Title of Invention	A METHOD FOR DETERMINING THE EARTH RESPONSE TO AN ELECTROMAGNETIC SIGNAL
Abstract	A method for removing the effects of an airwave from marine electromagnetic data comprising providing an electro-magnetic source and at least one receiver in the water; measuring the electromagnetic response at a first source-receiver separation; determining a scaled version of the airwave response at a source-receiver separation where the earth response is negligible and using the scaled airwave response to determine the earth response measured at the first separation. Using this method, an improved estimate of the earth"s response can be achieved.

Title of Invention

A METHOD FOR DETERMINING THE EARTH RESPONSE TO AN ELECTROMAGNETIC SIGNAL

Abstract

A method for removing the effects of an airwave from marine electromagnetic data comprising providing an electro-magnetic source and at least one receiver in the water; measuring the electromagnetic response at a first source-receiver separation; determining a scaled version of the airwave response at a source-receiver separation where the earth response is negligible and using the scaled airwave response to determine the earth response measured at the first separation. Using this method, an improved estimate of the earth"s response can be achieved.

Full Text	IMPROVEMENTS IN MARINE KM EXPLORATION The present invention relates to a method for removing the airwave from marine electromagnetic data. In particular, the invention relates to a technique for reducing the impact of the airwave in marine based multi-channel transient electromagnetic (MTEM) measurements. Background of the Invention Porous rocks are saturated with fluids. The fluids may be water, gas, or oil, or a mixture of all three. The flow of current in the earth is determined by the resistivities of such rocks, which are affected by the saturating fluids. For instance, brine- saturated porous rocks are much less resistive than the same rocks filled with hydrocarbons. By measuring the resistivity of geological formations, hydrocarbons can be detected. Hence, resistivity measurements can be made in an exploration phase to detect hydrocarbons prior to drilling. Various techniques for measuring the resistivity of geological formations are known, for example time domain electromagnetic techniques, as described in WO 03/023452, the contents of which are incorporated herein by reference. Conventionally, time domain electromagnetic investigations use a transmitter and one or more receivers. The transmitter may be an electric source, that is, a grounded bipole, or a magnetic source, that is, a current in a wire loop or multi-loop. The receivers may be grounded bipoles for measuring potential differences, or wire loops or multi-loops or magnetometers for measuring magnetic fields and/or the time derivatives of magnetic fields. The transmitted signal is often formed by a step change in current in either an electric or magnetic source, but any transient signal may be used, including, for example, a pseudo-random binary sequence. Measurements can be taken on land or in an underwater environment. Figure 1 shows a view of a typical setup for transient electromagnetic marine surveying. This has a bi-pole current source with mid-point xs on or near the sea floor for transmitting a transient current between two electrodes. The time function of the current might be a simple step change in current or a more complicated signal such as a pseudo-random binary sequence. The response of the earth-water system is measured by a line of bi-pole receivers on or near the sea floor, each receiver characterised by its mid-point position xr and measuring the potential difference between a pair of electrodes. All the electrodes are essentially in the same vertical plane. In use, the electromagnetic signal generated by the source of Figure 1 can follow three transmission paths to the receiver electrodes, these being directly through the earth, directly through the water, and via the water through the air and back through the water again. The signal transmitted by this third path is known as the airwave. In deep water, the airwave has a negligible impact. In contrast in shallow water, the signal (hat is transmitted through the water is negligible, but the airwave can have a significant impact and so make interpretation of the data difficult. Summary of the Invention According to one aspect of the present invention, mere is provided a method for removing the effects of an airwave from marine electromagnetic data comprising providing a source and at least one receiver in the water; measuring the electromagnetic response at a first source-receiver separation; determining a scaled version of the airwave response at a source-receiver separation where the earth response is negligible and using the scaled airwave response to determine the earth response measured at the first separation. The step of determining the scaled airwave may involve measuring or estimating the airwave response. For an impulsive source current, the airwave response decays approximately as the cube of the source-receiver separation at separations large compared with the water depth, whereas the response of the component travelling directly through the earth decays approximately as the fifth power of the source-receiver separation. At very large offsets, therefore, the airwave dominates the total response. Hence, by measuring the electromagnetic response at a large source-receiver separation where the earth response is negligible, a measure of the airwave at that source receiver separation can be determined. This is a scaled version of the airwave response at the first source-receiver measurement separation, and can be used to allow removal of the airwave from the measured data and consequently a more accurate measure of the earth response at the first source-receiver separation. Using the scaled airwave response to determine the earth response may involve finding an inverse filter f(t) of the scaled airwave response a(t); convolving the inverse filter f(t) with the measured data x(t) to compress the airwave to an impulse; removing the airwave impulse from the result of the convolution with the air wave data and convolving the result with the scaled determined airwave a(t) to recover the earth response without the airwave. Preferably, the source is a current bi-pole or a magnetic loop. Preferably, the receiver is a bi-pole receiver or a magnetic loop. Preferably, the source and receiver are located on or near the seabed. The electromagnetic measurements are transient electromagnetic measurements; that is, the response to the input signal at the source must have reached essentially steady state before the measurement is complete. Preferably, the larger source-receiver separation is approximately five or more times greater than the shorter separation. Ideally, both source-receiver separations are at least five times greater than the depth of the water. The larger source-receiver separation is selected so that the earth response measured at the receiver is substantially zero. According to another aspect of the present invention, there is provided a computer program, preferably on a computer readable medium or data carrier, for removing the effects of an airwave from marine electromagnetic data as measured by at least one source and at least one receiver, the computer program having code or instructions for using an airwave response at a source-receiver separation where the earth response is negligible to allow removal of an airwave response in measurements at a shorter source-receiver separation, thereby to allow the earth response to be determined. Preferably, the larger separation is approximately five or more tiroes greater than the shorter separation. Preferably, the larger separation is selected so that the earth response measured at the receiver is substantially zero. Preferably, the program has code or instructions for subtracting the determined airwave from the measurement at the shorter separation. According to yet another aspect of the invention, there is provided a system for deterrnining the earth response to an electromagnetic signal using an electromagnetic source and at least one receiver in water, the system being adapted to measure the electromagnetic response at a first source-receiver separation; determine the airwave response or a scaled version thereof at a source-receiver separation where the earth response is negligible and use the determined airwave response to determine the earth response measured at the first separation. The system may be adapted to use the airwave response to determine the earth response involves finding an inverse filter f (f) of the scaled airwave response a(t); convolve the filter f(t) with the measured response at the first source-receiver separation to provide a result that includes an airwave impulse; remove the airwave impulse from the result of the convolution and convolve the remainder with the determined airwave response a(t) to recover the earth response at the first source- receiver separation without the airwave. A system may be adapted to determine the earth response by measuring or estimating the airwave response. The larger separation may be approximately five or more times greater than the shorter separation. Both separations may be at least five times greater than the depth of the water. The larger separation may be selected so that the earth response measured at the receiver is substantially zero. The source may be a current bi-pole or a magnetic loop. The receiver may be a bi- pole receiver or a magnetic loop. The source and receiver may be located on or near the seabed. According to still another aspect of the present invention, there is provided a method of measuring an electromagnetic response, the method comprising positioning an electromagnetic source and at least one electromagnetic receiver underwater; transmitting an electromagnetic signal from the source to the receiver, wherein the transmitted signal comprises an earth component and an airwave component, and the receiver is positioned relative to the source so that the measured response is substantially due to the airwave. In any aspect of the invention, the transmitted signal may be formed by a step change in current in either an electric or magnetic source, although any transient signal may be used, including, for example, a pseudo-random binary sequence. Brief Description of the Drawings Various aspects of the invention will now be described by way of example only and with reference to the accompanying drawings, of which: Figure 2 is a model of the system of Figure 1; Figure 3 shows an impulse response at 2 km for the arrangement of Figure 2 in which the earth resistivity is 1 ohm-m; Figure 3(a) shows the response out to 9s, and Figure 3(b) shows it out to Is; Figure 4 shows the impulse response at 10 km offset for a lohnv-m half-space beneath 100 m of water, where the dipole source and receiver are on the sea floor; Figure 4 (a) shows the response out to 9 s, and Figure 4 (b) shows it out to 1 s; Figure 5 shows the marine impulse response, the earth impulse response and the airwave for a 2 km offset measurement, and Figures 6(a) and (b) show the result of removing the airwave from the impulse responses of Figure 3. Detailed Description of the Drawings The present invention provides a method for removing the effects of an airwave from shallow water marine electromagnetic data. The invention will be illustrated using the model of Figure 2, which shows a seawater layer of depth d and resistivity pw overlying a homogeneous isotropic halfspace. The dipole source is on the sea floor and the in-line electric field is calculated at a receiver position at some offset r from it on the sea floor. For the sake of example, it will be assumed that the water layer is 100 m deep and has a resistivity of 0.3 ohm-m, and the half space has a resistivity of lohm-m. Figure 3 shows an impulse response at 2 km for the arrangement of Figure 2. Figure 3(a) shows the response out to 9 s, and Figure 3(b) shows it out to 1 s. A sharp initial peak occurs at 0.008 s and has an amplitude of 1.82E-10 V/m/s. This is the airwave. This has a finite rise time to the peak and a long tail. There is a second much broader peak at about 0.45 s with an amplitude of 2.4E-11 V/m/s. This is caused by the earth response. The objective is to separate the airwave and the earth impulse response. At a given offset and after deconvolution for the system response, the impulse response data, which are causal, can be expressed as: in which a(t) is the air wave and g(t) is the earth impulse response, with g(0) = 0. Suitable deconvolution techniques are described for example by Wright, D., et al in the article Hydrocarbon detection and monitoring with a multichannel transient electromagnetic (MTEM) survey: The Leading Edge, 21, 852-864. The airwave is expected to be minimum-phase. By this it is meant that without the water the airwave is an impulse and the propagation effects in the water must be factors involving decaying exponentials, which are minimum-phase. An estimate a(t) of the air wave is assumed such that This is an estimate of the shape, but the exact airwave amplitude A is not known. Next a filter f(t) has to be found, such that in which the asterisk denotes convolution and δ(t) is the impulse function: As mentioned above a(t) and hence a(t) are expected to be minimum-phase. Therefore the inverse f(t) is causal, realizable and minimum-phase; that is, it exists only for t ≥ 0, and it has finite amplitude. Convolving the filter f (t) with the data yields Now the airwave is removed by considering only t > 0, so that: This result can then be convolved with a(t): This allows the earth impulse as measured to be recovered, but without the airwave. This is what is needed, and it turns out that the unknown amplitude factor A is irrelevant. Hence, by merely having an estimate or measure of the shape of the airwave, the earth impulse can be determined. Because of the presence of noise, an exact inverse of a(t) cannot be used. First equation (1) is re-written to include the noise: Then equation (2) is modified to define a new filter f1(t), such that in which d(t) is a band-limited impulse whose integral is unity, for example a Gaussian, of the form d(t) - αexp(-πα2t2) with α a frequency close to the highest frequency of interest in the data, and t is a time delay introduced to make /,(r) causal. The integral of d(t) is 1. Convolving this filter with the data yields The value of α is chosen to be as large as possible but not so large that the high frequency components of the noise are amplified too much. Then Apart from the known time delay t this is what is desired, plus noise. The time delay can easily be removed. The shape of the airwave can be estimated by looking at an offset that is large compared with this offset and where the attenuation of the earth response is relatively high. It is suspected that the shape of the airwave is invariant with offset for a 1-D earth - beyond a certain offset ~ and the hypothesis is that an almost pure airwave could be measured, if the offset is large enough and the time window restricted. This gives an estimate of the shape of the airwave, which according to the method described above would allow the effects of the airwave at the measurement source- receiver separations to be removed. Figure 4 shows the impulse response at 10 km offset for a lohm-m half space beneath 100 m of water, where the dipole source and receiver are on the sea floor. Figure 4 (a) shows the response out to 9 s, and Figure 4 (b) shows it out to 1 s. The sharp initial peak occurs at 0.008 s and has an amplitude of 1.46E-12 V/m/s. There is no discernible second peak. It should be noted that the peak of the airwave occurs at exactly the same time as for the 2 km impulse response. Figure 5 shows the marine impulse response, the earth impulse response and the airwave for a 2 km offset measurement. The earth impulse response was obtained according to the scheme described above; the airwave was obtained by subtracting the. earth impulse response from the marine impulse response. A measure of the quality of this result is to compare the recovered impulse response with the analytic function: the impulse response of a lohm-m half space at an offset of 2 km. Figure 6 shows the result of removing the airwave from the impulse responses shown in Figure 3. This is very similar to the analytic function for the impulse response of a lohm-m half space. In particular the time and amplitude of the peak of the two functions are in close agreement. The present invention provides a very simple and effective technique for removing the airwave from measured MTEM data. This can be summarised as follows: estimate the shape of the airwave using an airwave at a large source-receiver separation and find a filter f(t) based on the estimated airwave. This filter is then convolved with the measured data x(t). The result of this is very messy data, but there is a very sharp peak at time t = t. This is the airwave. The airwave peak is then sliced out. The remaining data is returned to its original state by convolving it with the scaled airwave a(t). This operation undoes the effect of convolving with the filter f(t). The result is the original data, i.e. the earth response, without the airwave. The data captured may be processed in accordance with the invention using any suitable hardware or software. A skilled person will appreciate that variations of the disclosed arrangements are possible without departing from the invention. Accordingly the above description of the specific embodiment is made by way of example only and not for the purposes of limitation. It will be clear to the skilled person that minor modifications may be made without significant changes to the operation described. Claims 1. A method for determining the earth response to an electromagnetic signal using a source for transmitting the electromagnetic signal to at least one receiver in water, the method comprising; using an electromagnetic response measured at a first source-receiver separation; determining the airwave response or a scaled version thereof at a source-receiver separation where the earth response is negligible and using the determined airwave response to determine the earth response measured at the first separation. 2. A method as claimed in claim 1 wherein using the airwave response to determine the earth response involves finding an inverse filter f (t) of the determined airwave response a(t); convolving the filter f (t) with the measured response at the first source-receiver separation to provide a result that includes an airwave impulse; removing the airwave impulse from the result of the convolution and convolving the remainder with the determined airwave response a(t) to recover the earth response at the first source-receiver separation without the airwave. 3. A method as claimed in any of the preceding claims wherein the step of determining involves measuring or estimating the airwave response. 4. A method as claimed in any of the preceding claims wherein determining the airwave response involves estimating its shape. 5. A method as claimed in any of the preceding claims wherein the larger separation is approximately five or more times greater than the shorter separation. 6. A method as claimed in any of the preceding claims wherein both separations are at least five times greater than the depth of the water. 7. A method as claimed in any of the preceding claims wherein the larger separation is selected so that the earth response measured at the receiver is substantially zero. 8. A method as claimed in any of the preceding claims wherein the source is a current bi~pole or a magnetic loop. 9. A method as claimed in any of the preceding claims the receiver is a bi-pole receiver or a magnetic loop. 20. A method as claimed in any of the preceding claims comprising locating the source and receiver on or near the seabed. 11. A method as claimed in any of the preceding claims comprising measuring the electromagnetic response at the first source-receiver separation 12. A system for determining the earth response to an electromagnetic signal using an electromagnetic source and at least one receiver in water, the system being adapted to measure the electromagnetic response at a first source-receiver separation; determine the airwave response or a scaled version thereof at a source-receiver separation where the earth response is negligible and use the determined airwave response to determine the earth response measured at the first separation. 13. A system as claimed in claim 12 adapted to use the airwave response to determine the earth response involves finding an inverse filter f(t) of the determined airwave response a (t); convolve the filter f(t) with the measured response at the first source-receiver separation to provide a result that includes an airwave impulse; remove the airwave impulse from the result of the convolution and convolve the remainder with the determined airwave response d(t) to recover the earth response at the first source-receiver separation without the airwave. 14. A system as claimed in claim 12 or claim 13 that is adapted to determine the earth response by measuring or estimating the airwave response. 15. A system as claimed in any of claims 12 to 14 wherein the larger separation is approximately five ox more times greater than the shorter separation. 16. A system as claimed in any of claims 12 to 15 wherein both separations are at least five times greater than the depth of the water. 17. A system as claimed in any of claims 12 to 16 wherein the larger separation is selected so that the earth response measured at the receiver is substantially zero. 18. A system as claimed in any of claims 12 to 17 wherein the source is a current bi-pole or a magnetic loop. 19. A system as claimed in any of claims 12 to 18 wherein the receiver is a bi-pole receiver or a magnetic loop. 20. A system as claimed in any of claims 12 to 19 wherein the source and receiver are located on or near the seabed. 21. A computer program, preferably on a computer readable medium or data carrier, and/or computer program product and/or a processor for processing marine electromagnetic data measured by at least one source and at least one receiver to remove the effects of an airwave, wherein the computer program/product/processor has code or instructions for using an airwave response at a source-receiver separation where the earth response is negligible to allow removal of an airwave response in measurements at a shorter source- receiver separation, thereby to allow the earth response to be determined. 22. A computer program and/or a processor as claimed in claim 21 configured to find an inverse filter f(t) of the airwave response &(t) at the source-receiver separation where the earth response is negligible; convolve the filter f(t) with the measured response at the shorter source-receiver separation to provide a result that includes an airwave impulse; remove the airwave impulse from the result of the convolution and convolve the remainder with the determined airwave response a(t) to recover the earth response at the shorter source-receiver separation without the airwave. 23. A computer program and/or a processor as claimed in claim 21 or claim 22 having code or instructions for estimating the airwave response at the source- receiver separation where the earth response is negligible. 24. A method of measuring an electromagnetic response comprising positioning an electromagnetic source and at least one electromagnetic receiver underwater; transmitting an electromagnetic signal from the source to the receiver, wherein the transmitted signal comprises an earth component and an airwave component, and the receiver is positioned relative to the source so that the measured response is substantially due to the airwave. A method for removing the effects of an airwave from marine electromagnetic data comprising providing an electro-magnetic source and at least one receiver in the water; measuring the electromagnetic response at a first source-receiver separation; determining a scaled version of the airwave response at a source-receiver separation where the earth response is negligible and using the scaled airwave response to determine the earth response measured at the first separation. Using this method, an improved estimate of the earth's response can be achieved.

Full Text

IMPROVEMENTS IN MARINE KM EXPLORATION
The present invention relates to a method for removing the airwave from marine
electromagnetic data. In particular, the invention relates to a technique for reducing
the impact of the airwave in marine based multi-channel transient electromagnetic
(MTEM) measurements.
Background of the Invention
Porous rocks are saturated with fluids. The fluids may be water, gas, or oil, or a
mixture of all three. The flow of current in the earth is determined by the resistivities
of such rocks, which are affected by the saturating fluids. For instance, brine-
saturated porous rocks are much less resistive than the same rocks filled with
hydrocarbons. By measuring the resistivity of geological formations, hydrocarbons
can be detected. Hence, resistivity measurements can be made in an exploration
phase to detect hydrocarbons prior to drilling.
Various techniques for measuring the resistivity of geological formations are known,
for example time domain electromagnetic techniques, as described in WO 03/023452,
the contents of which are incorporated herein by reference. Conventionally, time
domain electromagnetic investigations use a transmitter and one or more receivers.
The transmitter may be an electric source, that is, a grounded bipole, or a magnetic
source, that is, a current in a wire loop or multi-loop. The receivers may be grounded
bipoles for measuring potential differences, or wire loops or multi-loops or
magnetometers for measuring magnetic fields and/or the time derivatives of magnetic
fields. The transmitted signal is often formed by a step change in current in either an
electric or magnetic source, but any transient signal may be used, including, for
example, a pseudo-random binary sequence. Measurements can be taken on land or
in an underwater environment.
Figure 1 shows a view of a typical setup for transient electromagnetic marine
surveying. This has a bi-pole current source with mid-point xs on or near the sea floor
for transmitting a transient current between two electrodes. The time function of the
current might be a simple step change in current or a more complicated signal such as

a pseudo-random binary sequence. The response of the earth-water system is
measured by a line of bi-pole receivers on or near the sea floor, each receiver
characterised by its mid-point position xr and measuring the potential difference
between a pair of electrodes. All the electrodes are essentially in the same vertical
plane.
In use, the electromagnetic signal generated by the source of Figure 1 can follow three
transmission paths to the receiver electrodes, these being directly through the earth,
directly through the water, and via the water through the air and back through the
water again. The signal transmitted by this third path is known as the airwave. In
deep water, the airwave has a negligible impact. In contrast in shallow water, the
signal (hat is transmitted through the water is negligible, but the airwave can have a
significant impact and so make interpretation of the data difficult.
Summary of the Invention
According to one aspect of the present invention, mere is provided a method for
removing the effects of an airwave from marine electromagnetic data comprising
providing a source and at least one receiver in the water; measuring the
electromagnetic response at a first source-receiver separation; determining a scaled
version of the airwave response at a source-receiver separation where the earth
response is negligible and using the scaled airwave response to determine the earth
response measured at the first separation. The step of determining the scaled airwave
may involve measuring or estimating the airwave response.
For an impulsive source current, the airwave response decays approximately as the
cube of the source-receiver separation at separations large compared with the water
depth, whereas the response of the component travelling directly through the earth
decays approximately as the fifth power of the source-receiver separation. At very
large offsets, therefore, the airwave dominates the total response. Hence, by
measuring the electromagnetic response at a large source-receiver separation where
the earth response is negligible, a measure of the airwave at that source receiver
separation can be determined. This is a scaled version of the airwave response at the
first source-receiver measurement separation, and can be used to allow removal of the

airwave from the measured data and consequently a more accurate measure of the
earth response at the first source-receiver separation.
Using the scaled airwave response to determine the earth response may involve
finding an inverse filter f(t) of the scaled airwave response a(t); convolving the
inverse filter f(t) with the measured data x(t) to compress the airwave to an
impulse; removing the airwave impulse from the result of the convolution with the air
wave data and convolving the result with the scaled determined airwave a(t) to
recover the earth response without the airwave.
Preferably, the source is a current bi-pole or a magnetic loop. Preferably, the receiver
is a bi-pole receiver or a magnetic loop. Preferably, the source and receiver are
located on or near the seabed.
The electromagnetic measurements are transient electromagnetic measurements; that
is, the response to the input signal at the source must have reached essentially steady
state before the measurement is complete.
Preferably, the larger source-receiver separation is approximately five or more times
greater than the shorter separation. Ideally, both source-receiver separations are at
least five times greater than the depth of the water.
The larger source-receiver separation is selected so that the earth response measured
at the receiver is substantially zero.
According to another aspect of the present invention, there is provided a computer
program, preferably on a computer readable medium or data carrier, for removing the
effects of an airwave from marine electromagnetic data as measured by at least one
source and at least one receiver, the computer program having code or instructions for
using an airwave response at a source-receiver separation where the earth response is
negligible to allow removal of an airwave response in measurements at a shorter
source-receiver separation, thereby to allow the earth response to be determined.

Preferably, the larger separation is approximately five or more tiroes greater than the
shorter separation.
Preferably, the larger separation is selected so that the earth response measured at the
receiver is substantially zero.
Preferably, the program has code or instructions for subtracting the determined
airwave from the measurement at the shorter separation.
According to yet another aspect of the invention, there is provided a system for
deterrnining the earth response to an electromagnetic signal using an electromagnetic
source and at least one receiver in water, the system being adapted to measure the
electromagnetic response at a first source-receiver separation; determine the airwave
response or a scaled version thereof at a source-receiver separation where the earth
response is negligible and use the determined airwave response to determine the earth
response measured at the first separation.
The system may be adapted to use the airwave response to determine the earth
response involves finding an inverse filter f (f) of the scaled airwave response a(t);
convolve the filter f(t) with the measured response at the first source-receiver
separation to provide a result that includes an airwave impulse; remove the airwave
impulse from the result of the convolution and convolve the remainder with the
determined airwave response a(t) to recover the earth response at the first source-
receiver separation without the airwave.
A system may be adapted to determine the earth response by measuring or estimating
the airwave response.
The larger separation may be approximately five or more times greater than the
shorter separation. Both separations may be at least five times greater than the depth
of the water.

The larger separation may be selected so that the earth response measured at the
receiver is substantially zero.
The source may be a current bi-pole or a magnetic loop. The receiver may be a bi-
pole receiver or a magnetic loop.
The source and receiver may be located on or near the seabed.
According to still another aspect of the present invention, there is provided a method
of measuring an electromagnetic response, the method comprising positioning an
electromagnetic source and at least one electromagnetic receiver underwater;
transmitting an electromagnetic signal from the source to the receiver, wherein the
transmitted signal comprises an earth component and an airwave component, and the
receiver is positioned relative to the source so that the measured response is
substantially due to the airwave.
In any aspect of the invention, the transmitted signal may be formed by a step change
in current in either an electric or magnetic source, although any transient signal may
be used, including, for example, a pseudo-random binary sequence.
Brief Description of the Drawings
Various aspects of the invention will now be described by way of example only and
with reference to the accompanying drawings, of which:
Figure 2 is a model of the system of Figure 1;
Figure 3 shows an impulse response at 2 km for the arrangement of Figure 2 in
which the earth resistivity is 1 ohm-m; Figure 3(a) shows the response out to 9s, and
Figure 3(b) shows it out to Is;
Figure 4 shows the impulse response at 10 km offset for a lohnv-m half-space
beneath 100 m of water, where the dipole source and receiver are on the sea floor;
Figure 4 (a) shows the response out to 9 s, and Figure 4 (b) shows it out to 1 s;
Figure 5 shows the marine impulse response, the earth impulse response and
the airwave for a 2 km offset measurement, and
Figures 6(a) and (b) show the result of removing the airwave from the impulse
responses of Figure 3.

Detailed Description of the Drawings
The present invention provides a method for removing the effects of an airwave from
shallow water marine electromagnetic data. The invention will be illustrated using the
model of Figure 2, which shows a seawater layer of depth d and resistivity pw
overlying a homogeneous isotropic halfspace. The dipole source is on the sea floor
and the in-line electric field is calculated at a receiver position at some offset r from it
on the sea floor. For the sake of example, it will be assumed that the water layer is
100 m deep and has a resistivity of 0.3 ohm-m, and the half space has a resistivity of
lohm-m.
Figure 3 shows an impulse response at 2 km for the arrangement of Figure 2. Figure
3(a) shows the response out to 9 s, and Figure 3(b) shows it out to 1 s. A sharp initial
peak occurs at 0.008 s and has an amplitude of 1.82E-10 V/m/s. This is the airwave.
This has a finite rise time to the peak and a long tail. There is a second much broader
peak at about 0.45 s with an amplitude of 2.4E-11 V/m/s. This is caused by the earth
response. The objective is to separate the airwave and the earth impulse response.
At a given offset and after deconvolution for the system response, the impulse
response data, which are causal, can be expressed as:

in which a(t) is the air wave and g(t) is the earth impulse response, with g(0) = 0.
Suitable deconvolution techniques are described for example by Wright, D., et al in
the article Hydrocarbon detection and monitoring with a multichannel transient
electromagnetic (MTEM) survey: The Leading Edge, 21, 852-864.
The airwave is expected to be minimum-phase. By this it is meant that without the
water the airwave is an impulse and the propagation effects in the water must be
factors involving decaying exponentials, which are minimum-phase.

An estimate a(t) of the air wave is assumed such that

This is an estimate of the shape, but the exact airwave amplitude A is not known.
Next a filter f(t) has to be found, such that

in which the asterisk denotes convolution and δ(t) is the impulse function:

As mentioned above a(t) and hence a(t) are expected to be minimum-phase.
Therefore the inverse f(t) is causal, realizable and minimum-phase; that is, it exists
only for t ≥ 0, and it has finite amplitude.
Convolving the filter f (t) with the data yields

Now the airwave is removed by considering only t > 0, so that:

This result can then be convolved with a(t):

This allows the earth impulse as measured to be recovered, but without the airwave.
This is what is needed, and it turns out that the unknown amplitude factor A is
irrelevant. Hence, by merely having an estimate or measure of the shape of the
airwave, the earth impulse can be determined.
Because of the presence of noise, an exact inverse of a(t) cannot be used. First
equation (1) is re-written to include the noise:

Then equation (2) is modified to define a new filter f1(t), such that

in which d(t) is a band-limited impulse whose integral is unity, for example a
Gaussian, of the form d(t) - αexp(-πα2t2) with α a frequency close to the highest
frequency of interest in the data, and t is a time delay introduced to make /,(r)
causal. The integral of d(t) is 1. Convolving this filter with the data yields

The value of α is chosen to be as large as possible but not so large that the high
frequency components of the noise are amplified too much. Then

Apart from the known time delay t this is what is desired, plus noise. The time delay
can easily be removed.
The shape of the airwave can be estimated by looking at an offset that is large
compared with this offset and where the attenuation of the earth response is relatively
high. It is suspected that the shape of the airwave is invariant with offset for a 1-D
earth - beyond a certain offset ~ and the hypothesis is that an almost pure airwave
could be measured, if the offset is large enough and the time window restricted. This
gives an estimate of the shape of the airwave, which according to the method
described above would allow the effects of the airwave at the measurement source-
receiver separations to be removed.
Figure 4 shows the impulse response at 10 km offset for a lohm-m half space beneath
100 m of water, where the dipole source and receiver are on the sea floor. Figure 4 (a)
shows the response out to 9 s, and Figure 4 (b) shows it out to 1 s. The sharp initial
peak occurs at 0.008 s and has an amplitude of 1.46E-12 V/m/s. There is no
discernible second peak. It should be noted that the peak of the airwave occurs at
exactly the same time as for the 2 km impulse response.
Figure 5 shows the marine impulse response, the earth impulse response and the
airwave for a 2 km offset measurement. The earth impulse response was obtained

according to the scheme described above; the airwave was obtained by subtracting the.
earth impulse response from the marine impulse response. A measure of the quality
of this result is to compare the recovered impulse response with the analytic function:
the impulse response of a lohm-m half space at an offset of 2 km. Figure 6 shows the
result of removing the airwave from the impulse responses shown in Figure 3. This is
very similar to the analytic function for the impulse response of a lohm-m half space.
In particular the time and amplitude of the peak of the two functions are in close
agreement.
The present invention provides a very simple and effective technique for removing the
airwave from measured MTEM data. This can be summarised as follows: estimate
the shape of the airwave using an airwave at a large source-receiver separation and
find a filter f(t) based on the estimated airwave. This filter is then convolved with the
measured data x(t). The result of this is very messy data, but there is a very sharp
peak at time t = t. This is the airwave. The airwave peak is then sliced out. The
remaining data is returned to its original state by convolving it with the scaled airwave
a(t). This operation undoes the effect of convolving with the filter f(t). The result is
the original data, i.e. the earth response, without the airwave.
The data captured may be processed in accordance with the invention using any
suitable hardware or software.
A skilled person will appreciate that variations of the disclosed arrangements are
possible without departing from the invention. Accordingly the above description of
the specific embodiment is made by way of example only and not for the purposes of
limitation. It will be clear to the skilled person that minor modifications may be made
without significant changes to the operation described.

Claims
1. A method for determining the earth response to an electromagnetic signal
using a source for transmitting the electromagnetic signal to at least one
receiver in water, the method comprising; using an electromagnetic response
measured at a first source-receiver separation; determining the airwave
response or a scaled version thereof at a source-receiver separation where the
earth response is negligible and using the determined airwave response to
determine the earth response measured at the first separation.
2. A method as claimed in claim 1 wherein using the airwave response to
determine the earth response involves finding an inverse filter f (t) of the
determined airwave response a(t); convolving the filter f (t) with the
measured response at the first source-receiver separation to provide a result
that includes an airwave impulse; removing the airwave impulse from the
result of the convolution and convolving the remainder with the determined
airwave response a(t) to recover the earth response at the first source-receiver
separation without the airwave.
3. A method as claimed in any of the preceding claims wherein the step of
determining involves measuring or estimating the airwave response.
4. A method as claimed in any of the preceding claims wherein determining the
airwave response involves estimating its shape.
5. A method as claimed in any of the preceding claims wherein the larger
separation is approximately five or more times greater than the shorter
separation.
6. A method as claimed in any of the preceding claims wherein both separations
are at least five times greater than the depth of the water.

7. A method as claimed in any of the preceding claims wherein the larger
separation is selected so that the earth response measured at the receiver is
substantially zero.
8. A method as claimed in any of the preceding claims wherein the source is a
current bi~pole or a magnetic loop.
9. A method as claimed in any of the preceding claims the receiver is a bi-pole
receiver or a magnetic loop.
20. A method as claimed in any of the preceding claims comprising locating the
source and receiver on or near the seabed.
11. A method as claimed in any of the preceding claims comprising measuring the
electromagnetic response at the first source-receiver separation
12. A system for determining the earth response to an electromagnetic signal using
an electromagnetic source and at least one receiver in water, the system being
adapted to measure the electromagnetic response at a first source-receiver
separation; determine the airwave response or a scaled version thereof at a
source-receiver separation where the earth response is negligible and use the
determined airwave response to determine the earth response measured at the
first separation.
13. A system as claimed in claim 12 adapted to use the airwave response to
determine the earth response involves finding an inverse filter f(t) of the
determined airwave response a (t); convolve the filter f(t) with the measured
response at the first source-receiver separation to provide a result that includes
an airwave impulse; remove the airwave impulse from the result of the
convolution and convolve the remainder with the determined airwave response
d(t) to recover the earth response at the first source-receiver separation
without the airwave.

14. A system as claimed in claim 12 or claim 13 that is adapted to determine the
earth response by measuring or estimating the airwave response.
15. A system as claimed in any of claims 12 to 14 wherein the larger separation is
approximately five ox more times greater than the shorter separation.
16. A system as claimed in any of claims 12 to 15 wherein both separations are at
least five times greater than the depth of the water.
17. A system as claimed in any of claims 12 to 16 wherein the larger separation is
selected so that the earth response measured at the receiver is substantially
zero.
18. A system as claimed in any of claims 12 to 17 wherein the source is a current
bi-pole or a magnetic loop.
19. A system as claimed in any of claims 12 to 18 wherein the receiver is a bi-pole
receiver or a magnetic loop.
20. A system as claimed in any of claims 12 to 19 wherein the source and receiver
are located on or near the seabed.
21. A computer program, preferably on a computer readable medium or data
carrier, and/or computer program product and/or a processor for processing
marine electromagnetic data measured by at least one source and at least one
receiver to remove the effects of an airwave, wherein the computer
program/product/processor has code or instructions for using an airwave
response at a source-receiver separation where the earth response is negligible
to allow removal of an airwave response in measurements at a shorter source-
receiver separation, thereby to allow the earth response to be determined.
22. A computer program and/or a processor as claimed in claim 21 configured to
find an inverse filter f(t) of the airwave response &(t) at the source-receiver

separation where the earth response is negligible; convolve the filter f(t)
with the measured response at the shorter source-receiver separation to
provide a result that includes an airwave impulse; remove the airwave impulse
from the result of the convolution and convolve the remainder with the
determined airwave response a(t) to recover the earth response at the shorter
source-receiver separation without the airwave.
23. A computer program and/or a processor as claimed in claim 21 or claim 22
having code or instructions for estimating the airwave response at the source-
receiver separation where the earth response is negligible.
24. A method of measuring an electromagnetic response comprising positioning
an electromagnetic source and at least one electromagnetic receiver
underwater; transmitting an electromagnetic signal from the source to the
receiver, wherein the transmitted signal comprises an earth component and an
airwave component, and the receiver is positioned relative to the source so that
the measured response is substantially due to the airwave.

A method for removing the effects of an airwave from marine electromagnetic data comprising providing an electro-magnetic source and at least one receiver in the water; measuring the electromagnetic response at a first source-receiver separation; determining a scaled version of the airwave response at a source-receiver separation where the earth response is negligible and using the scaled airwave response to determine the earth response measured at the first separation. Using this method, an improved
estimate of the earth's response can be achieved.

Documents:

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Patent Number

279755

Indian Patent Application Number

2544/KOLNP/2009

PG Journal Number

05/2017

Publication Date

03-Feb-2017

Grant Date

30-Jan-2017

Date of Filing

10-Jul-2009

Name of Patentee

METEM LTD

Applicant Address

10 BANKHEAD CROSSWAY SOUTH, EDINBURGH EH11 4EP

Inventors:

#	Inventor's Name	Inventor's Address
1	ZIOLKOWSKI, ANTONI, MARJAN	17 GORDON TERRACE, EDINBURGH EH16 5QR

PCT International Classification Number

G01V3/12; G01V3/12

PCT International Application Number

PCT/GB2008/000467

PCT International Filing date

2008-02-11

PCT Conventions:

#	PCT Application Number	Date of Convention	Priority Country
1	0702661.0	2007-02-12	U.K.