The borehole controlled‐source audiomagnetotelluric response of a three‐dimensional fracture zone

Richard C. West; Stanley H. Ward

doi:10.1190/1.1442457

The borehole controlled‐source audiomagnetotelluric response of a three‐dimensional fracture zone

Geophysics ◽

10.1190/1.1442457 ◽

1988 ◽

Vol 53 (2) ◽

pp. 215-230 ◽

Cited By ~ 6

Author(s):

Richard C. West ◽

Stanley H. Ward

Keyword(s):

Magnetic Fields ◽

Half Space ◽

Fracture Zone ◽

Body Position ◽

Imaginary Component ◽

Model Parameters ◽

Simple Relationship ◽

Real Component ◽

Wave Source ◽

Electric And Magnetic Fields

Approximate theoretical borehole CSAMT profiles of the normalized vertical electric and magnetic fields [Formula: see text] and [Formula: see text] were computed for several models of practical interest using a 3-D MT computer program based on the method of integral equations. [Formula: see text] and [Formula: see text] are the horizontal fields measured at the surface. A conductive tabular prism in a layered and homogeneous half‐space was chosen to simulate a 3-D fracture zone composed of individual, interconnected fractures. Model parameters varied during this study were depth and dip of the tabular body, the conductivity and layering of the half‐space, the frequency of the plane‐wave source, and the separation between the borehole and target. In addition, a model composed of two horizontal prisms was investigated. Decreasing the host conductivity, the depth of the prism, or the separation between the borehole and prism increases the magnitude of the subsurface normalized vertical electric and magnetic fields. Depth to the top of a dipping prism in a half‐space can be determined from the crossover of the profile of the [Formula: see text] real component. Peak amplitudes of the [Formula: see text] profiles provide information about the location of the maximum current density within the prism, which is quite variable for the imaginary component. There is no simple relationship between a small borehole‐to‐prism separation and the separation between the antisymmetric peaks of the [Formula: see text] profiles. Without knowledge of the borehole‐to‐prism separation, the dip of a nonhorizontal prism cannot be determined accurately. However, the down‐dip side of a dipping prism is indicated by the larger peak anomaly in the real component of the profile. The normalized [Formula: see text] anomalies of the conductive prism seem more sensitive to body position and also to variation in the host resistivity than are the normalized [Formula: see text] anomalies, thus making the former parameter more susceptible to geologic noise. The resistivity of the half‐space and overburden and the frequency of the source significantly influence the amplitude and phase of the secondary electric fields. Current channeling is a significant contributor to the response of the prism within a half‐space of even moderate resistivity at frequencies of 10 to 100 Hz. The [Formula: see text] field is little influenced by horizontal layering, so the borehole profiles reflect mainly subsurface inhomogeneities. The two main advantages of this technique are that the signal is much larger than the level of natural‐field noise and data acquisition is rapid because of the high frequency of the source (10–1000 Hz). However, the borehole profiles can be significantly affected by nearby inhomogeneities and by the incident field when the borehole and sensor are not vertically aligned.

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Finite-difference modeling of magnetotelluric fields: Error estimates for uniform and nonuniform grids

Geophysics ◽

10.1190/1.2195991 ◽

2006 ◽

Vol 71 (3) ◽

pp. G97-G106 ◽

Cited By ~ 9

Author(s):

Catherine de Groot-Hedlin

Keyword(s):

Finite Difference ◽

Magnetic Fields ◽

Electric Field ◽

Half Space ◽

Interpolation Method ◽

Discrete Approximations ◽

Nonuniform Grids ◽

Electric And Magnetic Fields ◽

Analytic Expressions ◽

Solution Accuracy

In the finite-difference (FD) method, one solves a set of discrete approximations to continuous differential equations; thus, the solutions only approximate the true values. For the magnetotelluric (MT) method, errors in the electric and magnetic fields computed by the staggered FD method are precisely quantifiable for a model with uniform conductivity. In this case, the errors in the electric and magnetic fields are equal in magnitude but increase with rising node separation. In this paper, I show that errors in MT responses, which rely on ratios of the field values, depend strongly on the method used to interpolate electric field values to the surface where the magnetic field is sampled. Analytic expressions for the FD estimates of the MT responses for a half-space are derived and compared for three different methods of electric field interpolation. The best results are achieved when the electric field values just above and below the surface are interpolated exponentially. For a half-space, the FD estimates of the MT responses are independent of node separation and are precisely equal to the analytic values when the electric field is interpolated exponentially. For models with sharp conductivity contrasts, the errors in the responses derived using this interpolation method increase with rising node spacing but still perform better than other examined interpolation methods. Varying the vertical node separation within a half-space model degrades the solution accuracy. The magnitude of the error depends primarily on the magnitude of the change in vertical node spacing. Lateral variations in the grid spacing do not necessarily yield errors in the FD solutions to the MT equations.

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Orthogonality in CSAMT and MT measurements

Geophysics ◽

10.1190/1.1443483 ◽

1993 ◽

Vol 58 (7) ◽

pp. 924-934 ◽

Cited By ~ 8

Author(s):

David E. Boerner ◽

Ron D. Kurtz ◽

Alan G. Jones

Keyword(s):

Magnetic Fields ◽

Plane Wave ◽

Field Data ◽

Necessary Condition ◽

Far Field ◽

Single Plane ◽

Wave Source ◽

Near Surface ◽

Layered Earth ◽

Electric And Magnetic Fields

The electric and magnetic fields from a single plane‐wave source on a one dimensional (1-D) earth, or a plane‐wave source polarized parallel or perpendicular to strike on a two-dimensional (2-D) earth, are orthogonal. On a layered earth and in the far‐field of a controlled source, the electric and magnetic fields are also orthogonal. Therefore, orthogonality of E and H data is a necessary condition to justify the application of 1-D or 2-D modeling algorithms having a plane wave source. A strict criterion to prove orthogonality, and thus provide a rationale for the choice of interpretation methods, can be defined directly in terms of field data. However, field data acquired in the intermediate and near‐field of any electromagnetic (EM) source are generally not orthogonal, even on a plane‐layered earth. Representing these nonorthogonal data in an orthogonal coordinate system can be misleading, particularly for the minor axis components of the polarization ellipses. Nonorthogonality also arises because of 3-D scattering, with one common example being the electric field response of near surface structure. An example of field data illustrates the nonorthogonality in CSAMT measurements caused by the response of surficial geology. In these EM data, the angle between E and H is a sensitive indicator of geological contacts and faults. Quantitative analysis of these data can be performed with the assumptions of a “bulk” 1-D earth (i.e., orthogonal E and H in the far‐field) and purely galvanic scattering of the EM fields.

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