Method and apparatus for marine electrical exploration

Abstract

A method and apparatus for offshore electromagnetic surveying for the purpose of hydrocarbon exploration and detection is described. The method comprises the step of A) measuring a measurement vector u between receiver electrodes, where the measurement vector u comprises a plurality of measurement signals u.sub.i, being dependent on a geological characteristic m.sub.k at an geological parameter index k providing information about the geological structure of the geological target area. The method is further characterized in that it also comprises the following steps: B) calculating a transformed vector v as a function of the measurement vector u, where said transformed vector v is designed to optimize the sensitivity to changes in the geological characteristic m.sub.k and C) performing, for each time t, at least one of minimizing uncertainty v(k,t) of the transformed vector v with respect to the geological characteristic m.sub.k, where said uncertainty v(k,t) comprises a non-systematic uncertainty v(k,t) and a systematic uncertainty .sub.wdv(k,t), maximizing a target response v(k,t)/m.sub.k of the transformed vector v with respect to the geological characteristic m.sub.k and minimizing a ratio (k,t) between at least the square of the non-systematic uncertainty <v(k,t).sup.2> of the transformed vector v and the square of the target response (v(k,t)/m.sub.k).sup.2 of the transformed vector v with respect to the geological characteristic m.sub.k.

Claims

1. A method of measuring and analyzing measurement data from an electromagnetic survey of a geological target area that potentially contains a hydrocarbon reservoir, the method comprising the step of A) measuring a measurement vector u between receiver electrodes, said measurement vector u comprising a plurality of measurement signals u.sub.i, wherein at least one of the plurality of measurement signals u.sub.i is dependent on a geological characteristic m.sub.k at a geological parameter index k, where said geological characteristic m.sub.k provides information about the geological structure of the geological target area, wherein the method further comprises the following step: B) calculating a transformed vector v as a function of the measurement vector u. where each component v(k,t) of the transformed vector v at a geological parameter with index k and a time t is calculated by projecting the measurement vector u in the direction given by a unit vector e(k,t), said unit vector e(k,t) being governed by the geological characteristic m.sub.k, said transformed vector v being designed to optimize the sensitivity to changes in the geological characteristic m.sub.k by performing, for each time t, at least one of minimizing uncertainty v(k,t) of the transformed vector v with respect to the geological characteristic m.sub.k, where said uncertainty v(k,t) comprises a non-systematic uncertainty v(k,t) and a systematic uncertainty .sub.wdv(k,t), maximizing a target response v(k,t)/m.sub.k of the transformed vector v with respect to the geological characteristic m.sub.k and minimizing a ratio (k,t) between at least the square of the non-systematic uncertainty <v(k,t).sup.2> of the transformed vector v and the square of the target response (v(k,t)/m.sub.k).sup.2 of the transformed vector v with respect to the geological characteristic m.sub.k.

2. The method in accordance with claim 1, wherein minimizing the uncertainty v(k,t) of the transformed vector v with respect to the geological characteristic m.sub.k is performed using an equation defined as $\begin{array}{cc}.Math..Math.v\left(k,t\right)=\sqrt{(.Math..Math.{v^{}(k,t}^2)+{\left({}_{\mathrm{wd}}.Math.v\left(k,t\right)\right)}^2}=\sqrt{\frac{1}{N_B}.Math.\underset{i=1}{\overset{N_B}{.Math.}}.Math..Math.{\left(v^i\left(k,t\right)-\stackrel{\_}{v}\left(k,t\right)\right)}^2+{\left(v\left(k,h+.Math..Math.h,t\right)-v\left(k,h,t\right)\right)}^2}& \left(29\right)\end{array}$ where N.sub.B is the number of spatial bins along a measurement line, which spatial bin size corresponds to the geological scale of interest, i is an integer number indexing each spatial bin, v.sup.i(k,t) is the value of the transformed vector v at spatial bin i, index k and time t, v(k,t) is an average over a local spatial domain of the response at index k and time t, h is a parameter that generates a systematic error in the transformed vector v, and v(k,h,t) and v(k,h+h,t) are calculated components of the transformed vector v for the systematic errors h and h+h, respectively, at a geological parameter index k and a time t.

3. The method in accordance with claim 1 or 2, wherein maximizing the target response v(k,t)/m.sub.k of the transformed vector v with respect to the geological characteristic m.sub.k is performed using an equation defined as $\begin{array}{cc}\frac{v\left(k,t\right)}{m_k}\frac{v\left(k,m_k+.Math..Math.m_k,t\right)-v\left(k,m_k,t\right)}{.Math..Math.m_k}& \left(30\right)\end{array}$ where m.sub.k is an increment of the geological characteristic m.sub.k and v(k,m.sub.k,t) and v(k,m.sub.k+m.sub.k,t) are calculated components of the transformed vector v for the geological characteristics m.sub.k and m.sub.k+m.sub.k, respectively, at a given geological parameter index k and a time t.

4. The method in accordance with claim 1, wherein the optimization is carried out for a plurality of k values corresponding to a plurality of geological characteristics {m.sub.k}, thereby enabling a subsequent identification of at least one direction of the transformed vector v that optimize sensitivity for a corresponding geological characteristic m.sub.k.

5. The method in accordance with claim 4, wherein the method further comprises the step of minimizing an objective function defined as $\begin{array}{cc}=\underset{k=1}{\overset{N^{}}{.Math.}}.Math..Math.\left(\underset{t}{.Math.}.Math..Math.\frac{{\left(v^d\left(k,t\right)-v^m\left(k,t\right)\right)}^2}{{\left(.Math..Math.v\left(k,t\right)\right)}^2}\right)& \left(31\right)\end{array}$

6. where N is the total number of geological characteristics {m.sub.k} corresponding to said plurality of k values, v.sup.d(k,t) is a value of the transformed vector v corresponding to the measurement signal u.sub.i at geological parameter index k and time t, v.sup.m(k,t) is a calculated value of the transformed vector v based on a geological characteristic m.sub.k corresponding to a predetermined model.

7. The method in accordance with claim 1, wherein the method further comprises the step of measuring locations of said receiver electrodes.

8. The method in accordance with claim 6, wherein the step A and the step of measuring locations of said receiver electrodes are performed simultaneously, or near simultaneously.

9. The method in accordance with claim 1, characterized in that at least one of measurement signals u.sub.i is a potential difference.

10. The method in accordance with claim 1, wherein the geological characteristic m.sub.k is a geo-electric characteristic.

11. An apparatus for measuring and analyzing electromagnetic data over a geological target area that potentially contains a hydrocarbon reservoir, wherein the apparatus comprises at least two receiver electrodes suitable for recording measurement signals u.sub.i from the geological target area and a computer program product stored on a computer usable medium comprising computer readable program means to control an execution of the method in accordance with any one of claims 1-9.

12. The apparatus in accordance with claim 10, wherein the apparatus further comprises a towing system comprising a plurality of lowing cables, where at least one towing cable comprises said at least two receiver electrodes and at least one towing cable comprises a plurality of transmitter (TX) electrodes, the transmitter (TX) electrodes being configured to broadcast electromagnetic signals to the geological target.

13. The apparatus in accordance with claim 11, wherein the plurality of transmitter (TX) electrodes are configured to broadcast electromagnetic signals in form of a plurality of current pulses with finite durations, and the at least one receiver electrode pair is configured to record the measurement signals u.sub.i at points in time between the transmitted plurality of current pulses.

14. The apparatus in accordance with claim 11 or 12, wherein least one of the position of the plurality of transmitter (TX) electrodes and the transmitted current pulses from the plurality of transmitter (TX) electrodes is, by use of the computer program product, adjusted iteratively during the recording of the measurement signals u.sub.i in order to optimize sensitivity to at least one geological characteristic m.sub.k of a given geological target.

15. The apparatus in accordance with claim 10, wherein the at least two receiver electrodes are arranged on a buoyant object.

Description

BRIEF DESCRIPTION OF THE DRAWING

[0047] FIG. 1 is a conceptual illustration of the towed system, showing N transmitter electrodes and M receiver electrodes attached to separate towing cables, where u.sub.1 is the voltage difference between electrodes 1 and 2,

[0048] FIG. 2 is an one-dimensional geo-electric model and its associated geo-electrical parameters of a layered rock strata situated under a body of water and

[0049] FIGS. 3(a) and (b) show graphs of the initial potential difference parameter u.sub.1 (a) and the transformed parameter v.sub.5 as function of position along survey lines.

DETAILED DESCRIPTION OF THE INVENTION

[0050] Transmission and Recording System

[0051] The principal layout of transmission and recording system of the present invention is illustrated in FIG. 1, showing towing cables with transmitter electrodes (i=0 . . . N1) and receiver electrodes (i=1 . . . M). The currents flowing from the i electrode into the water are imposed individually. I.e. the current imposed between electrode 0 and 1 is denoted I.sub.1, the current from electrode 1 to electrode 2 I.sub.2, the current from electrode 1 to electrode 3 I.sub.3, etc. The total current is thus I.sub.tot=.sub.iI.sub.i. Apart from the electrodes this system may include magnetometers, pressure sensors and transponders (not shown).

[0052] Generally, inversion of EM data is an exercise in data-fitting where a so-called objective function, or difference function, is minimized with respect to the geo-electrical parameters of the earth. These parameters typically include resistivity, and the objective function measures the difference between the recorded data and the corresponding calculated values that results from Maxwells equations and the geo-electric parameters.

[0053] When measuring IP effects by means of inversion of EM data, there is generally a significant equivalence between the values of different geo-electric parameters, such as local resistivity and charge values. This problem may be significantly reduced by combining signals which give complementary information on the subsurface. In particular, during a survey the relative strengths of the currents will be varied in order to reduce equivalence.

[0054] Data Treatment by Means of the Method of Optimized ParametersMOPS

[0055] The inventive method, hereinafter referred to as the Method of Optimized ParametersMOPS, is based on the idea that a set of measurement data should be combined and weighted in a way that maximizes the sensitivity to the target geological structure and minimizes the noise.

[0056] Normally inversion of the measured data is carried out to obtain the geo-electrical parameters that describe the target geological structure. These parameters may be grouped in the vector m.sub.k, where k=1, 2, . . . N. As an example, if the model is one-dimensional and one is only looking of the vertical resistivity profiles, .sub.i, and the chargeability profiles, .sub.i, then the vector m={m.sub.k} will take the form

[00010]$\begin{array}{cc}m=\left[\begin{array}{c}{}_1\\ {}_2\\ {}_2\\ {}_2\\ {}_3\\ \mathrm{.Math.}\end{array}\right],& \left(18\right)\end{array}$

where the geo-electric parameters are indicated in FIG. 2, showing schematically a layered rock strata (layers 2-5) situated below sea (layer 1).

[0057] The inventive MOPS procedure is defined by identifying the data-parameters that are most sensitive to a given set of target geo-electric parameters m.sub.k, distributed over the various layers as shown in FIG. 2.

[0058] In the context of hydrocarbon detection by means of electromagnetic responses to either a controlled source or a natural source (like the electromagnetic fields originating in the ionosphere, or generated by lighting storms), we start from a set of measurements that may include potential differences u.sub.0i, magnetic background field B.sub.i and/or concentrations of chemical species C.sub.i taken from sea bottom samples. The index i labels both times and locations/offsets from the source and may take the form i=j+nN.sub.T, where j=0, . . . , N.sub.T1 labels N.sub.T different discrete times (or frequencies, depending on whether the data is collected in the time- or frequency domain) and n=1, . . . , N.sub.0 labels the different locations or offsets. If N.sub.T=1, then i labels offset values only. By combining these variables into a vector

[00011]$\begin{array}{cc}u=\left[\begin{array}{c}{u}_0\\ B\\ C\end{array}\right],& \left(19\right)\end{array}$

or simply u=u.sub.0 if we are only considering E-field-data.

[0059] The data in the u vector will have been subject to normal processing steps so as to reduce unwanted drift and other noise contributions. For concreteness, assume u is just the normal potential differences measured along a sequence of towed electrodes trailing behind a transmitter. These differences may be normalized by their initial values so as to become dimensionless numbers. The data processing may also include standard procedures such as binning, band-pass filtering and stacking. In the following we will assume that the data has been subjected to at least one of these standard procedures and averaged into N.sub.B spatial bins of size that match(es) the geological scales of interest (for instance, the signal may be averaged over 1 km blocks, see above), and positions x.sub.i, which may be the distance from the start of a survey line, and discrete time bins of a size that corresponds to the desired resolution. The time then takes discrete values t. So the number of spatial bins along a data-line is N.sub.B, and there are N.sub.T different time values in each response after binning

[0060] We may define a new MOPS variable v being a function of the u vector, where each of these MOPS variable v(k,t) is designed to optimize the sensitivity to the particular geo-electric parameter m.sub.k. For example, each MOPS variable v(k,t) may be defined as

v(k,t)=e(k,t).Math.u(t) (20)

which is the projection of the data-vector u in the direction given by the unit vector e(k,t) (which may vary in time). In the final inversion of the EM data, several k-values will be used. In order to optimize sensitivity we are actually optimizing the signal to noise ratio, and we thus need to estimate the noise contributions. Noise measurements are therefore carried out as part of the data processing.

[0061] The noise may be measured as variations around the local average values obtained at each bin position x.sub.i. Then the deviation

[00012]$\begin{array}{cc}.Math..Math.{v^{}\left(k,t\right)}^2=\frac{1}{N_B}.Math.\underset{i=1}{\overset{N_B}{.Math.}}.Math..Math.{\left(v^i\left(k,t\right)-\stackrel{\_}{v}\left(k,t\right)\right)}^2& \left(21\right)\end{array}$

where i is a pulse number and v(k,t) is the stacked average of the response at time t. The result is a measure of the uncertainty in v(k,t). The above result may also be obtained by Fourier methods.

[0062] In addition to the above non-systematic uncertainty comes the uncertainty in v(k,t) itself which is caused by various systematic contributions such as uncertainties in tow depths, bathymetry and unknown 3D structures (for example horizontal contrasts in conductivity). In order to represent these systematic uncertainties, which are all proportional to the strength of the transmitter current, we may add a contribution .sub.wdv(k,t) to the above non-systematic uncertainty. This contribution may as a first approximation be taken as .sub.wdv(k,t)v(k,t). However, an even better estimate of the above-mentioned systematic uncertainty may be obtained by the equation

.sub.wdv(k,t)=v(k,h+h,t)v(k,h,t) (22)

where h is a parameter that generates a systematic error, for example a water depth variation, and v(k,h,t) is the calculated field parameter based on a given h-value. h is the estimated uncertainty in h. The total uncertainty, i.e. from both non-systematic (v(k,t)) contributions and systematic (.sub.wdv(k,t)) contributions, may thus be estimated by

v(k,t).sup.2=v(k,t).sup.2+(.sub.wd(k,t)).sup.2 (23)

[0063] Finally, the last input to the MOPS procedure is the calculation of the target response (k,t)/m.sub.k, which may be calculated as a finite difference

[00013]$\begin{array}{cc}\frac{v\left(k,t\right)}{m_k}\frac{v\left(k,m_k+.Math..Math.m_k,t\right)-v\left(k,m_k,t\right)}{.Math..Math.m_k}& \left(24\right)\end{array}$

where v(k,m.sub.k,t) is a forward calculation based on an initial assumption of a geological model giving an initial data set{m.sub.k}, and m.sub.k is an increment of the particular m.sub.k-value.

[0064] In a preferred embodiment of the invention, the MOPS procedure identifies the most sensitive data-parameter by minimizing the function

[00014]$\begin{array}{cc}\left(k,t\right)=\frac{.Math..Math.{v\left(k,t\right)}^2+{\left({}_{\mathrm{wd}}\left(t\right)\right)}^2}{{\left(v\left(k,t\right)/m_k\right)}^2}& \left(25\right)\end{array}$

or, if the systematic contribution .sub.wdv(k,t) of the uncertainty is ignored

[00015]$\begin{array}{cc}\left(k,t\right)=\frac{.Math..Math.{v\left(k,t\right)}^2}{{\left(v\left(k,t\right)/m_k\right)}^2},& \left(26\right)\end{array}$

with respect to the projection e(k,t) (equation 20). This particular embodiment of the MOPS procedure singles out the direction in u-space that has an optimized signal-to-noise ratio.

[0065] Case Example Focusing on Chargeability Over a Known Reservoir

[0066] It is well known that anomalies (i.e. anomalies in chargeability within the geological structure) are correlated with underlying hydrocarbon reservoirs. In this example we optimize (k=5,t), which means focusing on the chargeability .sub.3. In this case .sub.3 represent the chargeability in a layer of 500 meters thickness located 200 meters below the sea bottom, and 1.5-2 kilometers above known hydrocarbon reservoirs. FIG. 3 shows the result of the measurements, both of the original potential differences u.sub.1(t) and for the transformed variable v(k=5,t), at a time t about 1 second after a pulse shut-off. The locations of three known reservoirs (Field 1, Field 2 and Field 3) are indicated on the horizontal axis showing the positions along the survey lines. Normally, a full inversion with respect to .sub.3 would be required to see a correlation with the reservoir locations as these usually are not observable directly in the u.sub.i values. However, the maxima of the transformed variable v(k=5,t) are seen to correlate well with the reservoir locations Field 1, Field 2 and Field 3. This implies that interpretation may be done directly in the processed data instead of, or in addition to, inversion (providing potentially ambiguous inversion results).

[0067] Inversion with MOPS Parameters

[0068] The operation of projecting out a single direction in u-space discards the information along the orthogonal components. This may be corrected for by carrying out the optimization for several k-values, systematically identifying the directions that optimize sensitivity for the different m.sub.k-values. Hence, the other directions in u-space will be represented.

[0069] The inversion is afterwards carried out by minimizing the objective function

=.sub.k=1.sup.N.sub.k(t) (27)

where N<N and where the objective function .sub.k at k includes the measured data v.sup.d(k,t)

[00016]$\begin{array}{cc}{}_k=\underset{t}{.Math.}.Math..Math.\frac{{\left(v^d\left(k,t\right)-v^m\left(k,t\right)\right)}^2}{.Math..Math.{v\left(k,t\right)}^2}& \left(28\right)\end{array}$

where v.sup.m(k,t) are the calculated values obtained from the model parameters m. The same minimization algorithm may be applied to obtain the most sensitive direction in u-space at incremental changes in m.sub.k, thus giving the e(k,t) vector (as in the actual inversion for the m-vector). In the above mentioned example (FIG. 3), which includes only e(k,t), the well known Levenberg-Marquart algorithm was used. Using N=N.sub.0, the number of e(k,t) vectors is the same as the number of data-points. In other words, all the dimension of the data-space are accessed, except in the rare case where the set of e(k,t) vectors is linearly dependent.

[0070] Note that when m.sub.k is a parameter that has little impact on the data (for example a deep resistivity), it will have a corresponding weak effect in the objective function .sub.k. The same is the case for t-values where the sensitivity is small.

[0071] This method differs from the linear methods of synthetic steering [3] and principal component analysis, most notably by virtue of being entirely non-linear. Standard transformations of the m.sub.k-values, such as m.fwdarw.log(m), may be applied for numeral reasons in order to reduce the dynamic range of the variables that the method inverts for.

[0072] Transmitter Pulse Optimization with the MOPS Method

[0073] The above steps are all steps that optimize the use and processing of acquired data. However, the MOPS parameters may also be used to optimize the pulse currents I.sub.i's during the progression of a survey. This may be done on the basis of on-board data inversion, since a preliminary geological model may be used to tune the currents I.sub.i so as to maximize .sub.k of equation (25) or (26). This is done by the same, or nearly the same, minimization algorithms as the one that finds the optimal e(k,t) directions and in the inversion process itself. Note that the recombination of currents allows a transition from a virtually vertical transmitter to a horizontal transmitter. Different targets k will favor different I.sub.i combinations. Hence, a possible outcome of the above described procedure is a survey having a number of separate current configurations.

[0074] In the preceding description, an aspect of the method and the apparatus according to the invention have been described with reference to an illustrative embodiment. For purposes of explanation, a method and apparatus were set forth in order to provide a thorough understanding of the invention and its workings. However, this description is not intended to be construed in a limiting sense. Various modifications and variations of the illustrative embodiment, as well as other embodiments of the method and apparatus, which are apparent to persons skilled in the art to which the disclosed subject matter pertains, are deemed to lie within the scope of the present invention.

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