The present disclosure generally relates to electromagnetic surveying and in particular to methods and apparatus for acquiring and processing geophysical information.
In the oil and gas exploration industry, geophysical tools and techniques are commonly employed in order to identify a subterranean structure having potential hydrocarbon deposits. One such technique utilizes electromagnetic energy in a process known as electromagnetic prospecting.
Electromagnetic prospecting is a geophysical method employing the generation of electromagnetic fields at the Earth's surface. The electromagnetic fields may have a wave character, a diffusive character, or a combination of the two. When the fields penetrate the Earth and impinge on a conducting formation or orebody, they induce currents in the conductors, which are the source of new fields radiated from the conductors and detected by instruments at the surface.
The following presents a general summary of several aspects of the disclosure in order to provide a basic understanding of at least some aspects of the disclosure. This summary is not an extensive overview of the disclosure. It is not intended to identify key or critical elements of the disclosure or to delineate the scope of the claims. The following summary merely presents some concepts of the disclosure in a general form as a prelude to the more detailed description that follows.
Disclosed is a method for gathering geophysical information that includes receiving electromagnetic energy emanating from a subsurface target using a plurality of receivers, and generating a pseudo-source based at least in part on a location of one or more of the plurality of receivers and the received electromagnetic information.
For a detailed understanding of the present disclosure, reference should be made to the following detailed description of the several non-limiting embodiments, taken in conjunction with the accompanying drawings, in which like elements have been given like numerals and wherein:
Portions of the present disclosure, detailed description and claims may be presented in terms of logic, software or software implemented aspects typically encoded on a variety of media including, but not limited to, computer-readable media, machine-readable media, program storage media or computer program product. Such media may be handled, read, sensed and/or interpreted by an information processing device. Those skilled in the art will appreciate that such media may take various forms such as cards, tapes, magnetic disks (e.g., floppy disk or hard drive) and optical disks (e.g., compact disk read only memory (“CD-ROM”) or digital versatile (or video) disc (“DVD”)). Any embodiment disclosed herein is for illustration only and not by way of limiting the scope of the disclosure or claims.
The present disclosure uses terms, the meaning of which terms will aid in providing an understanding of the discussion herein. For example, the term information processing device mentioned above as used herein means any device that transmits, receives, manipulates, converts, calculates, modulates, transposes, carries, stores or otherwise utilizes information. In several non-limiting aspects of the disclosure, an information processing device includes a computer that executes programmed instructions for performing various methods.
Geophysical information as used herein means information relating to the location, shape, extent, depth, content, type, properties of and/or number of geologic bodies. Geophysical information includes, but is not necessarily limited to marine and land electromagnetic information. Electromagnetic information as used herein includes, but are not limited to, one or more or any combination of analog signals, digital signals, recorded data, data structures, database information, parameters relating to surface geology, source type, source location, receiver location, receiver type, time of source activation, source duration, source frequency, energy amplitude, energy phase, energy frequency, wave acceleration, wave velocity and/or wave direction, field intensity and/or field direction.
Geophysical information may be used for many purposes. In some cases, geophysical information may be used to generate an image of subterranean structures. Imaging, as used herein includes any representation of a subsurface structure including, but not limited to, graphical representations, mathematical or numerical representation, strip charts or any other process output representative of the subsurface structure.
The sensors 104 may include any number of sensors useful in gathering geophysical information. In one or more embodiments, the sensors may include electromagnetic sensors such as antennas, electrodes, magnetometers or any combination thereof. In one or more embodiments, the sensors may include pressure sensors such as microphones, hydrophones and their combinations. In one or more embodiments, the sensors 104 may include particle motion sensors such as geophones, accelerometers and combinations thereof. In one or more embodiments, the sensors may include combinations of electromagnetic sensors, pressure sensors and particle motion sensors. The non-limiting example system of
Referring still to
The energy source 102 may include any one or combination of several source types. In this example, the energy source includes an energy generator 108 that produces electromagnetic energy useful in a process known as controlled source electromagnetics (CSEM). The energy generator 108 is coupled to a multi-dimensional electromagnetic energy radiator 110. The term radiator is used herein to mean any device, structure, mechanism, combination thereof, and subcomponents thereof suitable for radiating energy. In the example system 100 of
Other suitable radiator structures may include three-dimensional structures. For example, a cube structure 306 or a tetrahedron radiator structure 308 may be coupled to the vessel 112. In some cases, the towing configuration may be such that the tow cable 116 may be connected directly to a radiator structure as shown with the tetrahedron radiator structure 306.
While substantially straight-ribbed radiator structures are shown, curved structures and radiator structures having a combination of curved and straight-ribbed structures may be used. In one or more embodiments, curved portions of a radiator structure may include at least a portion of curved shapes. Non-limiting examples include a curved structure such as a circle, oval or the like. Each branch of the multi-dimensional radiator structure 300, 304, 306, and 308 may carry electrical current 126 in a selected circuitous direction. Those skilled in the art with the benefit of the present disclosure will appreciate that the several circuitous current paths will generate both electrical fields and magnetic fields, each having multiple respective components depending on the particular current path selected.
The computer 1304 may be in communication with the storage device 1302 via any known interface and an interface for entering information into the computer 1304, 1306, 1308 may be any acceptable interface. For example, the interface may include the use of a network interface 1310.
The storage device 1302 according to one or more embodiments may be any useful storage device having a computer-readable media. Instructions for carrying out methods that will be described later may be stored on computer-readable media in the computer 1304, 1306, 1308 or may be stored on an external storage device 1302.
Operation of the exemplary geophysical information gathering system 100 will now be explained with reference to
The recorded signals may be processed on location or may be transmitted to a processing facility having a geophysical information processing system 1300 as described above and shown in
Introduction—Representation theorems in perturbed media
Let the general frequency-domain matrix-vector differential equation, {circumflex over (Ā)}{circumflex over (()}î{circumflex over (ω)}{circumflex over (Ā(iω
Theorems for dynamic systems satisfying the linear partial differential equation above include,
∫v[ûATKŝB−ŝATKûB]d3r=ûAT{circumflex over (M)}1ûBd2r+∫vûAT{circumflex over (M)}2ûBd3r (1)
with {circumflex over (M)}1=K[Nr−ÂA(vA·n)] and
{circumflex over (M)}
2
=K[Â
B(iω+vB·∇)−ÂA(iω−vA·∇)]+K[{circumflex over (B)}B−{circumflex over (B)}A]; and ∫v[ûA†ŝB+ŝA554 ûB]d3r=ûA†{circumflex over (M)}3ûBd2r+∫vûA†{circumflex over (M)}4ûBd3r, (2)
where {circumflex over (M)}3Nr−ÂA†(vA·n), and {circumflex over (M)}4=ÂB(iω+vB·∇)−ÂA†(iω+vA·∇)+{circumflex over (B)}B+{circumflex over (B)}A†. The subscripts A and B pertain to two wave states, to which we shall refer respectively as State A and State B. The matrix K is a real-valued diagonal matrix K=K−1 such that KAK=AT, KBK=BT and KDrK=−DrT. The superscript T denotes the transpose, while † represents the adjoint (i.e., the conjugate-transpose matrix). n is the outward-pointing normal at ∂v. The operator Nr is defined analogously to Dr but instead it contains the ni elements of the vector n.
Equation 1 is a convolution-type reciprocity theorem while equation 2 is a correlation-type theorem. When the field response is described by Green's tensors (see below), equation 1 results in a generalized source-receiver reciprocity theorem when ÂA=ÂB, {circumflex over (B)}A={circumflex over (B)}B and vA=−vB. In special cases for the material properties, the correlation-type theorem in equation 2 leads to a general form of Green's function retrieval by cross-correlations (i.e., a general form of interferometry).
Equations 1 and 2 may be rewritten for the special case of perturbed media. Physical phenomena in perturbed media can be described by the set of equations
Â(iω+v·∇)û+{circumflex over (B)}û+{circumflex over (D)}rû=ŝÂ0(iω+v0·∇)û0+{circumflex over (B)}0û0+{circumflex over (D)}rû0=ŝ (3)
where the subscript 0 denotes unperturbed field quantities and medium parameters, whereas its absence indicates field quantities and medium parameters that are perturbed. Every perturbed quantity or parameter can be written as a superposition of its unperturbed counterpart and a perturbation. Thus, Â=Â0+ÂS, {circumflex over (B)}={circumflex over (B)}0+{circumflex over (B)}S, v=v0+vS and û=û0+ûS, where the subscript S represents a perturbation. Note that to treat perturbed media, the source vector ŝ is the same for both the unperturbed and perturbed cases (equation 3). Subtracting the second in equation 3 from the first one yields the identity
{circumflex over (V)}û0={circumflex over (L)}ûS; (4)
where {circumflex over (L)} is the linear differential operator in the first line of equation 3, and {circumflex over (V)} is a perturbation operator given by {circumflex over (
A convolution-type representation theorem may be derived from equation 1 for general perturbed media. Throughout this paper, the discussion is centered on theorems that relate unperturbed fields in State A with perturbed fields in State B. In this perturbation approach we set ÂA=ÂB=Â, ÂA,0=ÂB,0=Â0, {circumflex over (B)}A={circumflex over (B)}B={circumflex over (B)}, {circumflex over (B)}A,0={circumflex over (B)}B,0={circumflex over (B)}0, and likewise for v and v0. Thus, from equation 1 we start with
∫v[ûA,0TKŝb−ŝATKûB]d3r=ûA,0T{circumflex over (M)}1PûBd2r+∫vûA,0T{circumflex over (M)}2PûBd3r; (5)
where {circumflex over (M)}1P=K[Nr−Â0(v0·n)] and {circumflex over (M)}2P=K[Â(iω+v·∇)−Â0(iω−v0·∇)+{circumflex over (B)}−{circumflex over (B)}0].
∫v[ûA,0TKŝB−ŝATKûB,0]d3r=ûA,0T{circumflex over (M)}10ûB,0d2r+∫vûA,0T{circumflex over (M)}20ûB,0d3r, (6)
with {circumflex over (M)}10={circumflex over (M)}1P=K[Nr−Â0(v0·n)] and {circumflex over (M)}20=K[2Â0(v0·∇)]. By using the identity û=û0+ûS, and after inserting equation 6 in the left-hand side of equation 5 we get
−∫vŝATKûB,Sd3r=ûA,0T{circumflex over (M)}1PûB,Sd2r+∫vûA,0T{circumflex over (M)}2PûB,Sd3r+∫vûa,0TK{circumflex over (V)}ûB,0d3r (7)
given that Δ{circumflex over (M)}2={circumflex over (M)}2P−{circumflex over (M)}20=K{circumflex over (V)}. This equation is a generalized convolution-type theorem that relates field perturbations at State B (left-hand side of the equation), with field perturbations and unperturbed fields in both States in the right-hand side.
The following step is to convert the reciprocity theorem in equation 7 into a representation theorem by replacing the field quantities by their corresponding Green's functions. The Green's matrices satisfy {circumflex over (L)}Ĝ=1δ(r′−r) and {circumflex over (L)}0Ĝ0=1δ(r′−r), with Ĝ−=Ĝ0+ĜS. In this formulation waves in State A are described by Ĝ0(rA, r), denoting the Green's matrix for the unperturbed impulse response observed at rA due to an excitation at r (for brevity we omit the dependency on the frequency ω). Likewise waves in State B are represented by the perturbed Green's matrix Ĝ(rB, r). This gives
K′Ĝ
S(rB,rA)=Ĝ0T(rA,r){circumflex over (M)}1PĜS(rB,r)d2r+∫vĜ0T(rA,r){circumflex over (M)}2PĜBS(rB,r)d3r. +∫vĜ0T(rA,r)K{circumflex over (V)}ĜB0(rB,r)d3r, (8)
where K′=−K. Equation 8 is important for the description of field perturbations for many physical systems. To illustrate this, let us consider a special case: that of fields in nonmoving media (i.e., v=v0=0), or when v=−v0. In either case, equation 8 simplifies to
K′Ĝ
S(rB,rA)=Ĝ0T(rA,r){circumflex over (M)}1PĜS(rB,r)d2r+∫vĜ0T(rA,r)K{circumflex over (V)}ĜB(rB,r)d3r. (9)
Equation 9 is a generalized version of Green's Theorem as it is usually presented in the physical description of many different physical phenomena. It shows that the Green's matrix for the field perturbations observed rB can be reconstructed by convolutions of unperturbed fields observed at rA with unperturbed fields and field perturbations observed at rB. The boundary integral vanishes when i) homogeneous boundary conditions are imposed on ∂v or ii) when the boundary tends to infinity and one or more of the loss matrices {circumflex over (B)}, {circumflex over (B)}0, Jm{Â} or Jm{Â0} are finite within the support of v (i.e., when fields are quiescent at infinity). In either case, equation 9 gives
K′Ĝ
S(rB,rA)=∫vĜ0T(rA,r)K{circumflex over (V)}Ĝ(rB, r)d3r. (10)
This equation is a general matrix-vector form of the Lippmann-Schwinger integral, yielding field perturbations for any physical phenomena described by equation 3. Along with series expansions for field perturbations that follow from equation 4, equations 8 and 10 describe scattering phenomena.
Correlation-type representation theorems may be derived for perturbed media, based on the more general theorems. We begin, in analogy to the previous derivation, by rewriting equation 2 to relate unperturbed fields in State A with perturbed fields in State B, with the following expression
∫v[ûA,0†ŝB+ŝA†ûB]d3r=ûA,0†{circumflex over (M)}3PûBd2r+∫vûA,0†{circumflex over (M)}4PûBd3r; (11)
where the matrices {circumflex over (M)}3P and {circumflex over (M)}4P are given by {circumflex over (M)}3P=Nr−Â0†(v0·n) and {circumflex over (M)}4P=Â(iω+v·∇)−Â0†(iω+v0·∇
∫v[ûA,0†ŝB+ŝA†ûB,0]d3r=ûA,0†{circumflex over (M)}30ûB,0d2r+∫vûA,0†{circumflex over (M)}40ûB,0d3r, (12)
with {circumflex over (M)}30={circumflex over (M)}3P=Nr−Â0†(v0·n) and {circumflex over (M)}40=Â0(iω+v·∇)−Â0†(iω+v0·∇)+{circumflex over (B)}0+{circumflex over (B)}0†. Given that {circumflex over (M)}4P−{circumflex over (M)}40={circumflex over (V)}− and û=û0+û̂s, then by inserting equation 12 in the left-hand side of equation 11 gives
∫vŝA†ûB,Sd3r=ûA,0†{circumflex over (M)}3PûB,sd2r+∫vûA,0†{circumflex over (M)}4PûB,Sd3r+∫vûA,0†{circumflex over (V)}ûB,0d3r (13)
This is a generalized correlation-type theorem that relates field perturbations at State B (left-hand side of the equation) unperturbed and perturbed fields on both States (right-hand side). Note that, as in the convolution theorem in equation 7, the surface integral contains unperturbed fields from State A and field perturbations from State B. With the same Green's matrix representation used in deriving equation 9, equation 13 can be written as
Ĝ
S(rB,rA)=Ĝ0†(rA,r){circumflex over (M)}3PĜS(rB,r)d2r+∫vĜ0†(rA,r){circumflex over (M)}4PĜS(rB,r)d3r+∫vĜ0554 (rA,r){circumflex over (V)}{circumflex over (G)}0(rB, r)d3r. (14)
This correlation-type representation theorem describes how the field perturbations sensed at rB due to a source at rA can be retrieved from cross correlations between unperturbed fields sensed at rA with unperturbed fields and field perturbations observed at rB. Equation 14 relates to the general formulations proposed by Wapenaar et al. (2006) and Snieder et al. (2007). In the formulation by Wapenaar et al. and Snieder et al., the reconstruction of the Green's functions by cross-correlations retrieves the causal and anticausal unperturbed responses Ĝ0(rB,rA) or Ĝ0†(rB,rA), or the perturbed ones Ĝ(rB,rA). or Ĝ†(rB,rA). Here, the theorem in equation 14 (as well as in equation 9) retrieves only the causal field perturbation matrix ĜS(rB,rA). Because the theorems of Wapenaar et al. and Snieder et al. retrieve both causal and anticausal responses, we refer to them herein as two-sided theorems; while equation 14 is a one-sided theorem because it only yields a causal response. In general, the volume integrals in equation 14 cannot be neglected, so the response ĜS(rB,rA) cannot typically be extracted only from the surface integral.
Reconstructing the Scattered Field Response
Monitoring parameter changes from volume sources. Although in general the correlation theorem in equation 14 is not suitable for the practice of “remote sensing without a source”, there are two important special cases that do allow for the retrieval of the medium's response from observed fields. Let us consider first the case of a nonmoving medium (v=v0=0) when the boundary integral in equation 14 vanishes (see necessary conditions in the derivation of equation 10). In that case, and given that {circumflex over (M)}4P={circumflex over (M)}40+{circumflex over (V)}, equation 14 becomes
Ĝ
S(rB,rA)=∫vĜ0†(rA,r){circumflex over (M)}40ĜS(rB,r)d2r+∫vĜ0†(rA,r){circumflex over (V)}Ĝ(rB,r)d3r. (15)
Now since {circumflex over (M)}40=Jm{Â)}+{circumflex over (B)}0+{circumflex over (B)}0\, the first integral in equation 15 accounts only for energy dissipation in the background medium. Hence, when the background loss parameters (represented by the matrix {circumflex over (M)}40 are negligible compared to the changes {circumflex over (V)}, the first integral in equation 15 can be ignored leaving
Ĝ
S(rB,rA)=∫vĜ0†(rA,r){circumflex over (V)}Ĝ(rB,r)d3r. (16)
Note that this integral is remarkably similar to the generalized Lippmann-Schwinger integral in equation 10, with Ĝ0(rA,r) replaced by −Ĝ0†(rA,r)− in the integrand. We shall explore this similarity later in our discussion. Next, we consider volume noise sources {circumflex over (σ)}(r,ω) distributed within V. For any two such noise sources, their respective vector elements {circumflex over (σ)}i(r,ω) and {circumflex over (σ)}j(r′,ω′) are uncorrelated for any i≠j and r≠r′; while their power spectrum is the same for any r and source-vector components, apart from frequency- and space-varying excitation functions. The uncorrelated noise sources obey the relation {circumflex over (σ)}(r){circumflex over (σ)}†(r′)=||{circumflex over (N)}||2{circumflex over (Σ)}{circumflex over (V)}(r)δ(r−r′), where the right-hand side is a spatial ensemble average, ||{circumflex over (N)}||2 is the noise power spectrum and the diagonal matrix {circumflex over (Σ)} contains the excitation functions. The presence of {circumflex over (V)} in the ensemble average above indicates that the perturbed-state volume sourcest {circumflex over (σ)}(r,ω) are locally proportional to the medium parameter changes at r. Under these conditions, the spatial averaging of the measured responses ûobs(r) is
(ûobs(rB){û0obs(rA)}†)=∫v||{circumflex over (N)}||2Ĝ0†(rA,r){circumflex over (Σ)}{circumflex over (V)}Ĝ(rB,r)d3r. (17)
Using this result together with that in equation 16 gives
Ĝ
S(rB,rA){circumflex over (N)}=(ûobs(rB){û0obs(rA)}†). (18)
For cases where equation 16 is valid, equation 18 states that one can obtain the scattered field response between the observation points at rA and rB by cross correlations of ambient noise records used in evaluating (ûobs(rB){û0obs(rA)}†). What sets this result apart from previous results for generalized representation theorems is that here the random volume noise sources are locally proportional to the medium parameter perturbation, e.g., observed signals can be thought of as being caused by changes in the medium. This interpretation of the general result in equation 18 is closely connected with the concept of coda-wave interferometry. Coda-wave theory relies on a energy propagation regime where the volume scatterers (i.e., the medium perturbations here described by the spatially-varying matrix {circumflex over (V)}) behave as secondary sources emitting waves that sample and average the medium multiple times. In the practice of coda-wave interferometry, cross-correlations of the late portions of the observed data (which represent waves in the multiple scattering regime) provide a measure of the medium perturbations and can be used to monitor changes in the medium. The result in equation 18 is related to that of coda-wave interferometry because the excitation is provided by volume sources that are proportional to the medium perturbation (i.e., to the local scattering strength), and the cross-correlations of the data observed at the two observation points yields an estimate of the scattered field impulse response between the two receivers. While coda-wave interferometry is typically accomplished by single receiver measurements (where rA=rB), equation 18 demonstrates that the cross-correlations of the responses sensed at two or more receivers can also extract information about scatterers and/or changes in the medium. Furthermore, the result in equation 18 applies not just to waves in lossless materials (e.g., acoustic and elastic); it also holds for dissipative acoustic, elastic and electromagnetic phenomena, quantum-mechanical waves, mass, heat or advective transport systems, etc. Therefore, the concept of monitoring medium perturbations introduced by coda-wave interferometry in fact applies to experiments with multiple observation points and all physical systems where equation 16 holds.
Reconstructing Perturbations from the Surface Integral
Another important special case for equation 14 occurs in the context of retrieving the Green's matrix of field perturbations by cross-correlations. Setting the loss matrices. {circumflex over (B)}={circumflex over (B)}0−=Jm{Â0}=Jm{Â0}=
Ĝ
S(rB,rA)=Ĝ0†(rA,r){circumflex over (N)}rĜS(rB,r)d2r+∫vĜ0†(rA,r){circumflex over (V)}Ĝ(rB,r)d3r; (19)
where {circumflex over (M)}4P={circumflex over (V)}. Since equation 19 holds when all loss matrices are set to zero, it is strictly valid for systems that are invariant under time-reversal. Thus, equation 19 retrieves the field perturbations ĜS−(rB,rA) for lossless acoustic and elastic wave propagation, for electromagnetic phenomena in highly resistive media, and for the Schrödinger equation, for example. Next, we consider a medium configuration as in
While the remaining contribution of the volume integral (given by Ĝ0†(rZ,r){circumflex over (V)}ĜS(rb,r) in the integrand) is not negligible, its contribution (to leading order in the scattered fields) has the same phase of that of the surface integral since the integrands also have the same phase. Therefore, it is possible to estimate the scattered field response according to
Ĝ
S(rB,rA)≈∫∂V
Evaluating solely the surface integral according to equation 20 should then retrieve ĜS(rB,rA) with correct phase spectra, but the amplitude spectra might be distorted by ignoring the volume integral in equation 19. Note also that the result in equation 20 is not valid for all sources in the closed surface ∂V. When ∂V1 is an infinite plane, and the wave propagation regimes can be described by coupled one-way operators, the result in equation 20 is exact: the out-going scattered waves propagating between receivers are obtained by cross-correlations of the scattered fields observed at ∂V1 with the measured in-going transmitted waves. The result in equation 20 can be used to retrieve ĜS(rB,rA) from remote sources on ∂V1. Here the terms out- and in-going waves to denote propagation direction with respect to the position of target scatterers; i.e., in-going waves propagate toward the scatterers, whereas back-scattered waves are out-going.
Referring now to
While a single pseudo-source record for a given radiator location can be generated from a minimum of two receivers, it is also possible to generate pseudo-source data from all possible receiver combinations from a plurality of receivers distributed over a chosen survey area. Increasing the number of receivers for which pseudo-source data is generated increases the overall volume of pseudo-source data and can provide additional information about the target subsurface structures and their physical properties.
The methods as described above may be conducted whether or not physical source parameters are known. Electromagnetic interferometry techniques according to one or more embodiments may include using interferometry to process information in the form of data signals generated by poorly known and/or controlled physical sources to generate pseudo-sources at the receiver locations, where the pseduo-sources have precisely-known parameters. The pseudo-sources can then be used to extract more complete and reliable information about the Earth's subsurface. Several embodiments may use aspects of the general theory discussed above to obtain the desired results from interferometry. We shall consider two examples, which lead to two different data processing routines.
In this example, sources and receivers may be densely sampled, and both the vertical electric and magnetic fields are reliably measured. The method includes using electric and magnetic fields recorded at receivers xA and x to separate the upward decaying fields in {circumflex over (P)}−(xA,xS) from the downward decaying fields in {circumflex over (P)}+(x,xS). Where {circumflex over (P)}− and {circumflex over (P)}+ are flux-normalized up-going and down-going vector fields, respectively. The method further includes solving the inverse integral equation for {circumflex over (R)}0+(xA,x), where {circumflex over (R)}0+ is the Fourier transform of an impulse response, from the input data {circumflex over (P)}−(xA,xS) and {circumflex over (P)}+(x,xS). Then, we may use {circumflex over (R)}0+(xA,x) (which is the pseudo-source response) to estimate subsurface information.
In this example, the receivers are coarsely sampled, and/or the separation of up- from down-decaying fields is not feasible, i.e., vertical fields cannot be measured or data are unreliable. A method suitable for these conditions includes establishing a prior background model describing electromagnetic properties of sea water and air, or use a best-fit subsurface model from standard processing of CSEM data. The method further includes numerically modeling fields Ĝ0(rA,r) and Ĝ0(rB,r) to simulate background response acquired by receivers at rA and rB. The method includes matching Ĝ0(rA,B,r) to the full-field acquired data û(rA,B,r) by adaptive subtraction and obtain û0(rA,B,r) and ûS(rA,B,r) as by-product.
One may then evaluate equation 14 above to estimate pseudo-source response ĜS(rB,rA). The surface integral is computed from the data û0(rA,B,r) and ûS(rA,B,r). The Green's function kernel can be computed via matrix-vector field deconvolutions. The volume integrals are evaluated numerically by setting the zero-order scattering approximation ĜS→Ĝ0; the matrix {circumflex over (M)}40 is computed from the background model, and {circumflex over (V)} is extracted fom a prior Earth model, which may come from standard CSEM processing, or from previous iterations of this processing routine.
In one or more embodiments, one may then use the estimated pseudo-source response ĜS(rB,rA) to infer or estimate subsurface properties. Where the estimated Earth model properties are not consistent with the originally acquired data, one may then iterate the above evaluation to estimate ĜS(rB,rA) and estimate the subsurface properties until reaching an acceptable Earth model that is within a predetermined threshold. An “acceptable” Earth model can be defined by some form of qualitative and/or quantitative measure of the differences between the acquired data and the data that would be predicted based on the current Earth model. In addition, the criteria for acceptable Earth models may also rely on other geophysical or geological information, e.g., maps, borehole data, seismic profiles, seismic images, gravity data, or resistivity profiles.
The methods of the present disclosure may be performed using electromagnetic information or in combination with any other useful geophysical information. For example, estimating parameters 406, 1514 may include the use of seismic information gathered before, concurrently with or after gathering the electromagnetic information. In one or more embodiments, other geophysical information such as seismic information may be used to generate, constrain, or otherwise clarify the Earth model 1506.
The present disclosure is to be taken as illustrative rather than as limiting the scope or nature of the claims below. Numerous modifications and variations will become apparent to those skilled in the art after studying the disclosure, including use of equivalent functional and/or structural substitutes for elements described herein, use of equivalent functional couplings for couplings described herein, and/or use of equivalent functional actions for actions described herein. Such insubstantial variations are to be considered within the scope of the claims below.
Given the above disclosure of general concepts and specific embodiments, the scope of protection is defined by the claims appended hereto. The issued claims are not to be taken as limiting Applicant's right to claim disclosed, but not yet literally claimed subject matter by way of one or more further applications including those filed pursuant to the laws of the United States and/or international treaty.
This application claims priority to Provisional U.S. Patent Application Ser. No. 61/057,606, filed May 30, 2008, which is hereby incorporated by reference in its entirety.
Number | Date | Country | |
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61057606 | May 2008 | US |