**Electromagnetic View of the Seismogenic Zones Beneath Island Arcs**

Hiroaki Toh and Takuto Minami

*Division of Earth and Planetary Sciences, Graduate School of Science, Kyoto University Japan* 

#### **1. Introduction**

182 Earthquake Research and Analysis – Seismology, Seismotectonic and Earthquake Geology

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dimensional structures. In: C.H. Thurber and N. Rabinowitz (Editors), Advances in Seismic Event Location. Modern Approaches in Geophysics. Kluwer, Dordrecht, The ring of fire is well-known by its intense seismic as well as volcanic activities. Most of those activities in the world are concentrated in this narrow circle around the Pacific rim. The Japanese Islands are one of the greatest island arcs in the circum-Pacific area and thus are located along the so-called seismogenic zone which is globally very unique in the sense that it consists of not only a very cold (i.e., old) but also a warm (young) subduction zone (Fig. 1). Namely, the very thick Pacific plate is subducting beneath northeast Japan while the relatively thin and young Philippine Sea plate is sliding under southwest Japan. The oldest parts of each subducting plate are approximately ~140 (Hirano et al., 2006) and ~30 Ma (Wang et al., 1995) respectively for the Pacific plate and the Philippine Sea plate at each trench's outer rise, although the latter age is more variable along the Nankai trough to the Ryukyu trench than the former along the Japan trench. The two subducting plates with different thermal states affect differently the seismic as well as the volcanic activity on the Japanese Islands, which makes the island arc an ideal place to conduct a comparative study on seismogenic zones with a contrasting tectonic setting. We, therefore, will pursue this theme as the main topic of this chapter.

From a geophysical point of view, there are a lot of physical properties that can give constraints on the current dynamics taking place beneath island arcs. Electrical conductivity is a physical property that can be determined independently of elastic properties such as seismic P- and S-wave velocities. Furthermore, it is known to be a strong function of subsurface temperature and very sensitive to presence of melts and/or fluids such as water. The electrical conductivity of the Earth's mantle as well as the seismic velocities changes discontinuously when phase changes dominate in the ongoing physical process at critical depths such as 410km and 660km. These features are very useful in interpreting the characteristics of the geophysical structure beneath an island arc because a joint interpretation of the electrical and elastic structures can provide further constraints on the island arc's thermal and physical states. For instance, fraction of fluids and/or melts can be estimated more precisely if the electrical properties are determined with known seismic geometries/boundaries as a priori information.

In addition, subduction-driven injection of surface water into the Earth's crust and mantle, and its circulation in the Earth have been a recent matter of hot debate in various disciplines in the geoscience community since Karato (1990) first pointed out a possible strong effect of water on the upper mantle properties (especially on electrical conductivity). A series of laboratory measurements has been conducted so far. However, those experimental results seem to differ severely in a quantitative sense. For example, Huang et al. (2005) reported a huge effect of water on electrical conductivity of both wadsleyite and ringwoodite, the two major minerals in the mantle transition zone. On the contrary, Yoshino et al. (2008) claimed that there is no need to include hydrous minerals in the mantle transition zone in order to explain the electrical conductivity profile determined by electromagnetic (EM) field works. The same contradiction is applicable for the asthenosphere, viz., there exist contrasting experimental results of strong (Wang et al., 2006) and weak (Yoshino et al., 2006) dependence of olivine conductivity on water content. Abundance of water in the mantle transition zone is important in the sense that it can form a filter just above the 410km discontinuity (Sakamaki et al., 2006) to segregate geochemical components in the lower mantle from those in the upper mantle (Bercovici & Karato, 2003). Coexistence of the geochemically enriched lower mantle and the very depleted upper mantle has been a long-lasting enigma in the geosciences community, and thus we need to identify a reasonable differentiation mechanism. Because there is no doubt that the mantle transition zone has high potential as a water reservoir (Inoue et al., 1995), this issue definitely requires further research. On the other hand, water in the crust is important in the sense that it can be the sources for shallow earthquakes, deep lowfrequency tremors and volcanic activities in the seismogenic zones of the island arcs (e.g., Obara & Hirose, 2006). It seems to have become a consensus that the subduction-driven water injection is strongly dependent on thermal states of each subducting plate beneath the island arcs. Namely, cold and warm subduction zones behave quite differently in terms of the amount and depth of water release from the slabs. This means that a report on electrical images beneath different parts of the Japanese Islands is nothing but the aforementioned comparative study itself.

Northeast Japan can be classified into the cold subduction regime and thus thought to have high potential, in turn, for water supply to the deep mantle (Iwamori, 2004). Injection of water into the deep mantle seems to produce electrical conductivity anomalies of regional to semi-global scale beneath back-arc regions. Furthermore, those electrical anomalies are present irrespective to whether the subducting slab is stagnant at the 660 km seismic discontinuity (Ichiki et al., 2006) or plunging into the lower mantle (Booker et al., 2004)., although their surface manifestations look, naturally, quite different (Worzewski et al., 2010). Arc volcanism in northeast Japan is known to be threedimensional (3-D) as typically depicted by Tamura et al's (2002) hot-finger model. A twodimensional (2-D) east-west slice of a 3-D P-wave seismic tomography (Mishra et al., 2003) at 39.5N showed a nearly uniform distribution of moderately fast velocity above the subducting Pacific plate within the slice. It can be attributed to the fact that the slice covers a non-volcanic part, viz., a region between the hot fingers, of the well-developed island arc. An electrical section (Toh et al., 2006), which covers the non-volcanic part of northeast Japan, reveals a resistive shallow mantle and a conductive anomaly beneath the back-arc region at depths 150-200 km. The electrical conductivity anomaly can be interpreted as a direct manifestation of slab dehydration associated with collapse of the high-temperature type serpentine such as antigorite. An EM 2-D section of northeast Japan at crustal depths (Ogawa et al., 2001) revealed several high conductive anomalies in

disciplines in the geoscience community since Karato (1990) first pointed out a possible strong effect of water on the upper mantle properties (especially on electrical conductivity). A series of laboratory measurements has been conducted so far. However, those experimental results seem to differ severely in a quantitative sense. For example, Huang et al. (2005) reported a huge effect of water on electrical conductivity of both wadsleyite and ringwoodite, the two major minerals in the mantle transition zone. On the contrary, Yoshino et al. (2008) claimed that there is no need to include hydrous minerals in the mantle transition zone in order to explain the electrical conductivity profile determined by electromagnetic (EM) field works. The same contradiction is applicable for the asthenosphere, viz., there exist contrasting experimental results of strong (Wang et al., 2006) and weak (Yoshino et al., 2006) dependence of olivine conductivity on water content. Abundance of water in the mantle transition zone is important in the sense that it can form a filter just above the 410km discontinuity (Sakamaki et al., 2006) to segregate geochemical components in the lower mantle from those in the upper mantle (Bercovici & Karato, 2003). Coexistence of the geochemically enriched lower mantle and the very depleted upper mantle has been a long-lasting enigma in the geosciences community, and thus we need to identify a reasonable differentiation mechanism. Because there is no doubt that the mantle transition zone has high potential as a water reservoir (Inoue et al., 1995), this issue definitely requires further research. On the other hand, water in the crust is important in the sense that it can be the sources for shallow earthquakes, deep lowfrequency tremors and volcanic activities in the seismogenic zones of the island arcs (e.g., Obara & Hirose, 2006). It seems to have become a consensus that the subduction-driven water injection is strongly dependent on thermal states of each subducting plate beneath the island arcs. Namely, cold and warm subduction zones behave quite differently in terms of the amount and depth of water release from the slabs. This means that a report on electrical images beneath different parts of the Japanese Islands is nothing but the

Northeast Japan can be classified into the cold subduction regime and thus thought to have high potential, in turn, for water supply to the deep mantle (Iwamori, 2004). Injection of water into the deep mantle seems to produce electrical conductivity anomalies of regional to semi-global scale beneath back-arc regions. Furthermore, those electrical anomalies are present irrespective to whether the subducting slab is stagnant at the 660 km seismic discontinuity (Ichiki et al., 2006) or plunging into the lower mantle (Booker et al., 2004)., although their surface manifestations look, naturally, quite different (Worzewski et al., 2010). Arc volcanism in northeast Japan is known to be threedimensional (3-D) as typically depicted by Tamura et al's (2002) hot-finger model. A twodimensional (2-D) east-west slice of a 3-D P-wave seismic tomography (Mishra et al., 2003) at 39.5N showed a nearly uniform distribution of moderately fast velocity above the subducting Pacific plate within the slice. It can be attributed to the fact that the slice covers a non-volcanic part, viz., a region between the hot fingers, of the well-developed island arc. An electrical section (Toh et al., 2006), which covers the non-volcanic part of northeast Japan, reveals a resistive shallow mantle and a conductive anomaly beneath the back-arc region at depths 150-200 km. The electrical conductivity anomaly can be interpreted as a direct manifestation of slab dehydration associated with collapse of the high-temperature type serpentine such as antigorite. An EM 2-D section of northeast Japan at crustal depths (Ogawa et al., 2001) revealed several high conductive anomalies in

aforementioned comparative study itself.

the lower crust that are considered to bear geofluid. The source of the lower crustal geofluid is attributed to the convection in the wedge mantle beneath northeast Japan, which is compatible with the distribution of the Quarternary volcanoes on the volcanic front as well.

Although the arc volcanism relevant to northeast Japan looks 3-D in terms of its structure, the magma source can be unique and simple. It stems from the deep mantle behind the mature island arc. On the contrary, that of southwest Japan cannot be presumed as simple as northeast Japan, if one studies basalt samples of this area (Iwamori, 1991; Kimura et al., 2003). The alkaline, sub-alkaline and adakite basalt magmas of southwest Japan imply multiple sources for its magma production in the mantle including slab-melting of the hot and young Philippine Sea plate. The presence of the adakite magma is a signature of fluid originating from the slab. Toh and Honma (2008) reported a possible mantle plume in the west of the Kyushu Island of southwest Japan, which can be another candidate of the multiple magma sources. On the other hand, seismic and EM observations on land have revealed coincidence of lower crustal conductors and epicenters of both deep low-frequency events and earthquakes in the upper crust, which suggests presence of crustal fluid (e.g., Kawanishi et al., 2009). 2-D slices of Nakajima & Hasegawa's (2007) 3-D seismic tomography results beneath southwest Japan imply the presence of a deep mantle plume released not from the Philippine Sea plate but from the Pacific plate that is located well below the younger plate. However, the link between the two kinds of fluid is still missing and needs further research, especially based on marine geophysical data or a combination of land and marine data.

In the following, we will first describe the principle and methods of electrical conductivity determination by EM field works. The principle and methods section will be followed by an EM case study on northeast Japan to illustrate usefulness of the principle as well as the methods. Thirdly, the EM image beneath southwest Japan will be presented and discussed in contrast to that of northeast Japan. Finally, results of the whole comparative study will be summarized and concluded.

### **2. Principles and methods in EM field works**

There exist lots of methods for delineating subsurface electrical conductivity structures by field works. They are classified broadly into two categories: one to make use of transient response of the conducting Earth in time domain, and the other is to derive the Earth's stationary response as a function of location in frequency domain. The latter category is often adopted irrespective to observation locations (viz., on land or at sea) and hence readers are advised to refer to standard textbooks for the former category (e.g., Kaufman & Keller, 1983). We will describe briefly the principles and typical methods in the frequency domain here in this section.

The principle of the EM methods in frequency domain is to use amplitude ratios and phase differences between different time-varying EM components observed on the Earth's surface including the seafloor rather than to model observed time-series themselves. Amplitudes of the raw time-series are dependent on each event, i.e., they differ from time to time. However, their ratios and phase differences are constant for a particular frequency and a fixed site, provided that one is really looking at induced parts of temporal variations by external

Fig. 1. Tectonic plates around the Japanese Islands. Pa: Pacific Plate, Ph: Philippine Sea Plate, Na: North American Plate, Eu: Eurasia Plate, Am: Amurian Plate.

geomagnetic disturbances. Another fundamental assumption of the frequency-domain EM methods is that the external source fields are either stationary plane waves or at least waves with known simple geometries such as dipole fields. If this assumption is applicable, the EM responses, *p* and *q*, of the conducting Earth can be estimated by the following linear regression formula in frequency domain:

$$\mathcal{W}(f) = p(f) \cdot \mathcal{U}(f) + q(f) \cdot V(f) \tag{1}$$

where *U*, *V* and *W* are the observed EM components and *f* is the frequency in concern. *U*, *V* and *W* are given by Fourier transforms of the observed time-series for respective EM components. If the source field is stationary enough, stable estimates of the Earth's EM responses (*p* and *q*) can then be yielded by standard stacking methods that divide the whole time-series into a number of segments of a suitable length.

There are several variants of the frequency-domain EM method represented by Eq. (1) because many combinations of EM components in the regression equation are possible. Of those, the geomagnetic depth sounding (GDS) method, the magnetotelluric (MT) method and the horizontal geomagnetic transfer function (HGTF) method are often favoured in actual field works since each method has its own distinct physical meaning and advantages. We will give succinct summaries of those methods in the following three subsections.

#### **2.1 Geomagnetic depth sounding method**

186 Earthquake Research and Analysis – Seismology, Seismotectonic and Earthquake Geology

Fig. 1. Tectonic plates around the Japanese Islands. Pa: Pacific Plate, Ph: Philippine Sea Plate,

geomagnetic disturbances. Another fundamental assumption of the frequency-domain EM methods is that the external source fields are either stationary plane waves or at least waves with known simple geometries such as dipole fields. If this assumption is applicable, the EM responses, *p* and *q*, of the conducting Earth can be estimated by the following linear

where *U*, *V* and *W* are the observed EM components and *f* is the frequency in concern. *U*, *V* and *W* are given by Fourier transforms of the observed time-series for respective EM

*W f pf Uf qf Vf* () () () () () (1)

Na: North American Plate, Eu: Eurasia Plate, Am: Amurian Plate.

regression formula in frequency domain:

This method is a case of *U=Bx*, *V=By* and *W=Bz*, where *Bx*, *By* and *Bz* denote the northward, eastward and downward geomagnetic components, respectively. The GDS method is usually applied when lateral contrast of the subsurface electrical structure is expected to be strong. This is because the anomalous *Bz* is most likely to be induced by the external inducing field of plain wave form than any other EM components. Vertically propagationg plane waves have *Bx* and *By* components alone. As for its detailed physical meaning and the graphical representation of the method, refer to Section 2 of Toh & Honma (2008).

In cases where the inducing source field can be approximated by a global-scale axial dipole, it is known that the Earth's scalar impedance *Z* is given by the following formula (e.g., Schultz & Larsen, 1987);

$$Z(f) = -\pi i f \mathcal{R}\_E \tan(\theta) \frac{B\_r(f)}{B\_\theta(f)} \, ^\prime \tag{2}$$

where *RE*, , *Br* and *B* are the mean radius of the Earth, co-latitude, radial and southward geomagnetic components, respectively. The ratio of the two geomagnetic components is equivalent to the Earth's EM response function *p*(*f*) if *W=*- *Bz*, *U=*- *Bx* and *V=*0. Eq. (2) is often invoked to estimate the Earth's one-dimensional (1-D) impedance at long periods (typically *T* > 4 days) for EM forcing by the magnetospheric ring currents. The global-scale ring currents can produce temporal variations of axially symmetric magnetic dipole fields that are the premises of the valid application of Eq. (2). In order to determine tensor impedances, however, it is required to measure not only the vector geomagnetic field but also the vector (or rather 'horizontal') geoelectric field, which will be described in the next subsection.

#### **2.2 Magnetotelluric method**

The MT method needs two linear regression equations in which two sets of *(U, V, W)* are substituted: (*Bx*, *By*, *Ex*) and (*Bx*, *By*, *Ey*). *Ex* and *Ey* are the horizontal geoelectric components. The resultant EM response functions are neither scalar nor vector but tensor, which are elements of the so-called 'MT impedance tensor'. Namely, the MT impedance tensor is defined by the following matrix formula:

$$
\begin{pmatrix} E\_x \\ E\_y \end{pmatrix} = \begin{pmatrix} Z\_{xx} & Z\_{xy} \\ Z\_{yx} & Z\_{yy} \end{pmatrix} \begin{pmatrix} B\_x \\ B\_y \end{pmatrix}. \tag{3}
$$

*Zij* (*i, j = x, y*) denotes each tensor element. The frequency *f* is intentionally dropped off from each variable in Eq. (3) for simplicity.

The MT impedance tensor is originated from the MT scalar impedance as in Eq. (2), which is a complex ratio of mutually orthogonal geomagnetic and geoelectric components. If the Earth's electrical conductivity varies in the vertical direction only, an external geomagnetic field variations polarized in a particular horizontal direction induces toroidal telluric currents in the Earth perpendicular to the magnetic field. It is the 1-D complex ratio of the MT scalar impedance *Z(=E/B)*, which has already appeared in Eq. (2). In this case, it follows that *Zxx=Zyy=0 and Zxy=-Zyx=Z*. If we substitute the magnetic field *(Hx, Hy)T* into Eq. (3) instead of the magnetic induction *(Bx, By)T*, it is straightforward to show that the physical dimension of each impedance tensor element becomes ohm. Thus, the primary physical meaning of the MT impedance is the resistance of the Earth. However, if we use 'magnetic induction' in place of 'magnetic field', the MT impedance has a physical dimension of 'velocity'.

When the subsurface electrical structure elongates in a specific direction and *x*-axis is aligned to the structural strike, the diagonal elements of the MT impedance tensor vanish again while the absolute values of off-diagonal elements are not necessarily equal to each other. It is well-known that the Maxwell equations decouple into two independent modes in 2-D cases: one mode involves *Ex, By, Bz* and *Zxy* alone and the other *Ey, Ez, Bx* and *Zyx*. The former combination is called 'TE-mode' or 'E-polarization' while the latter is called 'TMmode' or 'B-polarization' borrowing the nomenclatures of the EM wave-guide theory. It is evident that the GDS responses appear only in TE-mode for 2-D cases. The MT impedance tensors can be defined even for 3-D cases and remain being powerful tools in estimation of electrical structures. However, we need to work with full tensors rather than more simpler antisymmetric tensors after pertinent coordinate rotations in the horizontal plane.

#### **2.3 Horizontal geomagnetic transfer function method**

If one substitutes two sets of *(U, V, W)*, (*Bx0, By 0, Bx*) and (*Bx0, By 0, By*), into the linear regression formula (Eq. (1)), you will end up with the following matrix equation with a 2 x 2 matrix:

$$
\begin{pmatrix} B\_x \\ B\_y \end{pmatrix} = \begin{pmatrix} K\_{xx} & K\_{xy} \\ K\_{yx} & K\_{yy} \end{pmatrix} \begin{pmatrix} B\_x^{\ 0} \\ B\_y^{\ 0} \end{pmatrix}. \tag{4}
$$

The vector *(Bx, By)T* is horizontal geomagnetic variations at the observation site in concern while *(Bx*0, *By* <sup>0</sup>*)T* is that of a reference site. Both the observation site and the reference site can be either on land or at the seafloor. In any land-sea combinations, each element, *Kij* (*i, j = x, y*), of the horizontal transfer function matrix in Eq. (4) constitues another set of EM response functions representative of the electrical properties of the Earth. Among the various combinations, an interesting pair is a seafloor observation site and a near-by reference site on land. This combination involves vertical shears of each horizontal geomagnetic component, which are measures of the net electric currents induced in the ocean. The pair, therefore, is called as the vertical gradient sounding (VGS) method, which is a good alternative of the seafloor MT method when geoelectric measurements at the sealoor are missing. As for details of the VGS method, refer to Ferguson et al. (1990) and references therein.

The goal of the EM methods described above is to derive electrical conductivity structures that can explain the spatial distribution as well as the frequency dependence of the Earth's

The MT impedance tensor is originated from the MT scalar impedance as in Eq. (2), which is a complex ratio of mutually orthogonal geomagnetic and geoelectric components. If the Earth's electrical conductivity varies in the vertical direction only, an external geomagnetic field variations polarized in a particular horizontal direction induces toroidal telluric currents in the Earth perpendicular to the magnetic field. It is the 1-D complex ratio of the MT scalar impedance *Z(=E/B)*, which has already appeared in Eq. (2). In this case, it follows that *Zxx=Zyy=0 and Zxy=-Zyx=Z*. If we substitute the magnetic field *(Hx, Hy)T* into Eq. (3) instead of the magnetic induction *(Bx, By)T*, it is straightforward to show that the physical dimension of each impedance tensor element becomes ohm. Thus, the primary physical meaning of the MT impedance is the resistance of the Earth. However, if we use 'magnetic induction' in place of 'magnetic field', the MT impedance

When the subsurface electrical structure elongates in a specific direction and *x*-axis is aligned to the structural strike, the diagonal elements of the MT impedance tensor vanish again while the absolute values of off-diagonal elements are not necessarily equal to each other. It is well-known that the Maxwell equations decouple into two independent modes in 2-D cases: one mode involves *Ex, By, Bz* and *Zxy* alone and the other *Ey, Ez, Bx* and *Zyx*. The former combination is called 'TE-mode' or 'E-polarization' while the latter is called 'TMmode' or 'B-polarization' borrowing the nomenclatures of the EM wave-guide theory. It is evident that the GDS responses appear only in TE-mode for 2-D cases. The MT impedance tensors can be defined even for 3-D cases and remain being powerful tools in estimation of electrical structures. However, we need to work with full tensors rather than more simpler

antisymmetric tensors after pertinent coordinate rotations in the horizontal plane.

regression formula (Eq. (1)), you will end up with the following matrix equation with a 2 x 2

 

The vector *(Bx, By)T* is horizontal geomagnetic variations at the observation site in concern

can be either on land or at the seafloor. In any land-sea combinations, each element, *Kij* (*i, j = x, y*), of the horizontal transfer function matrix in Eq. (4) constitues another set of EM response functions representative of the electrical properties of the Earth. Among the various combinations, an interesting pair is a seafloor observation site and a near-by reference site on land. This combination involves vertical shears of each horizontal geomagnetic component, which are measures of the net electric currents induced in the ocean. The pair, therefore, is called as the vertical gradient sounding (VGS) method, which is a good alternative of the seafloor MT method when geoelectric measurements at the sealoor are missing. As for details of the VGS method, refer to Ferguson et al. (1990)

The goal of the EM methods described above is to derive electrical conductivity structures that can explain the spatial distribution as well as the frequency dependence of the Earth's

<sup>0</sup> . *x x xx xy y yx yy y B B K K B K K B*

*0, Bx*) and (*Bx0, By*

0

<sup>0</sup>*)T* is that of a reference site. Both the observation site and the reference site

*0, By*), into the linear

(4)

**2.3 Horizontal geomagnetic transfer function method**  If one substitutes two sets of *(U, V, W)*, (*Bx0, By*

has a physical dimension of 'velocity'.

matrix:

while *(Bx*0, *By*

and references therein.

EM response functions thus derived. We will illustrate how to estimate electrical structures that are compatible with EM field works by introducing a few case studies in and around the Japanese Islands using the two subsequent sections.
