# Patent

## Title
Method of imaging subsurface formations using a virtual source array

## Abstract

This invention relates generally to a method of simulating the signal of an electromagnetic source using one or more dipole sources. In the method a dipole source is located at an excitation location corresponding to a segment of the electromagnetic source to be simulated. The dipole source is activated, and an electromagnetic signal recorded at one or more receiver locations. This process is repeated for additional excitation locations corresponding to additional segments of the electromagnetic source. The data from the sequence of dipole source excitation locations is processed to determine the simulated signal of the electromagnetic source.

## Background
This application claims the benefit of U.S. Provisional Application No. 60/318,082 filed on Sep. 7, 2001.


FIELD OF THE INVENTION
This invention relates to the field of controlled-source electromagnetic surveys for geophysical applications. More specifically, this invention relates to a method of imaging subsurface formations using a virtual source array.
BACKGROUND OF THE INVENTION
Electromagnetic sources used in geophysical surveying generally produce unfocused regions of subsurface excitation. Unfocused excitations result both from the diffusive nature of low frequency electromagnetic wave propagation in the earth and from the use of relatively simple source configurations in the surveys. Unfocused excitations are a severe disadvantage when a target-oriented survey is needed, such as when it is desirable to probe the electrical properties of a prospective formation in a location where a complex geologic background may be present.
To eliminate the disadvantages of unfocused surveys, a method of source focusing is disclosed in U.S. patent application Ser. No. 09/656,191, filed Sep. 6, 2000 (hereinafter referred to as “Srnka”). The method, referred to as the remote reservoir resistivity mapping method (“R3M”) uses a spatially extended grounded electromagnetic source array that is positioned on the earth's surface, or near the seafloor, to focus electromagnetic energy on the subsurface target. The source array consists of two concentric electrode rings whose radii are optimally determined from theoretical modeling to focus the subsurface excitation at the approximate depth of the subsurface target. A limitation of the Srnka method, however, is that for typical reservoir depths, which range from 500 meters to greater than 5000 meters, the total length of electrode wire that is required in the concentric electrode rings ranges from about 23.5 km to greater than 235 km.
These extreme lengths of electrode wire raise numerous operational challenges. For example, difficulties in handling and deploying the electrode wires, and problems in ensuring accurate positioning of the wires in the desired electrode ring locations may be involved, and there is the need to avoid obstacles in the area of the desired ring locations, and the requirement that the electrodes be uniformly grounded along their lengths. Other problems influence the economics of the survey, including the large cost of the electrode wire, some of which is likely to be damaged or lost in each survey, and the large labor and logistics costs associated with mobilization, demobilization, deployment, and recovery of the wire.
For these reasons, Srnka also disclosed an alternative method that reduces the required length of electrode wire by substituting a set of equally spaced radial electric bipoles, each having a length equal to the difference in the lengths of the radii of the two concentric rings. FIG. 1 depicts both the R3M concentric ring method and this radial bipole alternative. Concentric electrode rings 4 and 5 lie on surface 1 of earth 2 and have radii a and b, respectively, and a center 7 generally above reservoir 3. In the radial bipole alternative method these concentric rings are replaced by radial electrode bipole sources 6. Each bipole source 6 has a length L=b−a. Srnka discloses that a minimum of six radial bipole sources 6 is preferable. A signal equivalent to the signal that a receiver array would receive from the concentric ring source array is produced mathematically by summing the signals received by the receiver array from each of the bipole sources 6 (For convenience, FIG. 1 does not depict the location of the receiver array). This alternative method, which allows the simulation of a concentric ring source array, is referred to as the virtual concentric ring source method, or as the radial bipole method, and substantially reduces the required length of electrode wire as compared to the R3M physical concentric ring source method.
The virtual concentric ring source method nevertheless uses relatively long lengths of electrode wire and inherently retains many of the operational challenges of the R3M physical concentric ring source method. In addition, both methods have other inherent disadvantages, in particular for certain aspects of the subsurface resistivity-imaging problem. Specifically, both methods produce maximum responses near a pre-specified subsurface excitation focus depth (in other words, at the approximate depth of the target), but provide little differential sensitivity to features within an appreciable vertical range of that depth. More specifically, the ability to image separately features above or below the target a distance of less than five percent of the target's depth below the surface is limited. This limitation greatly hinders the imaging of stacked reservoirs. In addition, amplifier saturation effects can influence data quality and hinder analysis of such data. A third issue is that both methods produce primarily vertical subsurface currents in the region of the target. These currents are not adequate for imaging reservoir electrical macro-anisotropy (vertical electrical isotropy), such as exists in many reservoirs due to the presence of shale interbeds. Imaging this anisotropy is essential for estimating reservoir net and gross volumes, and for determining hydrocarbon pore volumes.
Accordingly, a method is desired which retains the advantageous electromagnetic responses of the R3M physical concentric ring source and radial bipole methods, but which reduces or eliminates the disadvantages of those methods. The present invention satisfies that desire.
SUMMARY
This invention relates generally to a method of simulating the signal of an electromagnetic source using one or more dipole sources. In the method a dipole source is located at an excitation location corresponding to a segment of the electromagnetic source to be simulated. The dipole source is activated, and an electromagnetic signal recorded at one or more receiver locations. This process is repeated for additional excitation locations corresponding to additional segments of the source being simulated. The data from the sequence of dipole source excitation locations is processed to determine the simulated signal of the electromagnetic source.



BRIEF DESCRIPTION OF THE DRAWINGS
The features of the present invention will become more apparent from the following description in which reference is made to the drawings appended hereto. Reference numbers that are used in more than one of the drawings refer to the same function in each drawing.
FIG. 1 depicts a perspective view of the Srnka method.
FIG. 2 is a flow chart of the steps for implementation of a first embodiment of the present invention.
FIG. 3 depicts a perspective view of a first embodiment of the present invention.
FIG. 4 depicts a plan view of a second embodiment of the present invention.
FIG. 5 depicts a data acquisition procedure for a marine application of an embodiment of the present invention.
FIG. 6 depicts a plan view of a method for acquiring data for the marine application of FIG. 5.
FIG. 7 depicts a plan view of an embodiment of the present invention in which variations in the locations of the target depth and focal point can be made.
FIG. 8 depicts a model target for use with a bipole source processing example.
FIG. 9 depicts the total electric field calculated for the bipole source processing example of FIG. 8.
FIG. 10 depicts a model target for use with an embodiment of the present invention in which dipole sources are used to simulate the data acquired by the bipole source example of FIG. 8.
FIG. 11 depicts the total electric field calculated according to the embodiment of the present method depicted in FIG. 10.



Changes and modifications in the specifically described embodiments can be carried out without departing from the scope of the invention, which is intended to be limited only by the scope of the appended claims.
DETAILED DESCRIPTION OF THE INVENTION
The present invention is a method of simulating the advantageous multicomponent electromagnetic response of a resistive reservoir to excitation by a concentric ring source array, or its radial bipole equivalent, with a significantly reduced amount of electrode wire. In a preferred embodiment, the method uses one or more short dipole sources, each located sequentially at source excitation locations corresponding to a location of a radial bipole to be simulated, to obtain measurement data during field surveys in the region of the subsurface target to be imaged. Phase and amplitude receiver data are synchronized with data from the source locations and summed using a Green's function integration to determine the response of the target. The method has an inherent ability to create a large number of virtual source configurations by varying the number and positions of the source excitation locations that are integrated in the receiver data, thereby facilitating much higher spatial resolution of the near surface, as well as for other depths, than can be attained by previously proposed methods. Additional virtual source configurations can be created by use of Green's function reciprocity conditions which can be used to relate electric field recordings made with exchanged transmitter and detector locations.
The present method allows for the recording of signals from a large number of linear electric sources. Integration of receiver data from these linear sources facilitates the imaging of subsurface resistivity outside of the region that would be the focal point of a concentric ring source array. This advantage allows for measurement of the subsurface horizontal resistivity response over a range of depths, and allows for detection of reservoir resistivity anisotropy. An advantage of the use of a multiplicity of sources is production of a multiplicity of electric current probes of the subsurface target, which can have positive effects on data redundancy.
The method of the present invention can be more fully described with reference to the flow chart in FIG. 2 and the embodiment depicted in FIG. 3. The initial step, FIG. 2-step 100, requires calculation of the dimensions of the R3M method's concentric electrode rings for the subsurface target of interest. In FIG. 3, subsurface target 3 within earth 2 is at depth D below the earth's surface 1, and concentric electrode rings 4′ and 5′ have diameters a and b respectively. Rings 4′ and 5′ are not physical electrode rings, but rather are solely used in the calculations required in the present method (As used herein, the addition of a prime to a reference number indicates that the referenced item is part of a virtual source, i.e. a source to be simulated, as opposed to a physical source. For example, in the R3M method of FIG. 1, electrode rings 4 and 5 are physical sources, whereas in FIG. 3, electrode rings 4′ and 5′ are virtual sources). As specified in Srnka, to maximize source excitation at depth D it is preferable if a/D=1.5 and b/a≧9. In addition, Srnka also discloses that a minimum ratio b/a≧4 provides a sufficient source excitation at depth D.
Next, FIG. 2-step 102, the number, length L, and location of radial bipole sources for Srnka's virtual concentric ring source method must be determined. Srnka discloses that a minimum of six bipole sources, each of length L=b−a, is preferred for the radial bipole method. As will be understood from Srnka, the use of these bipole sources provide a mechanism for creating an electromagnetic source focal point at the depth D of target 3. In Srnka, the radial bipole sources (e.g. the radial bipole sources 6 of FIG. 1) are physical sources. An objective of the present invention is to simulate these radial bipole sources using shorter physical sources, referred to as dipole sources, and to thereby simplify the acquisition of electromagnetic survey data. Thus, in the present method, FIG. 2-step 102 results in the calculation of the number, length and location of the radial bipole sources to be simulated. For simplicity, the location of only one simulated radial bipole source 6′ is shown in FIG. 3.
In the method of the present invention, each radial bipole source of length L is replaced by N−1 shorter radial dipole sources of length l=b/N, FIG. 2-step 104. Length l is restricted to l≦a so that the radius of the inner virtual concentric ring 4′ is at least one radial dipole source length, for ease of data integration following the steps described below. For typical reservoir target depths D, which may range from 500 meters to 5000 meters subsurface, and for typical values of length l ranging for ease of deployment purposes from 100 meters to 1000 meters, the number N may range from about 3 to more than 300.
Next, FIG. 2-step 106, the position of receiver array 12 is determined. Factors to be considered in designing and determining a location for the receiver array, which will be understood to those skilled in the art, are further discussed in Srnka.
Next, FIG. 2-step 108, a first radial dipole source is placed at a first source excitation location corresponding to a first bipole source to be simulated. In FIG. 3, the first bipole source to be simulated is 6′, and radial dipole source 8 of length l is placed at first source excitation location 101 along a radius 9 of the virtual outer concentric ring 5′. In FIG. 3, first source excitation location 101 extends from virtual outer concentric ring 5′ along radius 9 inward toward center 7. The present method is not limited to this location of first source excitation location 101. As noted in Srnka for the virtual concentric ring source method, radial dipole source 8 should be grounded at each end over a distance of at least ten percent of length l, and, as will be understood to those skilled in the art, should be powered by variable frequency (preferably 10−4-104 Hz), high current (preferably 102-106 Amperes) electrical power sources and controllers. Further details on sources for use in electromagnetic surveying are provided by Srnka.
Next, FIG. 2-step 110, the physical location of the radial dipole source 8 at the source excitation location 101 must be determined. This location can be determined by geodetic or other methods well known to those skilled in the art. The required positioning accuracies for each end of the radial dipole source are preferably 1 meter on land and 5 to 10 meters offshore.
Next, FIG. 2-step 112, the radial dipole source is energized and the amplitude and phase of the source signal is recorded. The source signal at each source excitation location is preferably held constant, with variations in phase limited to 0.1 degree and in amplitude to 0.1%, as further described in Srnka.
In FIG. 2-step 114, the amplitude and phase of the response at the receiver array 12 are recorded.
The sequence encompassed by FIG. 2-steps 108 through 114 is repeated, FIG. 2-step 116, for a radial dipole source located at a second source excitation location. In FIG. 3, the second source excitation location is indicated as 102. Thereafter, the process of steps 108 through 114 is repeated for additional source excitation locations 103, 104, . . . 10N−1 until measurements have been recorded along the entire length of the radial bipole source 6′ being simulated. In FIG. 3, this length corresponds to the portion of radius 9 extending from virtual electrode ring 5′ to virtual electrode ring 4′. This process completes the source excitations and receiver response recordings necessary to simulate radial bipole source 6′.
The mathematical calculations of the present method require the normalizing of the multicomponent receiver responses to the source electric dipole signal (magnitude and phase) recorded for each source excitation location. Normalization assures that unwanted changes in receiver signals due to variations in either source coupling or power source current are removed from the receiver data. Source phase and amplitude control, as described above, together with recording of the source output with accuracies of 0.1 degree in phase and 0.1% in amplitude is preferred. Additional processing steps can include manipulation of the current in the transmitting electric dipole to achieve noise suppression and focusing effects. Manipulation of the dipole current can be achieved during data recording or by computational means after data is recorded.
The sequence encompassed by FIG. 2-steps 108 through 116 is then repeated, FIG. 2-step 118, for the second and each subsequent bipole source locations, as specified in FIG. 2-step 102 (the second and subsequent bipole sources to be simulated are not shown in FIG. 3). This process completes the recording of the data required in the present method to compute the response of target 3 in FIG. 3.
Finally, FIG. 2-step 120, the received signals for dipole source excitations corresponding to each bipole source are integrated in either the frequency or time domain using received signal amplitude and phase control relative to the source signal. This process is referred to as amplitude and phase normalized Green's function integration. Each integration constructs the signals that would have been recorded if physical radial bipole sources of length L=b−a and extending from virtual electrode ring 5′ to virtual electrode ring 4′ at each of the locations specified in FIG. 2-step 102 had been used as physical sources. The integration results in the creation of a virtual radial bipole source at each of the locations specified in FIG. 2-step 102. Upon completion of these integrations, the virtual concentric ring source method of Srnka can be applied to determine the characteristics of the target.
A second novel aspect of the present invention involves the ability to create a large number of virtual concentric ring source array configurations (in other words, to obtain simulated data for virtual concentric rings with a range of values of a and b). This advantage derives from the ability to vary the number and locations of source excitations that are summed in the receiver data, and allows accurate target characterizations over a broader range of depths than can be characterized by the R3M or virtual concentric ring source array methods. FIG. 4 demonstrates this aspect of the present invention.
FIG. 4 depicts a sequence of virtual outer concentric electrode rings 251, 252, 253, . . . 25m, with diameters b1, b2, b3, . . . bm, and a sequence of virtual inner concentric electrode rings 241, 242, 243, . . . 24m, with diameters a1, a2, a3, . . . am. All rings are centered at 27. A first virtual bipole radial source to be simulated, extending from ring 241 to ring 251, is shown as 261. Dipole source excitation locations 301, 302, 303, . . . 30N extend inward from ring 251, along radius 29 toward center 27. (For convenience in discussing FIG. 4, the prime reference, which otherwise signifies the distinction between a virtual and a physical source, has been omitted).
The diameters b1 and a1 of virtual concentric electrode rings 25i and 241 and length l of the dipole sources to be used at each dipole source excitation location 301 are determined as discussed above. Note that the constraint l≦a noted above will determine the radius for the innermost, inner concentric electrode ring 24m. This constraint thereby establishes the total number of virtual concentric electrode rings in this embodiment of the present invention. Since N−1 radial dipole positions exist which exclude one electrode end at zero radius, (in other words, for which the constraint l≦a is satisfied), it follows from the well-known binomial theorem of mathematics that ((N−1)!)/(2!(N−3)!) virtual ring source combinations exist. This will be understood to one skilled in the art. These virtual ring source combinations cover a range of aspect ratios of the radius of the virtual outer concentric ring to the radius of the virtual inner concentric ring (in other words, of the ratio b1/a1), including aspect ratios near unity that produce narrow (annular) and shallow subsurface excitations. As a result, a broad range of virtual bipole sources 26i can be simulated, resulting in a characterization of the subsurface region over a much broader range of depths than has previously been possible. Note also that as will be known to one skilled in the art additional virtual source array configurations can be generated using Green's function symmetries.
For example, using b1=10 km and l=500 m gives N=20, which allows for creating 19!/(2!17!)=171 virtual ring sources. The combinations of ring sources having radial aspect ratios b/a≧4 produce focused vertical electric field excitations that range by a factor of 5 over depth. For the b/a=4 case, the range of depths is from the near surface (D=333 m) to the deep subsurface (D=1.67 km). As noted in Srnka, for each virtual concentric ring source so constructed, the radius of maximum vertical electric field excitation is approximately 2 a. Note also that the optimum frequency of excitation for each virtual ring increases as D decreases due to the skin depth effect, allowing much higher spatial resolution for the near surface, in other words small D, excitations.
The implementation of this embodiment follows directly from the discussion of FIGS. 2 and 3 above. Source and receiver data is recorded for each source excitation location extending along the entire length of radius 29. In contrast to the process of FIG. 3, these source excitation locations extend from outer concentric ring 251 along radius 29 to the innermost inner concentric ring 24m. This data recording process continues for each radius 29 along which a virtual radial bipole source is to be simulated (only a first radius 29 is depicted in FIG. 4). As noted above, a minimum of six virtual bipole sources is preferred, separated by no more than 60 degrees.
The processing of data in this embodiment also follows from the discussion of FIGS. 2 and 3 above, except that the additional amount of data acquired in this embodiment adds additional processing steps. First, referring to FIG. 4, the data corresponding to source excitation locations for a virtual radial bipole source 261, extending from outer concentric ring 251 to inner concentric ring 241, are processed. This processing step is repeated for each of the other virtual radial bipole sources that correspond to outer concentric ring 251 and inner concentric ring 241. Processing of the data corresponding to these virtual radial bipole sources allows characterization of the subsurface at a depth centered on D1.
Next the data corresponding to source excitation locations for a virtual radial bipole source (not shown in FIG. 4) extending from outer concentric ring 252 to inner concentric ring 242 are processed. This processing step is repeated for each of the other virtual radial bipole sources that correspond to outer concentric ring 252 and inner concentric ring 242. Processing of the data corresponding to these virtual radial bipole sources allows characterization of the subsurface at a depth centered on D2 
This data processing sequence is repeated for the source excitation locations that correspond to each additional pair of concentric rings 25i and 24i, each pair of which facilitates the characterization of the subsurface at depth D1. The characterizations corresponding to depths Di derive from the aspect ratio bi/ai which correspond to the dimensions of the concentric ring pairs 251 and 24i. As noted above, this ratio will generally be b/a=4. Additional processing of the data may be performed for other aspect ratios b/a>4 by creating additional pairs of concentric rings. In FIG. 4, for example, data may be processed for source excitation locations extending along radius 29 from ring 251 to 242, thereby creating a distinct virtual bipole to be simulated, and a distinct subsurface target depth. Therefore, in the present method, data can be acquired once over the areal region on the surface of the earth overlying the target of interest, with multiple processing sequences used to increase the ability to characterize the entire subsurface below that areal region.
Although one or more short dipole sources may be used, either simultaneously or sequentially in the present invention, a preferred embodiment for land-based surveys uses only one electromagnetic dipole source that is moved sequentially in a radial direction inward, outward, or in an alternating sequence in both directions. Use of only one dipole source reduces the total amount of source electrode wire from tens or hundreds of kilometers to only a few hundred meters, as is determined by the specified dipole length l. The dipole length l for land-based surveys is preferably 500-1000 meters, to minimize the number of necessary source locations, since deployment of grounded source dipoles on land is relatively difficult. This deployment difficulty is due primarily to the need to physically move the electrode wire across the surface of the land, and also due to the need to ground the electrode ends to the earth at each new position. In the land survey implementation, the source dipole occupies positions 301, 302, 303, and so on corresponding to a first bipole source to be simulated (FIG. 4). The process is repeated for each bipole source to be simulated.
FIGS. 5 and 6 show sequential source dipole movement in the marine case. The marine implementation of the present invention has advantages over the land-based survey implementation, including the ease of re-positioning the source dipole and the improved electrical coupling of the source electrodes to the seafloor and/or water so that the effort to ground the ends of the electrode is unnecessary. FIG. 5 shows a survey vessel 35 at the surface 60 of a body of water and an electric source dipole 63 at or near, but preferably within 50 meters of, the bottom 61 of the body of water, such as the seafloor. Source dipole 63 has a length l of typically 100-500 meters in the marine case, so as to minimize the difficulties of controlling the source remotely and accurately measuring its position from the survey vessel. The survey is carried out by the vessel either: 1) sequentially moving the source from a first source excitation location 641 to a second source excitation location 642, where sequential source excitation locations are centered at a distance separated by the length l of the source dipole, and then remaining stationary during the excitation of the source, with the process repeated for the source excitation locations required to simulate the bipole source of interest; or 2) continuously towing the dipole at low speed (typically 1 to 4 knots, approximately 0.5 to 2.0 meters/sec) while the source is under excitation. In the towed dipole source case, the source towing speed must be sufficiently slow so that distortion of the source excitation waveform due to the Doppler effect is negligible. In the case of diffusive electromagnetic waves in the earth, as are involved in this invention, the fractional change Δf in source frequency f detected at a fixed electromagnetic receiver due to the Doppler effect is equal to the source speed vs divided by the phase velocity of the wave vp=3,162×(ρf)1/2, where ρ is the average resistivity. For typical offshore basin electromagnetic survey values of vs=1 meter/sec, f=0.5 Hertz, and ρ=1 Ω-m, Δf=0.045%, which is negligible. This analysis will be well understood to those skilled in the art. As in the land case, the length of the virtual bipole thus formed is N×1.
An additional important consideration in the continuously towed dipole case is minimization of the geometric smearing of the source position due to its speed vs during the transmission of one or more cycles of the source electrical current. This geometric effect must be minimized so that the receiver data integration using Green's function methods for a given source location is accurate. The fractional length Δl/l that a source dipole of length l moves during M cycles of the emitted current at frequency f is given by Δl/l=(M×vs)/(l×f). Preferably, Δl/l<<1 so that excitations from only one source position are integrated into the receiver data. It is well known to practitioners of the art that M values, also referred to as data stacks, greater than one are usually required to achieve acceptable signal-to-noise values at the receivers. For typical offshore basin electromagnetic survey parameters, in other words l=100 meters, f=0.5 Hertz, and vs=1 meter/sec, it is preferable if the data stack value M<<50. It is well known in the marine electromagnetic art that data stacks as small as M=5 can result in acceptable signal-to-noise values for receiver data, depending upon the environmental conditions in the survey area. Data stacks of M=20 or higher may be appropriate for deep targets and long transmitter to detector offsets. The effects of transmitter smearing can be mitigated by comparing measured results to models with smearing effects included.
A preferred method of acquiring data for the marine case is depicted in FIG. 6. Vessel 35 tows an electric dipole source 36 of length l along a first diameter 371 of virtual concentric ring 381. Upon completion of data acquisition along the entire length of diameter 371, vessel 35 turns and commences data acquisition along a second diameter 372, separated by angle φ from first diameter 371. Repeating this process along a series of diameters 371 (where the subscript i refers to each of the individual diameters along which data is to be acquired), preferably from 3 to 16, separated by equal angles φ, allows formation of a series of virtual concentric source rings of diameter ratios b1/ai, as described above. Model studies have shown that 3 to 16 equally spaced diameters are preferable to approximate concentric ring sources.
In addition to simulating the source and receiver signals generated by concentric circular ring sources, the present method allows for the simulation of a large number of linear sources. These simulations derive from the integration of the data using other combinations of signals resulting from the excitations by the short dipoles, and thus can be carried out at no additional survey cost. This aspect of the invention allows for imaging of subsurface resistivity outside of the central focusing zones of the concentric ring sources, such as near the location of the outer concentric electrode ring which is simulated in the processing described above. For example, in FIG. 7, a set of full-diameter bipole sources 401, 402, . . . 40D, corresponding to virtual concentric rings 441, 442, . . . 44M and 451, 452, . . . 45M are depicted. Each of these full-diameter bipole sources can be simulated using the method of the present invention, as described above. During the data acquisition phase of the present method, it is preferable that data are acquired between the innermost inner concentric ring 44M and center 47. This preference results in source and receiver data recordings for the entire length of each full-diameter bipole source.
As noted above, data acquisition for the dipole source locations used to simulate each full-diameter bipole source produces significant vertical and horizontal electric field excitation over a range of depths extending to a depth approximately equal to the diameter of the outer concentric ring 451, and centered symmetrically about center 47 of the concentric rings. In the method of the present embodiment, however, the dipole source excitation locations at a first end of the simulated bipole source may be excluded from the Green's function integration, thereby shifting the symmetry point from center 47 along the simulated bipole source in a direction away from the end at which the sources were excluded. This exclusion also reduces the effective depth of excitation, and allows for a different central focusing zone to be probed, in other words for a different subsurface region both in depth and in source focal point to be evaluated. For example, in a first processing sequence involving all data obtained for source excitation locations corresponding to full diameter 401, the source focal point will be directly below the midpoint of diameter 401, in other words directly below center 47. In a second processing sequence the data corresponding to dipole source excitation location 401A is excluded from the Green's function integration. This exclusion shifts the source focal point to a point which is nevertheless below diameter 401, but which is shifted horizontally by the distance 1⁄2 away from location 401A. A second exclusion of the data corresponding to dipole source excitation location 401B will shift the source focal point an additional distance of 1⁄2 in that direction. Each of these exclusions will also reduce the depth of the source focal point. Continued repetition of this process provides a method for developing a broader characterization of the subsurface. The horizontal electric field excitations resulting from exclusion of these individual dipole source locations in the integration, when combined with the primarily vertical excitation due to the virtual concentric ring sources, allows for detection of reservoir resistivity anisotropy, as discussed in Srnka.
Comparisons have been made of the numerical calculation of the electromagnetic response of the earth to excitation by a grounded linear bipole source (FIGS. 8 and 9) to the response calculated according to the present method using eight summed dipole sources (FIGS. 10 and 11), as further described in the following.
In both FIG. 8 and FIG. 10, a hypothetical model reservoir target 50 is a 5000 meter×5000 meter square slab 20 meters thick of 100 Ω-m (ohm-meter) resistive rock that is buried in a uniform background of 1 Ω-m conductive rock 51. The top of target 50 is buried 1000 meters below the seafloor, which in turn is covered by 1000 meters of uniform 0.25 Ω-m seawater. An insulating air layer 5000 meters high is placed above the seawater. In both figures a uniform grid of 5,329 electromagnetic receivers 52, spaced 250 meters apart in both horizontal (X and Y) directions, is placed at the seafloor, uniformly distributed within the coordinates −9000≦Y≦9000 and −9000≦X≦9000.
In FIG. 8 a single bipole 53 is placed along the Y-axis, centered at the coordinate origin (X=0, Y=0) and having length L=8000 meters. Bipole 53 is assumed to be placed in the seawater one meter above the seafloor and emits 100 Amperes of electrical current at a sinusoidal frequency of 1.0 Hertz. FIG. 9 shows the magnitude of the total vertical electric field in Volts/meter at the receiver positions, calculated at a frequency of 1.0 Hertz, for the single bipole model of FIG. 8. The response is smoothly varying in X and Y, except for large, mathematically infinite, values at the two ends of the bipole where current is injected. Persons skilled in the art will understand the source of these singularities in the numerical calculation procedure, and will further understand the decrease of the total vertical electric field with distance from source bipole 53.
In FIG. 10, the single 8000 meter electric bipole 53 of FIG. 8 has been replaced by eight grounded electric dipoles 60, each of length l=1000 meters and emitting 100 Amperes, so that the total electric dipole-moment (length times current) of the source is preserved. The ends of adjacent dipoles 60 are separated by one meter in the Y direction for more stable calculation in the numerical simulation (This separation is not depicted at the grid scale of this figure). In all other respects the model of FIG. 10 is identical to the model of FIG. 8. FIG. 11 shows the calculated response for the model of FIG. 10 using the present method, again at a frequency of 1.0 Hertz. The response in FIG. 10 is substantially identical to the response of FIG. 8, with differences limited only by the number of significant digits which are used in the numerical, i.e. Green's function, calculation. Note that due to the scale of the calculation grid, which has 100 meter horizontal cells, only a total of only nine singularity points are shown. At this calculation grid scale the singularities for the ends of adjacent dipoles 60 appear as a single singularity. As can be observed from comparison of FIG. 9 to FIG. 11, the results of these calculations illustrate the capability of the principle of grounded source superposition for electromagnetic arrays, as described in the present invention, to simulate the electromagnetic response that would be obtained from a full length electromagnetic bipole source.
FIG. 11 depicts the response calculated according to the present method for a model target of specified characteristics. Data processing techniques will be required to determine the resistivity and depth characteristics of a target for which data have been acquired according to the present method. These processing techniques generally involve one of two methods. Curve matching techniques, in which modeled responses, such as in FIG. 11, are compared to actual measured data to thereby infer the actual characteristics of the data acquisition target, are a first such method. A second method involves use of an imaging algorithm such as described by Srnka in which a wave equation based algorithm is used to invert the acquired data into a model that contains the characteristics of the target. These processing techniques, which will be well understood to those skilled in the art, are further discussed by Srnka.
It should be understood that the preceding is merely a detailed description of specific embodiments of this invention. Other embodiments may be employed and numerous changes to the disclosed embodiments may be made in accordance with the disclosure herein without departing from the spirit or scope of the present invention. Furthermore, each of the above embodiments is within the scope of the present invention. The preceding description, therefore, is not meant to limit the scope of the invention. Rather, the scope of the invention is to be determined only by the appended claims and their equivalents.

## Claims

1. A method of imaging a subsurface formation, comprising the steps of:
computing the inner and outer radii of a grounded electromagnetic concentric ring source focused on the formation;
using the radii to compute the length of a radial electric bipole corresponding to the ring source;

using the length of the radial electric bipole to determine the length of a radial dipole source;
positioning the radial dipole source at a first position along a radius of the ring source;
energizing the radial dipole source;
measuring an electromagnetic signal at one or more receiver locations;
repeating steps d, e, and f for one or more additional positions of the radial dipole source along the radius;
using the measured electromagnetic signals to compute the signal of a virtual radial bipole corresponding to the radius;
repeating steps d, e, f, g, and h for at least five additional radii of the ring source; and
using the signals of the virtual radial bipoles to image the formation.

2. The method of claim 1, wherein the image of the formation is created using virtual source configurations created from use of Green's function reciprocity conditions.

3. The method of claim 1, wherein said formation is imaged at two or more depths, each said depth corresponding to a specific set of virtual concentric ring sources, wherein signals of virtual radial bipoles corresponding to each said set of virtual concentric ring sources are used to image said formation at the depth corresponding to said virtual concentric ring sources.