Approximate treatment of seafloor topographic effects in three-dimensional marine magnetotelluric inversion
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2012
Received: 14 July 2011
Accepted: 7 April 2012
Published: 26 November 2012
Seafloor magnetotelluric (MT) observations using ocean bottom electromagnetometers (OBEMs) provide information on the electrical conductivity structure of the oceanic mantle. A three-dimensional (3-D) analysis is particularly important for marine MT data because the electric and magnetic fields observed on the seafloor are distorted by the rugged seafloor topography and the distribution of land and ocean. Incorporating topography into 3-D models is crucial to making accurate estimates of the oceanic mantle’s conductivity structure. Here we propose an approximate treatment of seafloor topography to accurately incorporate the effect of topography without significantly increasing the computational burden. First, the topography (lateral variation in water depth) is converted to lateral variation in effective conductivity by volumetric averaging. Second, we compute the electric and magnetic field components used to calculate the MT responses at arbitrary points from the electric field components on staggered grids, using a modified interpolation and extrapolation scheme. To verify the performance of this approximate treatment of seafloor topography in 3-D inversions, we tested the method using synthetic seafloor datasets and both 3-D forward modeling and inversion. The results of the synthetic inversions show that a given conductivity anomaly in the oceanic upper mantle can be recovered with sufficient accuracy after several iterations.
Magnetotelluric (MT) sounding is a powerful geophysical method to explore the Earth’s interior structure using its electrical conductivity. The electrical conductivity of Earth materials is known to be strongly dependent on physical conditions such as temperature, water content, and degree of partial melting (e.g., Yoshino, 2010; Yoshino et al., 2010) which control their mechanical properties. Especially in oceanic areas, therefore, a number of efforts have been made to obtain accurate images of the electrical conductivity distribution in the upper mantle since Filloux’s (1973) pioneering work was published.
In earlier times, one-dimensional (1-D) interpretation was the only way to infer the electrical conductivity distribution below the ocean bottom due to limits on either the number of observation sites or inversion techniques in higher dimensions (e.g., Filloux, 1981; Oldenburg, 1981). The number of instruments employed in each experiment has increased in recent years allowing researchers to attempt two-dimensional (2-D) inversions (e.g., Evans et al., 1999; Matsuno et al., 2010) or 1-D inversions assuming the presence of 3-D heterogeneity (e.g., Baba et al., 2010).
However, several technological difficulties that hamper inversion of seafloor MT data must be overcome to obtain accurate 3-D electrical conductivity images at a regional mantle scale. This paper deals with one such difficulty, the so-called topographic effect (e.g., Nolasco et al., 1998; Baba and Seama, 2002). The electric and magnetic (EM) fields observed on the seafloor are generally distorted in any direction by rugged seafloor topography, which is more significant than the effect such topography has on land MT data (e.g., Nam et al., 2008) because of seawater’s extremely high conductivity, which produces strong contrast at the seafloor (Schwalenberg and Edwards, 2004). In recent years, several works have attempted to solve the problem of topographic effects on seafloor MT data. Baba and Chave (2005) proposed a scheme to correct 3-D topographic effects, which was applied to 2-D inversion of seafloor MT results on a regional scale (Baba et al., 2006). Li et al. (2008) pointed out that such an approach might be effective for exploring large-scale structures but not for studying fine-scale subsea structures, and suggested another approach in which topography is explicitly incorporated into 2-D inversion using finite-difference approximations.
For an accurate estimation of deep mantle conductivity distributions in 3-D, these topographic effects have to be properly and accurately taken into account in the inversion. In reality, topography variations occur over a wide range of horizontal scales from local (~100 m) to regional (~1000 km) with amplitudes of only a few kilometers. We can generally expect more accurate solutions by using the incorporation approach described in Li et al. (2008), because inversion solutions obtained using the correction approach depend on the accuracy of the approximation of the sub-seafloor structure. It is, however, neither efficient nor practical to incorporate topographic variations into one forward calculation using finer grid cells, especially when focusing on heterogeneous conductivity structures in the oceanic upper mantle and deeper parts with that are typically on a scale of 100 km or more both in the horizontal and vertical directions.
The aim of this paper is to propose an approximate treatment of topography that can be incorporated into 3-D seafloor MT inversion codes to study regional-scale mantle structure. In this study, new techniques are incorporated into the 3-D inversion code, WSINV3DMT (Siripunvaraporn et al., 2005), which is, at present, one of the practical inversions applied to land MT data.
We introduce a general treatment for incorporating topography and bathymetry into the model in Section 2. In Section 3, methods for calculating MT responses at arbitrary points on the undulating seafloor are introduced. The accuracy of the methods described in Sections 2 and 3 is tested in Section 4. In Section 5, a method for calculating sensitivity during inversion is derived. Finally, we apply the method to three kinds of synthetic datasets to verify its performance and then discuss the results in Section 6.
2. Expression of Seafloor Topography
The horizontal length scale of the topography included in a model is dependent on its horizontal mesh dimensions, which are usually set to be fine enough to resolve the observation arrays and target structure. Topography with a length scale larger than the horizontal mesh, and having various amplitudes, is efficiently incorporated by the method proposed above. If smaller scale topographic changes exist and their effect is not negligible, we have to divide the horizontal mesh into a finer grid although it increases computational costs. The alternative is an indirect approach, in which such small-scale topographic effects are treated separately and removed from observed EM responses as has been done, for example, by Baba and Chave (2005) for 2-D target structures. Hereinafter, we assume that the responses input to our 3-D inversions are free from the effects of small-scale topography, either because the effect is separately corrected or because it is negligible.
3. Calculation of MT Responses at Arbitrary Points
When we make forward calculations using coarse grids, the location of an observation site does not necessarily coincide with a grid point or an edge. We propose to calculate electromagnetic fields to estimate theoretical MT responses at each observation site using spatial interpolation and extrapolation. The mathematical formulation is described in this section, and its accuracy is tested in the next section.
This approximate treatment of topography (hereinafter called ATT) includes expressing the ocean bottom conductivity by volumetric averaging and using interpolation and extrapolation methods to calculate the EM fields at arbitrary observation sites.
4. Synthetic Test of the Accuracy of Forward Calculations Using ATT
5. Calculation of Sensitivity
6. Synthetic Inversion and Discussion
Here the total performance of the WSINV3DMT with ATT was tested using three synthetic datasets. The three synthetic datasets were generated using the forward part of the WSINV3DMT with ATT code. The first dataset was calculated for a conductive block buried in a half-space below the ocean with constant water depth. The second was calculated for a conductive block buried in a half-space below the ocean with realistic topography, and the third was a checkerboard model below the ocean with realistic topography. All synthetic models were discretized every 60 km in the horizontal direction in the central part of the model domain. The vertical meshes were discretized every 700 m near the seafloor, and the length of the mesh increases exponentially with increasing depth. All the models included seven air layers in the default configuration, and the conductivity values of the seven air layers were fixed in all the inversion calculations. The number of observation sites is 25 where synthetic MT responses are computed.
6.1 Case I
6.2 Case II
Circles show the convergence of the full components in Fig. 10, and the fifth iteration of the inverted model is shown in Figs. 11(e)–(h). The inversion converged at the fifth iteration with an RMS d misfit of 1.04. The target RMS d misfit was set at one as in Case I. The inversion recovers a reasonable image of the conductive body as shown in Figs. 11(e)–(h), though the recovery is not perfect, especially at greater depths. Again, we confirmed that the ATT technique can be applied to invert seafloor MT data without serious loss of accuracy.
In order to display the importance of a proper topographical treatment, we attempted another inversion test using the synthetic data from Case II. However in this test, we assumed a priori the seafloor to be flat with a constant depth of 5000 m, an average value for all 25 sites. This inversion did not achieve the target RMS d within ten iterations, and the minimum RMS d was as large as 3.47 at the tenth iteration. The tenth iteration of the inverted model is shown in Figs. 11(i)–(1). The minimum RMS d of this inversion is more than three times larger than that of the inversion using ATT (Case II). As shown in Fig. 11(j), the resulting image of the conductivity anomaly is divided into two anomalies lying between depths of 100 and 150 km. Both anomalies have much higher conductivity (0.21 S m−1) than the given value (0.1 S m−1). Furthermore, there are several false anomalies, especially in the shallower regions (Fig. 11(i)), producing extremely anomalous values exceeding 2.0 S m−1 or as low as 0.001 S m−1. The results above indicate that an appropriate treatment of seafloor topography is definitely important in recovering an accurate conductivity model from marine MT data.
6.3 Case III
We also tested the inversion for a more complex model. This model consisted of blocks in a checkerboard pattern with alternating conductivity, 0.1 S m−1 and 0.01 S m−1, embedded in a 0.03 S m−1 half-space with real topography. Figures 13(a) and (b) show only the checkerboard part. The topography is the same as described in Fig. 12. Again, the initial and prior models are the same, 0.03 S m−1 halfspaces.
In this study, we propose an approximate treatment of topography (ATT) for seafloor MT data for use in practical inversions of 3-D conductivity structures beneath the seafloor. It expresses conductivity using volumetric averaging in order to describe seafloor topography and uses improved interpolation methods to calculate MT responses at arbitrary points. Incorporating the ATT method into the WSINV3DMT program allowed the inversion code to be used with marine MT data. We conducted three types of synthetic tests and demonstrated that the ATT method behaves properly for marine MT datasets. We conclude that the ATT technique is suitable for use in 3-D inversions of seafloor MT data without causing large increases in the computational burden.
The authors would like to thank the editor (M. Hyodo), Katrin Schwalenberg, and an anonymous reviewer for useful comments. This research was partially supported by grants 16075204 from the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), and 220003 and 23740346 from the Japan Society of the Promotion of Science (JSPS). This research has been supported by the Thailand Research Fund (TRF:RMU5380018) to WS. Figures were produced using Generic Mapping Tools (GMT) software (Wessel and Smith, 1998). For this study, we used the computer systems of the Earthquake Information Center of the Earthquake Research Institute, the University of Tokyo.
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