Characterizing Subsurface Structures using Very Low Frequency Electromagnetic Radiation - a Modeling Approach

Transcription

1 Characterizing Subsurface Structures using Very Low Frequency Electromagnetic Radiation - a Modeling Approach ERNST D. SCHMITTER University of Applied Sciences Department of Engineering and Computer Sciences Albrechtstr. 30, Osnabrueck GERMANY e.d.schmitter@fh-osnabrueck.de Abstract: Active and passive electromagnetic sounding of the earths interior is a well established technique. In this paper we refer to subsurface imaging using high-power Very Low Frequency (VLF) military transmitters as sources. The Finite Element Analysis (FEA) model we propose solves the harmonic Maxwell equations within a space containing part of the ionosphere and the subsurface domain in question together with the source. This allows for large scale inverse mapping of conductivity profiles taking into account VLF propagation conditions varying in space and time. Key Words: Geophysical Exploration, Electromagnetic Sounding, Finite Element Analysis, Inverse Modeling 1 Introduction The VLF method makes use of the carrier waves of permanent high-power military transmitters for submarine communication mainly in the frequency range from 15 to 50 khz. The low frequency yields a limited penetration into earths subsurface and even into salty water. Geophysically it is used in mineral exploration but also in engineering and groundwater surveys to detect conductive fault zones and other conducting zones. Especially the conductivity contrast between liquid water or hydrated rock melt or possibly even hydrocarbon filled reservoirs and the surrounding media can be traced down to depth and thickness [1], [2]. New application fields for subsurface EMmapping open up with the exploration of the Moon and Mars. On the other side since decades narrow band monitoring of VLF transmitter signal strength is used as a remote sensing method for ionospheric profile parameters which change with day and night but also with Sudden Ionospheric Disturbances (SIDs) caused by the ionization effect of solar flares or stellar Gamma Ray Bursts (GRBs) [6], [7], [8], [9]. Our model takes into account the conductivity profile of the atmosphere and lower ionosphere to accurately model VLF propagation in the earth surface-lower ionosphere cavity and its variations depending on the positions of transmitter and receiver with respect to the day-night terminator and solar activity. This is also a prerequisite for a realistic assessment of VLF EM fields near the surface and its modifications in the subsurface domain. 2 VLF propagation Maxwells macroscopic equations within a conducting medium are E = B t H = σ E + D t D = ɛ 0 ɛ r E B = µ0 µ r H All material parameters, i.e. relative permittivity ɛ r, relative permeability µ r and conductivity σ, may be functions of space and time as the fields itself and can be tensors in anisotropic media. The conductivity is frequency dependent near dielectric relaxations as for example in rocks containing water or certain minerals. Looking for solutions at a specified angular frequency ω we use the separations E = E( x)e iωt, B = B( x)e iωt. The resulting harmonic Maxwell equations for the space dependent field components are (µ 1 r E) = k0ɛ 2 eff E B = 1 iω E ISSN: ISBN:

2 with vacuum wave number k 0 := ω c 0, vacuum speed of light c 0 = 1 ɛ0 µ 0 and effective complex relative permittivity ɛ eff = ɛ r i σ ɛ 0 ω These equations can be interpreted in the way, that current densities j = σ E caused by the electric field vector of the source field within conductive regions generate magnetic fields that modify or tilt the source magnetic field. The vertical polarization of the transmitter for example causes a horizontal magnetic field in the far field. Near conductive structures a vertical component is developed and the horizontal component is changed - in total tilting the field vector. Figure 1: Example of the daily variation of VLF transmitter signal strength caused by change of ionospheric conditions, cp. fig. 2. Local sunrise and sunset at the receiver is indicated; f = khz, distance 800 km. The dips occur at the time when the terminator crosses the signal bounce region halfways between transmitter and receiver. 3 The FEA model As model space we choose a brick with x,y,z extensions 1200 km x 160 km x 210 km. The vertical 210 km are divided in 150 km for the lower ionosphere and 60 km for the subsurface domain. The continuous wave signal source is applied as vertical edge boundary condition at x=0, y=80 km and z=0 (earth surface) with a hight of 1 km. The extensions are compatible with the first Fresnel zone - where most of the energy of the transmitter is delivered - up to a distance of 1100 km for a signal frequency of 20 khz (i.e. a wavelength of 15 km). In each direction Figure 2: Ionosphere conductivities night and day. The earth magnetic field generates anisotropic conductivity contributions (Pedersen and Hall conductivities, s p, s h ) above km height. Within this paper the lower ionosphere up to 150 km is modeled. A midlatitude magnetic field strength of nt with 45 deg. inclination is accounted for. results can be used only up to a distance of about 1-2 wavelengths because a perfectly matched layer (PML) boundary condition is applied to absorb radiation and avoid artificial reflections. The FEA mesh (fig. 3) is refined near the transmitter source and around the high conductivity slab centered at a distance of 800 km. Fig. 4 shows the model space and on the central slice the electric field energy density distribution (logarithmic display). The popagation path within the non ideal cavity formed by the earths surface and the lower ionosphere is clearly to be seen. Field penetration into the subsurface region below the transmitter can reach substantial values. For mapping purposes the typical depths at large transmitter distances reach from some hundred meters to some kilometers strongly depending on material conductivity. Typical orders of magnitude are σ = S/m. The model has been realised with the software COMSOL 3.4 (reg. trademark). Figure 3: FEA mesh of model space with increased grid resolution near transmitter (left) and around subsurface structure. ISSN: ISBN:

3 Figure 4: Model space (1200 km x 160 km x 210 km) with time averaged logarithm of E-field energy density displayed along central slice. Transmitter to the left, vertical polarization. The position of the subsurface slab centered at x=800 km is indicated. The slab has an x-extension of 120 km, total depths of 30 km starting between 1 km and 5 km below the surface in different program runs. Slab width varies between 2 and 60 km in the simulations. The display plane for the following tilt angle result figures cuts the slab vertically at its center position as y-z plane. Subsurface conductivity is σ = 0.01 S/m everywhere with the exception of the slab, where its is 5 S/m. Also within the earth ɛ r = 12 is assumed. Within the atmosphere between 0 and 150 km height a standard ionosphere conductivity profile for night and day conditions (fig. 2) and ɛ r = 1 is used. Figure 5: Left: Tilt angle variation arctan( H z /H y ) (deg) across cut plane at subsurface slab mid position (starting at depth 1 km, width= 6 km as indicated). f = 20 khz. Right: Course of the tilt angle from left to right at the surface. Figure 6: Left: tilt angle variation arctan( H z /H y ) (deg); right: tilt angle variation arctan(h z /H y ) (deg) - no abs values here! -, slab width= 8 km, other data as with fig Results Figures 5 to 7 show typical modeling results through the test slab center in a plane perpendicular to the transmitter direction. As in the far field for vertically polarized waves the magnetic field is horizontal, vertical components indicate disturbances in the ground, so the tilt angle variation across the range in question is an important parameter. Its variation is shown for different slab widths, depths and frequencies. Also undisturbed waves exhibit a free space wave impedance Z = E z /H y of 377 Ohm, which is modified in the presence of underground conducting domains. The results confirm that the VLF method reacts very sensitive to vertical conductivity changes. Having confirmed that our model reproduces very well known results of the VLF method we propose to extend its application by taking into account daily propagation variations. Fig. 11 shows the near surface logarithmic magnetic field density difference without and with slab in place centered at 800 km modeled for night-day terminator distances km from the transmitter. Terminator position at x=900 km for example means that there are ionospheric night conditions (dottet lines in fig. 2) between the transmitter up to 900 km distance and day conditions (continuous lines in fig. 2) for larger distances. We see that for a receiver at x=500 km, which is nearer to the transmitter than the slab, the difference is about zero. For a receiver at x=900 km, that is significantly behind the slab seen from the transmitter, the difference is negative and for a receiver at the slab center (x=800 km), the difference is strongly positive. Stabilization of the signal at these levels occurs when the terminator is half ways between the slab center position and the transmitter. This is at x=400 km - just at the foot point of the one hop ionospheric bounce region of the VLF waves. We conclude: recording the daily course of the magnetic field density of a specified transmitter immediately below the surface on a grid of receiver sites allows for mapping subsurface conductivity structures within the grid range using the FEA model for inversion. Resolution is of the order of the VLF wavelength. ISSN: ISBN:

4 Figure 7: Same as fig. 5, but slab starting at depth 5 km. Identification possible with caution. Figure 9: Same as fig. 7, but transmitter frequency f = 200 khz. Identification at the critical limit. Figure 8: Tilt angle (deg) course for different slab widths: 2 km, 20 km, 60 km. Slab starting at depth 1 km. f = 20 khz. 5 Conclusion Our 3D FEA model takes into account a significant part of the ionosphere important for the propagation of the VLF waves. It is able to reproduce the known variations of tilt angle and impedance across conductive subsurface structures for inversion purposes and additionally can exploit the information that can be gained by recording simultanously from different receiver sites while propagation conditions within the earth-ionosphere cavity vary day and night over. Future work will include the modeling of anisotropic conductivity properties of subsurface domains [3] and solving the time dependent Maxwell equations in the model space described by using lightning strokes as transient sources [5], [9]. These natural sferic signals have their typical frequency maximum around 10 khz and are also successfully used to characterize subsurface structures (Audio-Frequency EM methods). Figure 10: Variation of the impedance Z = E z /H y across the structure zone and along the surface (logarithmic color display) exhibiting information about the slab position. All other data as with fig. 5. Within the not or only marginally conducting atmosphere below the ionosphere free space wave impedance (Z 0 = 377 Ω) is approximated. Figure 11: Surface logarithmic magnetic field density difference without and with slab centered at 800 km for terminator distances km from transmitter (f = 20 khz). ISSN: ISBN:

5 References: [1] Pedersen, L. B., Persson, L., Bastani, M., Bystrom, S., Airborne VLF measurements and mapping of ground conductivity in Sweden, Journal of applied geophysics vol. 67, no 3, 2009, pp [2] Beamish, D., Three-dimensional modelling of VLF data, Journal of Applied Geophysics 39, Issue 2, 1998, pp [3] Simpson, F., Resistance to mantle flow inferred from electromagntic strike of the Australian upper mantle, Nature 412, 2001, pp [4] Toffelmier, D.A., Tiburczy, J.A., Electromagnetic detection of a 410-km-deep melt layer in the southwestern United States, Nature 447, 2007, pp [5] Schmitter, E.D., Analysing and Classifying VLF Transients, International Journal of Signal Processing (IJSP) 3, 2006, pp [6] Schmitter, E.D., Analysing and Classifying Geomagnetic Activity Data in a Noisy Environment. Proceedings of the 11th WSEAS Int. Conf. on Systems (CSCC07), Agios Nicolaos, Crete, Greece, July 23-25, 2007, pp [7] Schmitter, E.D , Deriving Ionospheric System Parameters from VLF Transmitter Signal Analysis. Proceedings of the 12th WSEAS Int. Conf. on Systems (CSCC08), Heraklion, Crete, Greece, July 22-24, 2008,ID , pp [8] Advisory Group For Aerospace Reasearch and Development (AGARD, NATO), ELF/VLF/LF Radio Propagation and Systems Aspects AGARD Conference Proceedings 529, 1993 [9] Cummer, S.A., Inan, U.S., Bell, T.F., Ionospheric D region remote sensing using VLF radio atmospherics, Radio Science 33, pp , 1998 ISSN: ISBN: