc={Thickness[0.0008],RGBColor[0.6,0.4,0.5],
Map[Line,<<dv-4c]}
moh={PointSize[0.005],RGBColor[0.2,0.6,0],Map[Point,<<moho]}
slb={EdgeForm[],FaceForm[RGBColor[0.7,0.9,1],
RGBColor[0.7,0.9,1]],Map[Polygon,<<slab]}
meq=Map[Point,<<microearthq]
leq={PointSize[0.015],RGBColor[0.3,0.1,0],
Map[Point,<<largeearthq]}
ref={FaceForm[RGBColor[0.4,0.2,0.5],RGBColor[0.4,0.2,0.5]],
Map[Polygon,<<reflector]}
vol={PointSize[0.02],RGBColor[0.9,0.2,0.5],
Map[Point,<<volcano]}
nej={Thickness[0.0065],Map[Line,<<NEJapan]}
Show[Graphics3D[{dv1,dv2,dv3,dvc,moh,slb,meq,leq,ref,
vol,nej}],
PlotRange {{138.5,142.5},{36.5,41.6},{-120,0}},
BoxRatios {1,1.5,1.1},
ViewPoint {-2.84,-1,1.15},
Axes True,
Lighting False]

Listing 1. Programs for displaying 3D structure (Figure 1) of the Earth's interior beneath northeastern Japan. Parameter values given in ViewPoint give Figure 1a. The files, dv-3, dv-4, dv-5, dv-4c, moho, slab, microearthq, largeearthq, reflector, volcano, and NEJapan consist of the data of -3% velocity perturbation, less than -4% velocity perturbation, less than -5% velocity perturbation, -4% velocity perturbation, the Moho discontinuity, the upper plane of the subducting Pacific plate (slab), hypocenters of microearthquakes, hypocenters of large crustal earthquakes, S wave reflectors, locations of active volcanoes, and the coastline of northeastern Japan, respectively.

dv1={PointSize[0.001],RGBColor[1,0.3,0.7],Map[Point,<<dv-3]}
dv2={EdgeForm[],FaceForm[RGBColor[1,1,0],RGBColor[1,1,0]],
Map[Polygon,<<dv-4]}
dv3={EdgeForm[],FaceForm[RGBColor[1,0.74,0],
RGBColor[1,0.74,0]],Map[Polygon,<<dv-5]}
dvc={Thickness[0.0008],RGBColor[0.6,0.4,0.5],
Map[Line,<<dv-4c]}
moh={PointSize[0.0065],RGBColor[0.3,0.9,0],
Map[Point,<<moho]}
slb={EdgeForm[],FaceForm[RGBColor[0.8,1,1],
RGBColor[0.8,1,1]],Map[Polygon,<<slab]}
meq={PointSize[0.01],RGBColor[0.2,0,0.77],
Map[Point,<<microearthq]}
leq={PointSize[0.014],RGBColor[0.3,0.3,0.3],
Map[Point,<<largeearthq]}
ref={FaceForm[RGBColor[0.9,0.63,1],RGBColor[0.9,0.63,1]],
Map[Polygon,<<reflector]}
vol={PointSize[0.02],RGBColor[1,0,0],Map[Point,<<volcano]}
nej={Thickness[0.0065],Map[Line,<<NEJapan]}
a=0.15; b= -12; c=170
For[i=0,i<c, Show[Graphics3D[{dv1,dv2,dv3,dvc,moh,slb,meq,
leq,ref,vol,nej}],
PlotRange {{138.5,142.5},{36.5,41.6},{-120,0}},
BoxRatios {1,1.5,1.1},
ViewPoint {-3.6,i*a+b,3.2},
Lighting False];i++]

Listing 2. Programs for displaying 3D movie (Movie 1) of the Earth's interior beneath northeastern Japan from SSW to NNW.

dv1={PointSize[0.001],RGBColor[1,0.3,0.7],Map[Point,<<dv-3]}
dv2={EdgeForm[],FaceForm[RGBColor[1,1,0],RGBColor[1,1,0]],
Map[Polygon,<<dv-4]}
dv3={EdgeForm[],FaceForm[RGBColor[1,0.74,0],
RGBColor[1,0.74,0]],Map[Polygon,<<dv-5]}
dvc={Thickness[0.0008],RGBColor[0.6,0.4,0.5],
Map[Line,<<dv-4c]}
moh={PointSize[0.0065],RGBColor[0.3,0.9,0],
Map[Point,<<moho]}
slb={EdgeForm[],FaceForm[RGBColor[0.8,1,1],
RGBColor[0.8,1,1]],Map[Polygon,<<slab]}
meq={PointSize[0.01],RGBColor[0.2,0,0.77],
Map[Point,<<microearthq]}
leq={PointSize[0.014],RGBColor[0.3,0.3,0.3],
Map[Point,<<largeearthq]}
ref={FaceForm[RGBColor[0.9,0.63,1],RGBColor[0.9,0.63,1]],
Map[Polygon,<<reflector]}
vol={PointSize[0.02],RGBColor[1,0,0],Map[Point,<<volcano]}
nej={Thickness[0.0065],Map[Line,<<NEJapan]}
c=157
For[i=0,i<c, {If[i<17.5,{a=0.3,b= -15}],
If[And[17.5<i,i<32.5],{a=0.2,b= -13.3}],
If[And[32.5<i,i<124.5],{a=0.15,b= -11.7}],
If[And[124.5<i,i<139.5],{a=0.2,b= -17.9}],
If[139.5<i,{a=0.3,b= -31.8}],
Show[Graphics3D[{dv1,dv2,dv3,dvc,moh,slb,meq,leq,ref,
vol,nej}],
PlotRange {{138.5,142.5},{36.5,41.6},{-120,0}},
BoxRatios {1,1.5,1.1},
ViewPoint {-3,0.15,i*a+b},
Lighting False]};i++]

Listing 3. Programs for displaying 3D movie (Movie 2) of the Earth's interior beneath northeastern Japan, from the sky to the inside of the Earth from the west.

Here we focus our attention on low-velocity zones (where temperatures are potentially high, as described earlier), because they are closely tied to magma source regions and volcanoes. In Figure 1, S wave reflectors (purple rectangles) hypocenters of large crustal earthquakes (brown circles) and low-frequency microearthquakes (black points) are also shown. Although the actual size and shape of the reflectors are smaller and more irregular than those shown in the figures, they are represented by dipping rectangular planes. Large crustal earthquakes of magnitude above 6 () are based on observations since 1931 [3], and have caused at least some damage in property and human life.

For 3D animations, we successively change the parameters of the function ViewPoint as described in Listings 2 and 3. The speed, range, and axis of the rotation of the 3D structure are varied by the values, a, b, and c. In Movie 1 (Movie1.nb), y values in ViewPoint are varied from -12 to 13.35 at every 0.15 (see Listing 2), and there are 170 figures viewing from SSW to NNW. On the other hand, z values in ViewPoint are varied from -15 to 15 at every 0.15, 0.2, and 0.3 in the ranges of , , and , respectively (see Listing 3), in Movie 2 (Movie2.nb). This yields 157 figures viewed from the sky to the inside of the Earth from the west. Increasing a value with increasing absolute value of z yields a relatively homogeneous rotation of the 3D structure. For clear presentation of Movies 1 and 2 on the screen or on the monitor, we have used larger parameter values in RGBColor in Listings 2 and 3 than in Listing 1, and microearthquakes and large earthquakes are shown in blue and gray circles, respectively. The movies enable us to see the structure from various directions and to investigate the spatial relations between volcanoes, earthquakes, reflectors, and low-velocity zones in detail.


Copyright © 2002 Wolfram Media, Inc. All rights reserved.