GB2467108A

GB2467108A - Estimating receiver orientation in marine CSEM

Info

Publication number: GB2467108A
Application number: GB0900908A
Authority: GB
Inventors: Lars Ole Loseth; Alexander Kritski
Original assignee: Statoil ASA
Current assignee: Equinor ASA
Priority date: 2009-01-20
Filing date: 2009-01-20
Publication date: 2010-07-21
Also published as: GB0900908D0

Abstract

A method is provided for determining the orientation of a controlled source electromagnetic receiver. The method comprises forming a linear combination of first and second data records recorded by the receiver for different source positions with substantially equal source-receiver offsets and substantially equal source dipole moments. An orientation angle is selected for which the linear combination has a predetermined characteristic. For example, the linear combination may comprise the sum or difference and the predetermined characteristic may comprise a minimum.

Description

Estimating receiver orientation in marine CSEM

BRIEF DESCRIPTION

We present a new method to estimate receiver orientation angle from electric and/or magnetic data measured during a Controlled Source Electromagnetic (CSEM) survey.

The new method can be applied for conventional CSEM geometries with receivers positioned on the towline as well as for 3D surveys where the receivers can be positioned off the towline. Moreover, the method can resolve the receiver orientation for receivers positioned off the towline if the source dipole is towed at an angle to the tow direction. Estimating orientation angle for receivers positioned on the towline when using a two-component horizontal source requires that the source also has a vertical component. By summing or considering a difference between electric and/or magnetic responses from a pair of source dipole locations with equal dipole moments at equidistant offsets, the resulting field components will have minimum responses in certain directions. Thus, the receiver orientation angle is obtained by rotating the combined recorded field responses through a spectrum of angles. The underlying assumption in the procedure is based on symmetries in the electromagnetic field found in stratified media. By using all available pairs of source-receiver offsets with good quality CSEM data, the symmetry assumption provides accurate estimates of orientation angles for all marine CSEM data sets that we have analyzed.

TNTRODUCTION

The current types of acquisition systems for recording marine CSEM data include individ-ually deployed sensors with electric dipoles and magnetic coils. Sensors are deployed to the seabed by dropping from the vessel and do not provide good control of their orientation.

Of course, the estimates of the receiver orientation can be achieved by direct measurements during the deployment. However, these methods require complex technical arrangements which cannot always be satisfied during the survey (technically difficult or costly). Thus, in practice the receiver orientation is not known and accordingly, there is an increasing demand in data driven accurate and robust methods for estimating receiver orientation.

Existing methods for estimating CSEM receiver orientation are based on calculation of polarization ellipse parameters of the horizontal electric and/or magnetic field (e.g. Smith and Ward, 1974), or employing calculations similar to Alford rotation (e.g. Mittet et al., 2007) applicable in seismic exploration. The latest method seeks an angle at which the cross field is minimized assuming the transmitter is pointing in the towline direction, Thus, the rotation fixes the maximum electrical field-energy vector into the direction of the towline.

This approach is working well in assumption of the transmitter pointing in the direction of the towline and if the earth locally can be assumed to be plane-layered. The rninimiza-tion technique proposed by Mittet et al. (2007) is furthermore based on using a weighting function to compensate for offset dependence of the electric field amplltudes.

In this paper we present a new method that is based on exploiting symmetries in the electromagnetic fields. By using pairs of source positions with equal offsets to the receiver and where the sources are pointing in the same direction, the receiver does not have to he collinear with available towlines. The approach thus provides reliable angle estimates for azimuthal source-receiver acquisition geometry. Moreover, the method works when the source is towed with an angle to the towline, thus comprising both inline and broadside CSEM data. However, when the receiver is on the towline, this requires that the source also has a vertical component, and when the receiver is off the towline, the requirement is that the source has only horizontal components. Our method is still not free from the plane-layered earth model assumption, but this requirement is relaxed since all available pairs of offsets along the towhne can be used. Obviously, the new method has the ambiguity of giving the wrong direction of the rotated fields, i.e., receiver orientation 1800 away from the actual value. We resolve this problem in the same manner as in Mittet et al. (2007), that is, by considering the phase versus offset (PVO) of the rotated fields.

We first outline the theoretical background of the method in detail, and then demon-strate how it performs on synthetic data based on a plane-layered model. Then the new approach is tested on two field data examples, one where the receiver is positioned on the towline and one where the receiver is positioned off the towline. Finally, we discuss possible sources of crrors and how these might affect the orientation estimation.

THEORETICAL BACKGROUND

The frequency-domain description of electromagnetic fields from a horizontal electric dipole (TIED) in a stratified medium, see for example L�seth and Tjrsin (2007) can be given as: $cosfl{ (la) (ib) (Tc) Ha_cosfl{ (id) where the medium properties change along the z-direction, p is the radial distance in the horizontal plane, and /3 is the azimuthal angle. The dipole cnrrent moment is given by II, and the variables I in equation 1 describe the propagation of a spectrum of plane-wave components for TB and TM modes. From equation 1 we see that the angle dependence is explicit so that the field expressions can be written as: E(p, /3, z) = Ilcos /9 E(p, z), Ep(p, /3, z) = II sin 8 z), (2a) H(p, 3, z) = It sin/i 7-t(p, z), H8(p, /3, z) = Ii cos /9 Nfi(p, z), (2b) By rewriting the field vectors into a Cartesian coordinate system, we obtain: = Ecos/3 -Epsin/3 = Il(S0cos2/3 -Esin2/i), (3a) = E sin /3+ P18 cos /9 = Ii (S, + Ep) sin /3 cos /3, (3b) = IIcos/3 fI sin/I = It(R8 7-t3)sin/icosfi, (3c) = Hsinfl + H0cosd = Il(7-I8sin2 /3+ N8 cos2 /3), (3d) where the HED is pointing in the x-direction.

Source pointiiig aTong towline: Inline source Consider Figure in where two sources with the same dipole current moment at positions i and 2 are pointing in the x-direction (dipole current moment Il') and a receiver is positioned at R. The horizontal distance from two source positions i and 2 to the receiver is,o and P2, respectively. The corresponding angles are j3, and /32, respectively.

We may then form the sum of the field responses at R: +2 = 2Il (Si, cos2 /i S0 sin2 flu), (4a) E1+'52 = 0, (4b) H1+82 = 0, (4c) = 2Ii (7-c sin2 flu -1-R cos2 flu), (4d) since /32 = 180 /3, which gives that sin /32 = sin flu and cos /32 = -cos flu. Similarly for the

differences of the field components we have:

= 0, (4e) = 2.'l(S + S) sin /3, eos/3,, (4f) = 2Il(fl -R5) sin/3, cosfli, (4g) = 0. (4k) Note that when the receiver is positioned on the towline, all the difference-field components are zero since flu = 0. Tlus is also evident from considering symmetries in the field com-ponents for this case; the inline field component is symmetric about the zero-offset axis.

whereas the crosshne field component is zero for all offsets.

In a conventional SBL or marine CSEM measurement, the orientation of the receiver antennas is not known, but it is possible to find two source positions with equal offset to the receiver, cf. Figure 2. We may then either sum or subtract the data from the two offset pairs and rotate the measured field components between 00 and 1800. When scanning through this set of angles, an angle for which the electric and magnetic field combinations are zero will be passed. Of course, in the real data case, these sums or differences of field components will always give a non-zero amplitude, but it is still possible to minimize the resulting fields as a function of the scanning angle.

The obtained orientation angle is either an estimate of the actual orientation angle of the receiver or the orientation angle pius 180°. The.reason for this is that the zero criterions also include artgles where the rotated receiver axes point in the opposite direction to the reference coordinate frame (x-axis along the towline). However, this ambiguity is resolved by inspecting the rotated fields. Our approach is to require the phase versus offset (PVO) for the largest component of the horizontal electric field to stay within the interval between o and 71 for small and intermediate offsets, typically from zero offset np to 3-4 km offset.

This approach is quite similar to the one presented by Mittet et at (2007).

With the measured receiver components along the coordinate axes x' and with un-known orientation angle 9 to the coordinate system xyz, the minimization criterion can be written as follows: Esin& +$S2cos9 = 0 = ü = tan (_EJ+s2/Ei2), (5a) cosO -sinG =.o = tan1 (E;82/E;i-), (5h) H'cosG -II sinG = 0 9 = tan1 (H;_su/H:_82), (5c) H32 sinG + cos9 = 0 = tan1 (m31+82/ii812),. (5d) When the receiver is positioned off the towline, both zero conditions for the sum and difference of field components can be used. When the receiver is on the towline, however, the difference condition becomes degenerate (cf. equation 4 with th = 0), and thus the sum

of field components should he used-

Source pointing orthogonally to the towline: Broadside source When the source is orthogonal to the towline, ci Figure ib, the sums and differences of

the fields become:

= 0, (6a) Ej1+32 = 2Il(E sin2 -E0cos2fli), (6b) H' �2 = -2Il,, ( + k@ sin2 j3) (tic) II1�32 = 0, (6d) E132 = 2Il(E + E) sin$i cosfl1, (6e) = 0, (61) H;1-82 = o, (6g) -2Il(7-( -?-I) sin f3 cos (6h) Here, we have used equation 3 and rotated the coordinate system 900 in order to have the same reference coordinate system as for equation 4. Thus, the source antennas (Figure ib) are pointing in the v-direction with dipole current moineut Ii. As for the inline source case, when the receiver is positioned on the towline, all the difference field components are zero since flu = 0. Thus, when the receiver is on the towline the sum of field components should be used when estimating receiver orientation.

From equation 6 we obtain a similar optimization scheme as in equation 5 for the broadside source: sin 8 + cos 0 = 0 = cos 8 412 sin 8, (7a) H82 cosO -HS,IS2 sinG 0 HYF32 sinO + H,1+82 cosO. (Tb) Source with arbitrary angle to the towline; Two-component source If a two-component HED is at use or the source is towed at an angle (desired or undesired) to the towline, the orientation angle of the receiver can still be found if we know the decomposition angle of the source. With net dipole cm-rent moment Ii with angle a to the towline, cf. Figure ic: = lcosa and i, = isina, (8) the formulas in equations 4 and 6 are still valid, but the sum and difference of the measured electric and magnetic fields will be the snm of the contributions from ll and ll. Then none of the sum and difference components are nonzero anymore, but it can be noted that the difference fields, except from the dipole moment factor, are equal: = 211 sin a(S + S) sinfl1 cosfli, (9a) = 211 cosa(Sp +&3)sinthcosfll, (9b) = 211 cos aç1-1 R8) sin flu cos fl, (9c) = -211 sina(R -fl) sin fl cosfl1. (9d) In the general case, a zero condition can now be obtained by rotating the fields with the angle a, and considering the resulting field components in the xyz-coordinate system.

= E'2cosa E18sina = 0, (lOa) = H'82 sina + H'2 cosct = 0. (lob) The receiver orientation is thus found when this condition is met in the process of scanning the measured data through the spectrum of possible orientation angles: cos (8-F a) -E1S2 sin (8 + a) = 0, (ha) sin (0 + a) + cos (0 + a) = 0. (lib) However, for the situation where the receiver is situated on the towhne, equation 9 is zero for all possible orientation, angles. In this case, it is difficult to obtain the orientation angle without making further assumptions about the subsurface. However, if we in addition to the twocomponent horizontal source also have a vertical source component, we can still estimate the orientation angle.

Vertical source component The field components due to a vertical electric dipole (VED) source in cylindrical coordinates does not have a dependence on angle (L�seth and Tjrsin, 2007). In Cartesian coordinates the dependence on angle /3 and dipole current moment Ii can be written as: = Iicosflh(p,z), = IisinS(p,z). (12a) = Iisin/37-1(p,z), H1, = Iicos3R(p,z). (12h) The sums an.d differences of the field components now become: E+32 = 0, (13a) E1+32 = 2Ii2E sin 6, (13b) sin 13i, (13c) H1+$2 = 0, (13d) = 2IlEcos/3a, (13e) = 0, (13f) = 0, (13g) = 2Il7-(cosfli. (13h) This means that when we have a HED-component towed at an angle to the towline, and the receiver is situated on the towline, we can use the difference field to obtain the receiver orientation angle if the source has a VED component. For either a combined broadside and VED source or a combined inline and VIED source, we can still use the sum criterion, cf. equations 4, 6, and 13 with jIli 0. However, when the receiver is positioned off the towline, a VED source component makes the orientation angle estimate less accurate if the HED has an inline component since there is no zero criterion when field components from a VED and an inline RED are added, cf. equations 4 and 13.

In summary, we can resolve the receiver orientation with a three-component source if the receiver is positioned on the Lowline, but if the receiver is positioned off the towline, a zero-criterion with a three-component source cannot be found wfth the approach that we have presented here. However, when the vertical component is small compared to the horizontal component, the procedure in equation 11 will still give a minimum criterion since the measured field due to the VIED will be substantially smaller than the field due to the TIED.

SYNTHETIC DATA EXAMPLE

The method was tested on synthetic data generated by a 1.5D modelling tool (L�seth and Ursin, 2007). The performance of the method for all cases depicted in Figure 1 was tested using common CSEM models (e.g. water depth 300 m with conductivity 3.5 S/m, overburden 1000 m thick with conductivity 1.0 S/m, thin resistive layer 50 m thick with 0.01 S/in conductivity). First, we modelled the electric and magnetic responses at a certain location off the towline for a RED. These field components were rotated with a specific angle (the orientation angle). Assuming nnknown orientation angle the resulting data for all offset pairs were combined, cf. Figure 2, and read into the rotation procedure. Then the range of possible orientation angles was scanned.

An important issue when visualizing the results from the scanning of possible orientation angles is the normalization of the field data. In order to view the performance of the rotation algorithm for the entire offset range, the magnitude versus offset must be normalized. In our case, is was fonnd convenient to normalize to the largest combined field component in the unrotated data.

For the scenario depicted in Figure Ic, the results from scanning possible orientation angles (equation 11) are shown in Figure 3. In this particular case, the receiver was situated 2 km off the towline and the receiver had an angle to the towline of 21° (i.e. one of the dipole arms on the receiver is oriented 21° to the towline, the other arm is oriented 21° +90° to the towline). The normalized magnitude versus offset when normalizing with the largest field component in the unrotated data, is shown as a function of offset and scanned angles.

Foin the plot, the orientation angle of the receiver is selected by determining the angle where the combined field response has its lowest magnitude. Alternatively, an optimization algorithm that searches for the angles that minimizes the combined field response for a certain offset interval can be used.

We use the obtained orientation angle 8 to rotate the original magnitude versus offset (MVO) data in Figure 4a. The result is showu iu Figure 4b.

REAL DATA EXAMPLE

The real data presented here is from the iTorth Sea region. We present results for two receivers, one which is positioned on the towline (inline receiver), and another one which is positioned 2 km off the towline (azimuth receiver). For these data the source is to a good approximation pointing along the towline (Figure la). The rotation procedure was applied using all available data, i.e. for three source frequencies using both electric and magretic data.

The normalized magnitudes of summed electric field components as functiou of sean ning angle and offset are presented in Figure 5 and Figure 7 for iuline and azimuth data, respectively. The summation was done for equidistant source-receiver pairs as illustrated in Figure 2. The resulting sum was normalized to the largest field component in the unrotated data, before applying the optimization procedure given in equation 5.

By using all the offset pairs that have data above the noise level in Figures 5 and 7, we obtained the orientation angles 0 70° and 8 = 29°, respectively. The unrotated MVO curves for these receivers are shown in Figure 6a and 8a, respectively. The rotated data are shown in Figure 6b and 8h, respectively.

To obtain the best orientation angle, we use data for all available frequencies in the data, and we use both routines for the sum and difference of field components. In our experience quite accurate estimates are obtained when using an algorithm which first takes the set of optimal angles for each offset and orders the values into an ascending spectrum and then takes the mean of an intermediate subset of these values. Our investigations also show that the orientation angle obtained using electric field data is sometimes slightly different from the angle obtained using magnetic data. One explanation for this might be that the effective electric and magnetic antenna arms are sometimes slightly rotated to each other. Moreover, depending on the actual survey layout, either the sum or difference procedure gives the best result. Having obtained an estimate for the orientation angle manual inspection of plots such as in Figures 5 and 7 can be done to evaluate the results, The optimization criterion is then to have symmetries in the curves for receivers off the towline, and minimal field response on one of the components for receivers on the towline.

DISCUSSION OF ERROR CONTRIBUTIONS

From our experience with several sets of CSEM field data, our procedure which gives the rotated field components as for example shown in Figures 5 and 7 is well behaved, and the calculated avcrage angle from all the offset pairs (as long as the data are above the noise floor) gives quite good estimates for the orientation angle.

However, as is evident from Figures 5 and 7, the procedure is not free from uncertainties in the estimated angle. There is a set of angles around the average angle that satisfies the minimum criterion for specific offsets. One major source of error in the method comes from the assumption of having a plane-layered earth. For offset pairs where 2D and 3D effects are significant, we see different values for the orientation angle than the actual value. This is one explanation for the variation with angles of minima in Figures 5 and 7. Another source of error that also accounts for some of this variation is the feathering of the source antenna.

Obviously, noise in the recorded C'SEM responses leads to inaccurate angle estimation for the longest offsets.

When using our method, a dipping source as long as the dip angle is constant will not lead to errors in the angle estimation when the receiver is positioned on the towline, but if the receiver is positioned off the towline, the z-component of the antenna means that we do not have a zero criterion anymore as long as an inline source is employed as the main source component. However, when the VED component is small compared to the 11ED component, the rotation algorithm is applicable also in this case. Furthermore, in the procedure we assume that the receiver is positioned horizontally on the seafloor. For real data, this is not always the case, and it may for some receivers lead to errors when estimating the orientation angle since the measured field in this case has a vertical component.

CONCLUSION

We have demonstrated a new method for data-driven estimation of the orientation angles of EM receivers. Our method is based on calculating the sum or difference of the electric and/or magnetic fields for two source-receiver offsets that are equidistant. The only requirement is that the source points in the same direction at the pair of source positions. The theoretical foundation of the method is based on symmetries in the electromagnetic field found for stratified media. The new method will be particularly useful for processing CSEM data that have been recorded away from the towline and data that have been produced with a two-component horizontal and/or vertical electric dipole source. When the receiver is positioned on the towline, we cannot in principle resolve its orientation when we have a two-component source, but if a vertical source component is added, our method resolves the receiver orientation. When the receiver is positioned off the towline, the method resolves the receiver orientation when we have a two-component horizontal source. In our experience the method gives stable and accurate results for estimates of the orientation angles. The main sources of errors in the method come from the assumption of plane-layered media, and from the requirement that the applied source dipole pairs need to point in the same direction.

REFERENCES

L�seth. L. 0. and tjrsin, B., 2007, Electromagnetic fields in planarly layered anisotropic media: Geophysical Journal International, 170, 44-80.

Mittet. R., Aakèrvik, 0. M., Jensen, H. R.., Effingsrud, S., and Stovas, A.. 2007, On the orientation and absolute phase of marine CSEM receivers: Geophysics, 72, F145-F155.

Smith, B. and Ward, S. H., 1974, On the computation of polarization ellipse p&amets, Short note: Geophysics, 39, 867-869.

Claims

CLAIMS: 1. A method of determining the orientation of a controlled source electromagnetic receiver, comprising the steps of forming a linear combination of first and second data records recorded by the receiver for different source positions with substantially equal source-receiver offsets and substantially equal source dipole moments, and selecting an orientation angle for which the linear combination has a predetermined characteristic.
2. A method as claimed in claim 1, in which the linear combination comprises a sum or difference.
3. A method as claimed in claim 1 or 2, in which the predetermined characteristic is a minimum.
4. A method as claimed in any one of the preceding claims, comprising repeating the steps and forming an average of the orientation angles.
5. A method as claimed in any one of the preceding claims, in which the source azimuthal orientations are substantially equal for the first and second data records.
6. A method as claimed in any one of the preceding claims, in which there is a vertical source component at each of the source positions.