Method of and Apparatus for Processing Electromagnetic Data

The present invention relates to a method of and an apparatus for processing electromagnetic data, for example obtained by means of marine controlled source electromagnetic sounding.

Marine controlled source electromagnetic (mCSEM) sounding is a technique that can detect offshore hydrocarbon reserves or reserves below inland bodies of water such as lakes. Also known as SeaBed Logging (SBL) (Eidesmo et al., 2002; Ellingsrud et al., 2002), the technique uses a horizontal electric dipole (HED) antenna as a source, emitting an alternating current (AC) typically in the range of 0.01 Hz to 10 Hz. The HED source is towed some 20-4Om above the sea floor while an array of stationary receivers deployed on the sea bottom records the resulting electromagnetic (EM) field. The main principle exploited in mCSEM/SBL surveying is that hydrocarbon saturated reservoirs typically are between 5 and 100 times more resistive than the host sediments. Such a reservoir will guide EM energy over long distances with low attenuation. Where hydrocarbons are present in the subsurface, the electric fields at the receivers at long source-receiver separations will be larger in magnitude than the more-attenuated background electromagnetic fields caused by the host sediments.

In shallow water mCSEM/SBL surveying, the air layer is known to create a problem, namely the source-induced airwave component. As shown in Figure 1 of the accompanying drawings, the airwave component is dominated by the signal component that diffuses upwards from the source 1 to the sea surface 3 and then propagates through the air at the speed of light with no attenuation, before diffusing back down through the seawater column 2 of depth z _b to the sea bottom 4 where it is picked up by the receivers 5. The airwave component is of no particular concern to marine electromagnetic practitioners in the deep water environment due to the two-way attenuation of the signal. Unfortunately, for shallow water depth relative to the target depth and at low frequencies, the airwave signal may be dominant at intermediate to long offsets so that the signal from the subsurface, possibly containing valuable information about a resistive hydrocarbon reservoir, is hardly distinguishable.

The electromagnetic field radiated by the HED source can be considered to consist of two different modes: one transverse electric (TE) mode component and one transverse

magnetic (TM) mode component. The response of the sea water (and the subsurface) to the source signal is generally very different for the TE and TM mode components. The airwave component is known to be predominantly caused by the TE mode component of the source, since the TE mode component is efficiently inductively coupled across the sea water/air interface. In contrast, the TM mode component is known to couple less well across the sea water/air interface, and therefore does not contribute significantly to the airwave component for the finite offsets recorded in mCSEM/SBL surveys.

The airwave contribution was investigated by Chave and Cox (1982) in a numerical model study for mCSEM exploration with a HED source. They pointed out that the effect of the airwave component is important at large offsets, low frequencies or in relatively shallow water depth. However, they did not give any method to compute the airwave effect other than through numerical modeling.

Let the z-axis be positive downwards and let z _s and z _r denote the depths of the source and receivers, respectively. From the work of Wait (1961 ); Banos (1966); Bannister (1984) and King et al. (1992), it is well known that the airwave component shown in Figure 1 at offset r in the radial direction for the water halfspace problem has the asymptotic space domain expression

_H aτ) _ pcosφexp[ik(z _r + z _s )]exp(ik _o r) ^{tr "} 2π _σi r ³ ' ^{{ )}

Here, p is the dipole moment, φ is the azimuth angle, k = (/G^ ₀ O ₁ ) ¹ ' ² is the complex low frequency wavenumber for sea water with conductivity O ₁ , k ₀ = ω(μ ₀ ε ₀ ) ^1/2 ~ 0 is the wavenumber in air, co is the circular frequency, μ ₀ is the magnetic permeability in a vacuum and ε ₀ is the electric permittivity in a vacuum.

Equation 1 was recently used by Constable and Weiss (2006) to demonstrate the behaviour of the airwave. Constable and Weiss (2006) noted that equation 1 describes the propagation (including attenuation) vertically upwards of the source-side signal from the source through the water column to the sea surface. This upward travelling signal at the sea surface induces an airwave component travelling horizontally through

air. The airwave leaks signals into the water column, travelling vertically downward (including attenuation) through the water column to the receiver.

According to a first aspect of the invention, there is provided a method of processing electromagnetic data relating to a region of the earth covered by water and obtained by at least one electromagnetic receiver in response to at least one electromagnetic source, the method comprising providing the electromagnetic data and removing from the electromagnetic data an airwave contribution having a first component propagating without reflection from the at least one source to the at least one receiver and at least one second component whose propagation path from the at least one source to the least one receiver includes at least one vertical portion at at least one of the at least one source and the at least one receiver and which has at least one reflection from at least one of the water surface and the interface between the region and the water.

The airwave contribution may be removed by subtraction.

The at least one second component may comprise a plurality of components having propagation paths at the at least one source with different numbers of reflections. The airwave contribution may be proportional to:

(exp(ikz _s )) (l+Rexp(2ik(z _b -Z _s )))/(l-Rexp(2ikz _b ))

1 when k = (i Op ₀ O ₁ ) ² is the complex wavenumber for water of conductivity σ i, co is the circular frequency, μ ₀ is the magnetic permeability of a vacuum, z _b is the depth of the water, z _s is the depth of the source, R = - ) / (V^ ⁺ V^T ) ' ^{s tne} reflection coefficient at the interface between the region and the water, and σ ₂ is the conductivity of the region at the interface.

The at least one second component may comprise a plurality of components having propagation paths at the at least one receiver with different numbers of reflections. The airwave contribution may be proportional to:

(exp(ikz _r )) (l+Rexp(2ik(z _b -z _r )))/(l-Rexp(2ikz _b ))

where k = (i ω μ ₀ O ₁ ) is the complex wavenumber for water of conductivity O ₁ , ω is the circular frequency, μ _o is the magnetic permeability of a vacuum, z _b is the depth of the water, z _r is the depth of the receiver, ) ' ^{s tne} reflection coefficient at the interface between the region and the water, and O ₂ is the conductivity of the region at the interface.

Let the vector x=(x,y,z) denote the Cartesian coordinate system. The airwave contribution may be proportional to

2πr ³ (σ (x _r )σ (xJ) ² with receiver-side reflection-reverberation function

and source-side reflection-reverberation function

where p is the source dipole moment, φ is the azimuth angle of the receiver relative to the source, 1/r ³ takes into account the geometrical spreading associated with the HED source at location x _s , F(x _s ) is a function that accounts for the upward field propagation of the source induced airwave from the source to the sea surface, e.g., F(X ₅ )= exp(/ J _g ¹ dzk(x _s ,y _s ,z)

F(x _r ) is a function that accounts for the downward field propagation of the source induced airwave from the sea surface to the receiver at location x _r , e.g.,

R _r and R ₅ are reflection coefficients at the receiver and source side, respectively. The seabed conductivity σ ₂ may be obtained in several way, for instance by inversion of

EM data or calculated from data as - iμ ₀ ω(Hj / Ei) ² , when Hj and Ei are orthogonal components of the horizontal electric and magnetic fields induced by natural primary sources.

The electromagnetic data may be controlled source electromagnetic data.

The at least one source may comprise a horizontal electric dipole.

The method may comprise analysing the processed data for hydrocarbon reserves.

According to a second aspect of the invention, there is provided a drilling method comprising performing a method as defined above and controlling drilling in accordance with the result of the analysis.

According to a third aspect of the invention, there is provided a production method comprising performing a method as defined above and controlling hydrocarbon production in accordance with the result of the analysis.

According to a fourth aspect of the invention, there is provided an apparatus arranged to perform a method according the first aspect of the invention.

According to a fifth aspect of the invention, there is provided a computer program arranged to control a computer to perform a method according to the first aspect of the invention.

According to a sixth aspect of the invention, there is provided a computer-readable medium carrying a program according to the fifth aspect of the invention.

According to a seventh aspect of the invention, there is provided transmission of a program according to the fifth aspect of the invention.

According to an eighth aspect of the invention, there is provided a computer containing or programmed by a program according to the fifth aspect of the invention.

It is thus possible to provide a technique which allows the effects of the airwave to be substantially reduced or removed from electromagnetic data, for example obtained by mCSEM techniques. Detection or monitoring of hydrocarbon reserves may thus be made more reliable.

The invention will be further described, by way of example, with reference to the accompanying drawings, in which:

Figure 1 is a cross-sectional diagram illustrating an mCSEM data-gathering arrangement and an airwave;

Figures 2(a) to 2(f) are diagrams illustrating reflections and reverberations of a field from a HED source inducing an airwave;

Figures 3(a) to 3(c) are diagrams illustrating a downgoing field from the airwave at a receiver with reflections and reverberations;

Figures 4(a) to 4(c) are diagrams illustrating three models used during airwave analysis;

Figures 5 and 6 are graphs illustrating amplitude in volts per metre and phase in radians of a radial component of electric fields against source-receiver separation

(offset) in kilometres for different source and receiver depths for a water halfspace model;

Figures 7 to 9 are graphs similar to Figures 5 and 6 for a finite water column model.

Figure 10 is a graph similar to Figures 5 and 6 for models with and without a hydrocarbon reservoir;

Figure 11 is a graph of normalised amplitude of the radial electric fields against offset in kilometres;

Figure 12 is a graph similar to Figures 5 and 6 of models with and without a reservoir after subtracting the effect of the airwave; and

Figure 13 is a graph similar to Figure 1 1 after subtracting the effect of the airwave.

In the following description a generalization of the airwave component when the water layer has finite thickness z _b is provided. In particular, an asymptotic, space domain extension of the airwave expression is provided that includes the effect of the seabed.

It is believed that the vertically upward travelling TE mode from the source, in addition to inducing an airwave component at the sea surface, sets up a reverberation sequence of signals between the sea surface and the sea bottom. Each time a signal in the reverberation sequence hits the surface, a new airwave component is induced. Likewise, the vertically downgoing TE signal from the source to the seabed sets up a reverberation sequence, in which each signal induces an airwave component at the sea surface. Furthermore, on the receiver side, the initially vertically downgoing signal will reverberate between the seabed and the sea surface.

A formula for the generalised airwave is derived, in the special case that the seabed conductivity is constant and the seabed depth is the same at the source and receiver sides. Anyone skilled in the art of modelling will recognize that these two assumptions can be relaxed, and will lead to the results presented previously. The source induced airwave is modified due to source side and receiver side seabed reflections and water column reverberations. The generalised airwave response of a water layer with varying thickness is then numerically compared with the response obtained from full modeling of Maxwell's equations. For large offsets where the airwave dominates the water layer due to a HED source, the generalised asymptotic airwave modeling is an excellent approximation to the exact airwave. A numerical example is subsequently presented where the airwave dominates the measured electric field amplitude so that a resistive layer below the seafloor cannot be detected. After modeling and subtraction of the airwave from the electric field, however, the resistive layer can straightforwardly be mapped from the data.

Figures 2a to 2f illustrate how the source induced airwave is modified due to the seabed reflection and its associated reverberations. The seabed 4 at depth z _b has conductivity σ ₂ . Figure 2a shows the upward diffusing signal from the source 1 to the sea surface 3 at z = 0. Asymptotically, the signal at the sea surface 3 is represented by

exp(ikz _s ) .

Figure 2d shows that the downward diffusing signal from the source 1 to the seabed 4 is reflected into an upward travelling signal which induces an airwave component at the sea surface 3. This water column signal is represented asymptotically as

exp(ikz _s )Rexp[2ik(z _b -z _s )],

where R = ( _λ /σ7- _λ /σ7)/( _λ /σ7 + Is the seabed reflection coefficient for a vertically travelling plane wave TE mode and z _s is the source depth. Figures 2b and 2c show that the upgoing source signal depicted in Figure 2a can reverberate once and twice before the airwave is induced. In mathematical terms, the contributions at the sea surface are respectively:

exp(ikz _s )Rexp(2ikz _b ), and exp(ikz _s )R ² exp(4ikz _b ).

Likewise, Figures 2e and 2f show that the initially downgoing source signal depicted in Figure 2b can reverberate once and twice before the airwave is induced. The terms are, respectively:

exp(ikz _s )Rexp[2ik(z _b -z _s )]Re xp(2ikz _b ), and

exp(ikz _s )Re xp[2ik(z _b - z _s )]R ² exp(4ikz _b ).

This process continues in principle an infinite number of times, so that the total signal that arrives at the sea surface to induce the airwave asymptotically is:

exp(ikz _s ){1 + Re xp[2ik(z _b - z _s )]}[1 + Re xp(2ikz _b ) + R ² exp(4ikz _b ) + ...]

= exp(ikz _s )S, (2)

where _s _1 + Rexp[2ik(z _b -z _s )] 1-Rexp(2ikz _b ) (3)

is a filter that represents the source-side modification upon the airwave due to the seabed.

In a similar manner, Figures 3a to 3c how the airwave is modified at the receiver side, due to the seabed reflection and its associated reverberations. Figure 3a shows that the airwave hits the receiver 5 at depth z _r , then is reflected at the seabed 4 and returns upwards to the receiver. The process is described asymptotically as:

exp(ikz _r )[1 + Rexp[2ik(z _b - z _r )]].

Figures 3b and 3c account for one and two reverberations in the water column, described mathematically as:

exp(ikz _r )[1 + Rexp[2ik(z _b - z _r )]]Rexp(2ikz _b ),

and

exp(ikz _r )[1 + Rexp[2ik(z _b - z _r )]]R ² exp(4ikz _b ),

respectively. Taking into account an infinite number of reverberations, the receiver side reflection and reverberation sequence becomes

exp(ikz _r )R,

(4) where

_R _ 1 + Re xp[2ik(z _b _z _r )] 1 - Re xp(2ikz _b )

(5)

is a filter that represents the receiver side modification upon the airwave due to the seabed.

The airwave including the reverberations on the source and receiver side is then given by

_E (a,r ₊ rev) _{= E} <aιr) _{S R} _ ^

The derivation of equation 6 is based on the conjecture that the HED source in the water column will set up a reflection and reverberation sequence of vertically travelling modes, where each TE mode component at the sea surface 3 will asymptotically induce airwave components. At the receiver side, the airwave components reflect and reverberate in a similar manner to that on the source side.

In the following, equation 6 is verified numerically.

First we demonstrate the validity of equation 1 and calculate the airwave response for the seawater half-space model bounded by air (Figure 4a). Second, we verify equation 6 by taking into account the effect of a finite water layer (Figure 4b). The verification is achieved by comparing the responses given in equations 1 and 6 with full numerical modeling of Maxwell's equations for layered media, as described in Løseth (2000). An HED source directed in the radial direction with a frequency of 0.25 Hz and a unit dipole moment is used for all of the models. The seawater conductivity is O ₁ = 3.33

S/m. The receivers are situated on the seabed along a line in the same plane as the source.

Figure 5 shows graphs of amplitude and phase of the radial component of the electric field versus source-receiver separation for the water half-space model. The source and receiver depths are z _s = 5m and z _r = 10 m below the interface, respectively. The dashed curve gives the airwave component modeled according to equation 1 , and the dotted curve shows the response obtained from full EM modeling. The solid curve gives the amplitude of the difference between the signals. Figure 6 compares modeling in the case where the receivers are moved to a depth of z _r = 500 m below the sea surface. The source depth is now 25 m above the receiver level. Generally, where the airwave component is the dominant mode, equation 1 describes the airwave for the water half-space model with sufficient accuracy. In Figure 5, the airwave expression in equation 1 is calculated for a relatively shallow receiver depth of 10 m. A good approximation to the numerically obtained results is given for offsets greater than 1-2 km. When the airwave expression is calculated for 500 m receiver depths (see Figure 6), equation 1 shows good agreement with the responses obtained from full numerical

modelling of the electric field for offsets greater than 3-4 km. In this case, the direct field is probably more influential than the airwave component at offsets less than about 3 km.

Now, we consider the model shown in Figure 4b with a finite water column. The source, receiver, and seabed depths are varied with the three choices: z _s = 5 m, z _r = z _b =10 m; z _s = 75 m, z _r = z _b = 100 m; and z _s = 475 m, z _r = z _b = 500 m. The seabed conductivity is σ ₂ = 1 S/m. Figures 7 to 9 show graphs of amplitude and phase of the radial component of the electric field versus source-receiver separation for the three cases listed above. The dot-dashed and dotted lines compare modeling results according to the generalized airwave in equation 6 with full numerical modeling. For comparison, we also display the airwave response for the water half space according to equation 1 (dashed line). The presence of the seabed has significant effect on the airwave response. The solid curve shows the amplitude of the difference between the full electric field and the generalized airwave. The generalized expression for the airwave in equation 6 gives an excellent approximation to the airwave response derived from full numerical modeling. This can be seen from the overlap of the dotted and dot- dashed curves from offsets greater than 4-5 km, where the airwave starts to dominate the modeled response when the water depth is 10 m and 100 m, respectively. When the water depth is 500 m, the airwave component totally dominates for offsets greater than 6-7 km. For shorter offsets, the direct field from the source and the lateral field along the seabed are dominant. The phases derived from equations 1 and 6 are almost equal for all three water depths, which is consistent with the nearly instantaneous propagation of the airwave. Note that the difference between the amplitude of the generalized airwave (dot-dashed curve) and of the air airwave for a water half-space (dashed curve) becomes smaller for increasing water depths, indicating that the reverberations in the water layer have less effect in deeper waters.

The airwave problem in marine CSEM data analysis and interpretation can be illustrated by using the simple 1 D model in Figure 4c. From top to bottom, the model consists of five layers: a nonconductive air layer, a 100-m-thick layer of seawater, a

2000-m-thick sediment layer with a conductivity of 1 S/m, a 100-m-thick resistive layer

(0.02 S/m) that can be a hydrocarbon-saturated reservoir, and a sediment half-space with a conductivity of 1 S/m. The model in Figure 4c is normalized with the reference model in Figure 4b to see if there is an enhancement in the response because of the presence of a resistive layer. Figure 10 shows graphs of the amplitude and phase of

the radial component of the electric field versus offset for the model with a reservoir (dotted curve) and the reference model without a reservoir (solid curve), together with the generalized airwave (dot-dashed curve). The depth of the water layer is shallow, so the airwave dominates the received signal for offsets greater than about 3 km. This is seen from both the amplitude and phase curves. The phase is constant for offsets greater than about 4 km, showing where the airwave dominates the field measurements. As a consequence, the reservoir model and the nonreservoir model are hardly distinguishable for all offsets. Because the electric amplitude varies over a large range with offset, it is useful to consider the normalized electric amplitude. The curve in Figure 1 1 displays the normalized electric amplitude, which is close to unity for all offsets. Therefore, a geophysical interpreter cannot determine reliably whether a resistive hydrocarbon-saturated layer is present in the subsurface. This example clearly demonstrates the problem of the airwave in shallow water.

Various data processing schemes have been proposed to separate the airwave effect from the mCSEM/SBL field measurements. The simplest may be to include the air layer in the interpretation and inversion. The effect of the airwave can also be suppressed by choosing a frequency which gives the least airwave contribution at the given depth. It is also possible to decompose the EM signal into upgoing and downgoing constituents, where the upgoing component contains information about the subsurface whereas the airwave mode lies in the downgoing component (Amundsen et al., 2006). Another suppression technique is to model the effect of the airwave in the water layer and then subtract it from the collected data (Lu et al., 2005).

In the case where the seabed conductivity can be determined, the technique described hereinbefore may be used to model and subtract the airwave effect from the recorded electric field, as suggested by Lu et al. (2005), to enhance the response from the reservoir. The solid curves in Figure 12 show the amplitude and phase of the electric field versus offset for the five-layer reservoir model discussed above, after modelling according to equation 6 and subtracting the airwave effect. Amplitude and phase of the reference electric field, obtained by subtracting the airwave effect from the electric-field data from the nonreservoir model, are displayed by the dashed curves. Observe the large separation of the curves in the 4-10 km offset range, indicating a significant signal from the resistive layer buried 2 km below the seabed. The lack of separation between the reservoir model and the reference model data curves for small offsets is related to the low attenuation of the direct field and the lateral field along the seabed, because

these two signals dominate the field measurements at offsets less than 3 km. This is illustrated further in Figure 13, which displays the normalized electric amplitude response when the airwave is subtracted. The effect of the reservoir on the response now becomes significant.

The same principle as described hereinbefore may be used to model and subtract the airwave from the magnetic field. The method is the same and results in only a minor modification of the equation for modeling the airwave.

The airwave modeling for the electric field is given in equation (6). The airwave modeling for the magnetic field is straightforward to derive using the same principle. The total air wave response at the receiver location x _r for the source at x _s is

H< ^airtot) (x _rJ x _s ) = H< ^air) (x _r ,Xs)R'(x _r )S(x _s ) (7) where u _{(aιr)/v v λ} _ipcosφF(x _r )exp(ik ₀ r)F(x _s ) ^π φ \x _r >x _s ⁾ - i

2πr ³ [k(x _r )k(x _s )] ²

and

1-R _r exp[2iI ^Z z ^b _r ^(Xr ' ^yr) dzk(x _rJ y _rJ z)

R ¹ (Xr) =

1-R _r exp[2iJ* ^>(x '- ^y ' ⁾ dzk(x _r> y _r> z)

is the receiver-side reflection-reverberation function for the magnetic field.

Instead of using the seabed conductivity σ ₂ , another possibility is to use the apparent conductivity σ _a which can be calculated by the magnetotelluric (MT) method. In MT, orthogonal components of the horizontal electric and magnetic fields induced by natural primary sources are measured simultaneously as a function of frequency. Apparent conductivity as function of frequency is calculated as

The airwave contribution removal technique described herein may be used on electromagnetic data, for example obtained by means of mCSEM techniques. For

example, a plurality of receivers are disposed on the seabed above the region which is to be explored. One or more sources, such as horizontal electric dipoles, are towed in the water above the receivers while being actuated and the resulting measurements made by the receivers are stored for subsequent processing.

The processing comprises or includes a step for removing or at least reducing the contribution from the airwave recorded at each receiver in respect of the or each source. An optional preliminary step comprises normalisation as described hereinbefore. The airwave contribution is then determined in accordance with equation 6 and optionally in accordance with equation 7. In particular, the airwave contribution is at least partially removed by subtracting the contribution determined in accordance with these equations. The processed data may then be further processed and analysed in order to provide information about any hydrocarbon deposits or reservoirs in the region of interest. If appropriate, MT measurements as described hereinbefore may be used in order to determine apparent conductivity in accordance with equation 8 so as to determine the reflection coefficient at the lower interface of the water column. This may be used in determining airwave contribution.

This technique may be used in circumstances where the airwave contribution is problematic. For example, this technique may be used for relatively shallow water columns in relation to the frequency of the electromagnetic waves used during measurement. The resulting information about hydrocarbon reserve may then be used for a variety of purposes depending on the application. For example, the processed data may be used to identify new hydrocarbon reservoirs and to assess the quantities of hydrocarbons present in such reservoirs together with their locations. The drilling of wells may then be controlled or directed in order to extract, or optimise the extraction of, the hydrocarbons. For known reservoirs, the quantity of hydrocarbons remaining during production may be determined and used to control production, for example to optimise draining of a reservoir.

In practice, these processing techniques are performed by suitably programmed computers. A standard type of computer, for example of the type typically used for processing hydrocarbon exploration data, may be used and the processing techniques may be encoded as suitable application programs for controlling such computers to perform the processing techniques.

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