Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Detailed Action
Claims 1,3-11 and 13-22 are pending.
Response to Amendment
This action is in response to the Amendment filled on 12/19/2025. The amendment has been entered. Claims 1,3,11 and 13 have been amended, claims 2 and 12 have been cancelled (incorporated in independent claims 1 and 11), and further claims 21 and 22 have been newly added. Claims 1,3-11 and 13-22 are pending, with claims 1 and 11 being independent in the instant application.
Response to Arguments
Applicant's Arguments/Remarks filed on 12/19/2025 on page 8 regarding previous Objection on claim 11 have been fully considered and are found persuasive in view of the amended claim and presented Arguments/Remarks by the Applicant. However, a new objection on claim 21 is necessitated by Applicant's claim amendments. (See analysis below Claim Objections).
Applicant's Arguments/Remarks on page 8-14 regarding 35 U.S.C. 101 rejections have been fully considered and are found unpersuasive in view of the amended claim and presented Arguments/Remarks by the Applicant.
Applicant's Arguments/Remarks on page 10-11 stated: “Applicant respectfully disagrees with the Examiner's categorization of the limitations "forming one or more model parameters" and "identifying one or more inversion controls" as mental processes. … in independent claims 1 and 11, cannot reasonably be interpreted as reciting processes that can be performed in the human mind or by a human using a pen and paper because "the human mind is not equipped to perform the claim limitations."
Examiner respectfully disagrees with the argument/remark above. The limitation of claim 1 “forming one or more model parameters from one or more priori geological information and one or more downhole measurements;” is recitations of evaluation or judgement that fall within the Mental Processes enumerated category of abstract ideas because under BRI this limitation could be "performed by human without a computer", i.e., one or more model parameters can be formed/created from one or more priori geological information and by using one or more downhole measurements. Further, the limitation “identifying one or more inversion controls to be used as hyper-parameters;” is recitation of Mathematical Concepts. The Specification of current Application at para [0044] stated: “Hyper-parameters found in block 512 may include number of iterations, misfit threshold, initial solution for optimization, and/or regularization coefficients.”
Applicant's Arguments/Remarks on page 12-13 stated: “In particular, independent claims 1 and 11 recite specific technical operations, including forming parameters, identifying inversion controls to use as hyper-parameters, … updating the forward model operation based on the misfit, and using the inversion model to simulate one or more tool responses. Such recitations, taken individually or as a whole, are not merely "a drafting effort to monopolize the judicial exception," … Such limitations impose meaningful limits on practicing the alleged abstract idea and, therefore, cannot reasonably be interpreted as mere drafting effort to monopolize the judicial exception. Rather, such limitations recite additional elements that interact and impact each other and, as a whole, provide for a practical application of performing a particular and unique process for determining performing a well logging inversion.”
Examiner respectfully disagrees with the argument/remark above. The amended limitations of claim 1: “using the one or more model parameters to generate an inversion model for a geological formation based on a piecewise polynomial model (PPM) …; forming one or more initial models from the model parameters to be utilized in a forward model operation; performing, based on the one or more initial models the forward model operation using the PPM wherein the only unknown variables in the PPM are one or more coefficients of each polynomial segment in the series of polynomial segments; and simulating one or more tool responses based on the inversion model.” are recitations of Mathematical Concepts. The last limitation "simulating" using the inversion model, corresponds to merely applying/using generic computer to cover all the bases. Accordingly, claim 1 as a whole is found to recite a judicial exception and is drawn to an abstract idea.
Therefore, the previous rejections regarding 35 U.S.C.101 are being amended in this current office action. (See analysis below Claim Rejections-35 U.S.C. §101).
Applicant's Arguments/Remarks filed on pages 14-16 regarding 35 U.S.C. 103
rejections have been fully considered and are found persuasive in view of the amended claims and presented Arguments/Remarks by the Applicant. However, a new ground of rejections is necessitated by Applicant's claim amendments. Therefore, the previous rejections regarding 35 U.S.C.103 are being amended in this current office action. (See analysis below Claim Rejections-35 U.S.C. §103).
Examiner Notes
Examiner cites particular columns, paragraphs, figures and line numbers in the references as applied to the claims below for the convenience of the applicant. Although the specified citations are representative of the teachings in the art and are applied to the specific limitations within the individual claim, other passages and figures may apply as well. It is respectfully requested that, in preparing responses, the applicant fully consider the references in their entirety as potentially teaching all or part of the claimed invention, as well as the context of the passage as taught by the prior art or disclosed by the examiner. The entire reference is considered to provide disclosure relating to the claimed invention. The claims & only the claims form the metes & bounds of the invention. Office personnel are to give the claims their broadest reasonable interpretation in light of the supporting disclosure. Unclaimed limitations appearing in the specification are not read into the claim. Prior art was referenced using terminology familiar to one of ordinary skill in the art. Such an approach is broad in concept and can be either explicit or implicit in meaning. Examiner's Notes are provided with the cited references to assist the applicant to better understand how the examiner interprets the applied prior art. Such comments are entirely consistent with the intent & spirit of compact prosecution.
Claim Objections
Claim 21 is objected to because of the following informalities:
Claim 21 stated: “The system of claim 1, wherein the forward model operation uses the PPM …”. Examiner presumes a typo has been occurred in this scenario, since independent claim 1 is a method claim, whereas independent claim 11 is a system claim. Appropriate correction is required, to show claim 21 is dependent on claim 11 not on claim 1, suggested claim amendment for claim 21, e.g., The system of claim 11, herein the forward model operation uses the PPM …”). For the examination purpose, Examiner would construe claims 21 and 22 are dependent on independent claim 11 (since both of these claims are system claim).
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1,3-11 and 13-22 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor, or for pre-AIA the applicant regards as the invention.
Claims 1 and 11 in 5th limitation recites “wherein the only unknown variables in the PPM are one or more coefficients …”. There is insufficient antecedent basis for the term “the only unknown variables” in limitations claims 1 and 11, makes the scope of the claims indeterminate.
The dependent claims do not resolve the indefinite issue in the independent claim, and thus are also rejected under 112(b) by virtue of their dependence on the rejected independent claims 1 and 11. Appropriate correction is required (e.g.,
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1,3-11 and 13-22 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more. The claim(s) recite a mental process and a mathematical calculation; see MPEP 2106.04(a)(2)(I) and MPEP 2106.04(a)(2)(III).
Step 1
The claims under Step 1 are directed towards a method (claims 1,3-10) and a system (claims 11,13-22).
Claim 1 recites:
A method comprising: forming one or more model parameters from one or more priori geological information and one or more downhole measurements; (Mental Processes using evaluation or judgement)
using the one or more model parameters to generate an inversion model for a geological formation based on a piecewise polynomial model (PPM) comprising a series of polynomial segments, (Mathematical Concepts)
wherein generating the inversion model comprises: identifying one or more inversion controls to be used as hyper-parameters; (Mathematical Concepts)
forming one or more initial models from the model parameters to be utilized in a forward model operation; (Mathematical Concepts)
performing, based on the one or more initial models the forward model operation using the PPM wherein the only unknown variables in the PPM are one or more coefficients of each polynomial segment in the series of polynomial segments; (Mathematical Concepts)
performing an optimization using at least the forward model operation, the one or more model parameters, and the one or more inversion controls; (Mathematical Concepts)
determining if a misfit between the one or more downhole measurements and the one or more model parameters is greater than or less than a threshold; (Math Processes or using simple math)
and updating the forward model operation or the one or more priori geological information based at least in part on the misfit (insignificant extra solution activity)
and simulating one or more tool responses based on the inversion model. (merely use of a computer for applying the step)
Step 2A, prong 1:
The limitations of claim 1 “forming one or more model parameters from one or more priori geological information and one or more downhole measurements;” is recitations of evaluation or judgement that fall within the Mental Processes enumerated category of abstract ideas because under BRI this limitation could be "performed by human without a computer", i.e., one or more model parameters can be formed/created from one or more priori geological information and by using one or more downhole measurements. The limitation “identifying one or more inversion controls to be used as hyper-parameters;” is recitation of Mathematical Concepts. The Specification of current Application at para [0044] stated: “Hyper-parameters found in block 512 may include number of iterations, misfit threshold, initial solution for optimization, and/or regularization coefficients.” Further, the limitations “forming one or more initial models from the model parameters to be utilized in a forward model operation; performing based on the one or more initial models the forward model operation using the PPM wherein the only unknown variables in the PPM are one or more coefficients of each polynomial segment in the series of polynomial segments; and “performing an optimization using at least the forward model operation, …”, are recitations of Mathematical Concepts. The Specification of current Application at para [0045] states: “the global optimization may be employed, and a new cost function is defined as below, by minimizing Pm the polynomial models may be simplified, which may prevent over-fitting …”. Further, para [0046] in Spec. states: “a forward modeling operation, in which the predicted data and Jacobian matrix is evaluated, … All sensitivity information used in block 520 form a Jacobian matrix. In examples, two methods for forward modeling may be utilized. In the first method, a semi-analytical solution for each section may be derived using Equation (5) …”. The limitation “determining if a misfit between the one or more downhole measurements and the one or more model parameters is greater than or less than a threshold” is recitations of math Processes (or using simple math) and Math operation, respectively. Under BRI, any person can determine/find a misfit or anomaly using simple math process. Accordingly, claim 1 as a whole is found to recite a judicial exception and is drawn to an abstract idea.
Step 2A, Prong 2:
This judicial exception is not integrated into a practical application because the claim language only recites elements that can practically be performed in the human mind, and can be performed using Mathematical Concepts. Therefore, the claim 1 recites an abstract idea because it does not impose any meaningful limitations on practicing the abstract idea. Claim 1 has no additional limitations that integrate the abstract idea into a practical application. The limitation “updating the forward model operation or the one or more priori geological information based at least in part on the misfit” is recitation of insignificant extra solution activity. This limitation is similar to updating data based on some (misfit) information. The last limitation "simulating one or more tool responses based on the inversion model" is recitation of merely applying/using generic computer to cover all the bases. Therefore, the abovementioned limitations cannot integrate a judicial exception into a practical application.
Step 2B:
The claim 1 as a whole does not include any further additional elements that are sufficient to amount to significantly more than the judicial exception. As discussed above with in the Step 2A, Prong Two analysis, with respect to integration of the abstract idea into a practical application. The additional element: “A method comprising” that amount to merely indicating a field of use or technological environment and does not amount to significantly more than the judicial exception. The limitation “updating the forward model operation or the one or more priori geological information based at least in part on the misfit” is recitation of insignificant extra solution activity. This limitation is similar to updating data based on some (misfit) information. The last limitation "simulating one or more tool responses based on the inversion model" is recitation of merely applying/using generic computer to cover all the bases. Therefore, the abovementioned limitations do not amount to significantly more than the judicial exception.
Therefore, the claim 1 is not patent eligible under 35 USC 101.
Independent Claim 11 is substantially similar to claim 1 and therefore are rejected under the same rationale as stated above. Additionally, the claim elements “A system comprising: a downhole tool comprising: a transmitter disposed on the downhole tool and configured to transmit an electromagnetic field; and a receiver disposed on the downhole tool and configured to take one or more downhole measurements; and an information handling system communicatively connected to the downhole tool” is recited at a high-level of generality (i.e., as a generic computer/hardware components) such that it amounts no more than mere instructions to apply the exception using a generic computer. Accordingly, these additional elements do not integrate the abstract idea into a practical application because they do not impose any meaningful limits on practicing the abstract idea. See MPEP §2106.05(b) (“Merely adding a generic computer, generic computer components, or a programmed computer to perform generic computer functions does not automatically overcome an eligibility rejection. Alice Corp. Pty. Ltd. v. CLS Bank Int’l, 573 U.S. 208, 223-24, 110 USPQ2d 1976, 1983-84 (2014).”).
Claims 3-5 are dependent on independent claim 1 and includes all the limitations of claim 1. The limitations of claims 3-5 are recitations of Mathematical Concepts, according to the conventional meaning in the art and equations related to “cost function” recited in claim 5 and Specification of current Application. Therefore, the limitations of claims 3-5 do not amount to significantly more than the abstract idea.
Claims 6,7 and 10 are dependent on independent claim 1 and includes all the limitations of claim 1. The limitations of claims 6,7 and 10 are recitations of Mathematical Concepts.
Claims 8 and 9 are dependent on independent claim 1 and includes all the limitations of claim 1. The limitations of claims 8 and 9 are recitations of Mathematical Concepts. According to specification of current Application para [0044], Applicant stated “cost function for inversion is performed when determining sensitivities”; “inversion controls may be identified as hyper-parameters. Hyper-parameters found in block 512 may include number of iterations, misfit threshold, initial solution for optimization, and/or regularization coefficients.” Therefore, the limitations of claims 6-10 do not amount to significantly more than the abstract idea.
Dependent claims 13-20 are substantially similar to claims 3-10 and therefore are rejected under the same rationale as stated above.
Claims 21 and 22 are dependent on independent claim 11 and includes all the limitations of claim 11. The limitations of claims 21 and 22 are recitations of Mathematical Concepts. In light of Specification of current Application para [0046] stated: “a forward modeling operation, in which the predicted data and Jacobian matrix is evaluated, … All sensitivity information used in block 520 form a Jacobian matrix. In examples, two methods for forward modeling may be utilized. In the first method, a semi-analytical solution for each section may be derived using Equation (5) …”. Therefore, the limitations of claims 21 and 22 do not amount to significantly more than the abstract idea.
Therefore, the claims 1,3-11 and 13-22 are not patent eligible.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries set forth in Graham, v. John Deere Co., 383 U.S.1.148 USPQ 459 (1966), that are applied for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or non-obviousness.
11. Claims 1,5,6,8,10,11,15,16,18, 20,21 and 22 are rejected under 35 U.S.C. 103 as being unpatentable over Wilson et al. (US20170321545A1), in view of a Journal “History Matching by Spline Approximation and Regularization in Single-Phase Areal Reservoirs” by Tal-yong Lee et al. (hereinafter Lee, Journal published in 1986) and further in view of a journal “A framework to understand the asymptotic properties of Kriging and splines” Eva M. Furrer (hereinafter Furrer, journal published in 2007).
Regarding claim 1, Wilson teaches a method comprising: forming one or more model parameters from one or more priori geological information and one or more downhole measurements; (Wilson disclosed in Abstract: “An example method for modeling a geological formation includes receiving a set of measurements from an electro-magnetic logging tool and representing at least one characteristic of the geological formation as at least one continuous spatial function.” In page 3 para [0026]: “Electromagnetic logging tools, such as those described above, may take periodic measurements at different depths and times as they progress into the formation … Inversions are used to determine the resistivity values, distances to bed boundaries, and other downhole characteristics from the measurements.” Further, in page 3 para [0027]: “In the embodiment shown, each of the models 302 include five parameters that correspond to different formation characteristics of interest, including the resistivity σ1, of the formation layer 310a, the resistivity σ2, of the formation layer … Generating each model includes receiving the measurements collected by the logging tool at the corresponding measurement point and applying a 1D inversion to optimize values for each of the five earth model parameters. The 1D earth models 302 are then “stitched” together to form a continuous two-dimensional (2D) image of the geological formation.”).
Wilson teaches using the one or more model parameters to generate an inversion model for a geological formation (Wilson disclosed in page )
Wilson teaches forming one or more initial models from the model parameters to be utilized in a forward model operation. (Applicant of current Application stated in Specification para [0059 and 0069]: “identifying one or more sensitivities from the forward model operation”. Wilson disclosed in page 4-5 para [0036-0038]: “earth models may be generated from the splines by evaluating the 2D splines to identify the value of a spline at any x and y coordinate … The sensitivities (e.g., Frechet derivatives or Jacobians) of a given spline mesh with respect to the spline coefficients are shown in Equation (5): … The sensitivities (e.g., Frechet derivatives or Jacobians) of measured data dj (x, z) to the spline coefficients may be given by the product rule in Equation (6): … In certain embodiments, the type of continuous spatial functions applied to an earth model may depend on the complexity of the measurements generated by the down-hole tool. A dynamic misfit functional may be applied to switch the continuous spatial function used to parameterize the earth model to the continuous spatial function best able to represent the actual measurement data. This may include increasing the complexity of the interpolation function (e.g., piece-wise constant to piece-wise linear to polynomial/spline) …”.
The disclosure “earth model” corresponds to claim element “initial model” generated/formed from the model parameters to be utilizing the forward modeling operation (e.g., sensitivities such as “Frechet derivatives” or Jacobians of a given spline mesh with respect to the spline coefficients and further sensitivities of measured data dj (x, z) to the spline coefficients are shown. A dynamic misfit functional applied to switch/change the continuous spatial function used to parameterize the earth model to the continuous spatial function best able to represent the actual measurement data)).
Wilson teaches performing an optimization using at least the forward model operation, the one or more model parameters, and the one or more inversion controls; (Applicant stated in Specification of current Application para [0046]: “a forward modeling operation, in which the predicted data and Jacobian matrix is evaluated, … All sensitivity information used in block 520 form a Jacobian matrix.” Wilson disclosed in page 3 para [0027]: “In the embodiment shown, each of the models 302 include five parameters that correspond to different formation characteristics of interest, … Generating each model includes receiving the measurements collected by the logging tool at the corresponding measurement point and applying a 1D inversion to optimize values for each of the five earth model parameters.” In page 4 para [0032-0033]: “Each of the spline nodes in the model 400 may have associated spline coefficients. The spline coefficients may define, in part, the splines to which the spline nodes correspond. In certain embodiments, the spline coefficients may be determined from the inversion of measurements … the value of a spline surface at any lateral position (which corresponds to the value of the formation characteristic of interest at that lateral position) may be determined as the weighted sum of the four adjacent spline coefficients using Equation (1) … The spline weights Wpk (x) may be a function only of the lateral position of spline nodes, therefore remaining constant during an inversion. The sensitivities (e.g., Frechet derivatives or Jacobians) of a given spline with respect to the spline coefficients are shown in Equation (2) …”.).
Wilson teaches determining if a misfit between the one or more downhole measurements and the one or more model parameters is greater than or less than a threshold; (Wilson disclosed in page 5 para [0041]: “FIG. 7 is an example flow diagram illustrating a process whereby a discontinuity is added to an earth model, according to aspects of the present disclosure. At step 701 an earth model with continuous spatial functions is selected to parameterize formation. At step 702, measurement data is received, and the coefficients of the continuous spatial functions are solved and investigated with a misfit functional that may identify the degree of success with which the chosen continuous spatial functions represent the actual formation. In certain embodiments, a threshold may be set to determine the degree of success necessary to accept the earth model. At step 703 to the misfit functional determination may be compared to the threshold. If the misfit functional determination is below the threshold, the current model with continuous spatial functions may be selected at step 704. If, on the other hand, the misfit functional determination is above the threshold, a different earth model with continuous spatial function may be selected at step 705.”).
and Wilson teaches updating the forward model operation or the one or more priori geological information based at least in part on the misfit. (Wilson disclosed in page 5 para [0041]: “FIG. 7 is an example flow diagram illustrating a process whereby a discontinuity is added to an earth model, according to aspects of the present disclosure. At step 701 an earth model with continuous spatial functions is selected to parameterize formation. At step 702, measurement data is received, and the coefficients of the continuous spatial functions are solved and investigated with a misfit functional that may identify the degree of success with which the chosen continuous spatial functions represent the actual formation. … At step 703 to the misfit functional determination may be compared to the threshold. If the misfit functional determination is below the threshold, the current model with continuous spatial functions may be selected at step 704. If, on the other hand, the misfit functional determination is above the threshold, a different earth model with continuous spatial function may be selected at step 705. … If the process has iteratively selected and applied continuous functions of increasing complexity, and the threshold is still not satisfied, the process may select an earth model with discontinuous spatial functions, …”.
The disclosure above “the misfit functional determination compared to the threshold, if the misfit functional determination is below the threshold, the current model with continuous spatial functions may be selected; if the process has iteratively selected and applied continuous functions of increasing complexity, and the threshold is still not satisfied, the process may select an earth model with discontinuous spatial functions” corresponds to the claim limitation “updating the forward model operation or the one or more priori geological information based at least in part on the misfit”).
and Wilson teaches simulating one or more tool responses based on the inversion model. (Wilson disclosed in page 4 para [0032]: “Each of the spline nodes in the model 400 may have associated spline coefficients. … In certain embodiments, the spline coefficients may be determined from the inversion of measurements generated by the logging tool 408, by using any well-known inversion algorithm … In the embodiment shown, for example, the spline coefficient associated with nodes 412c and 412d may be extrapolated from the spline coefficients associated with nodes 412a and 412b. This may allow for “look ahead” functionality in which formation characteristics of interest ahead of the tool 408 are determined, which is of particular interest in LWD applications where a steering assembly controls the direction of the drilling assembly.” In same page para [0034]: “Once the spline coefficients are determined from a set of measurements, earth models may be generated at any position by evaluating the splines. … the inversion algorithm determines the spline coefficients, and this is sufficient to fully characterize the formation characteristics of interest. As will be appreciated by one of ordinary skill in the art in view of this disclosure, simulating the logging tool responses from the earth models generated from the splines may consist of any combination of analytical, semi - analytical, finite difference, finite-volume, boundary-element, and/or integral equation methods implemented in Cartesian, cylindrical, and/or polar coordinates.”
The disclosure above “the spline coefficients may be determined from the inversion of measurements generated by the logging tool; simulating the logging tool responses from the earth models generated from the splines” teaches the limitation “simulating one or more tool responses based on the inversion model”).
However, Wilson doesn’t explicitly teach the limitation “performing, based on the one or more initial models the forward model operation using the PPM,”
Lee teaches performing, based on the one or more initial models the forward model operation using the PPM, (Specification of current Application is silent about the meaning of claim term “piecewise polynomial”. In order to facilitate compact prosecution, Examiner would construe the claim term “piecewise polynomial” as “spline” (according to the conventional meaning in the art).
The prior art Lee disclosed in page 522 heading ‘History Matching by Regularization’: “The problem of history matching may be viewed in a general way by expressing the reservoir model, or simulator … The conventional history-matching problem can be viewed therefore as a nonlinear optimization problem of minimizing the sum of squares of differences between the observed and predicted pressures subject to the constraint of the reservoir model (Eqs. 2 through 4). In the regularization approach, we minimize an augmented objective function, called the smoothing functional, denoted by JSM, that consists of the sum of the least-squares term, JLS, and a stabilizing functional, JST. The stabilizing functional for a parameter α … is of the form …”. In page 523: “H3(Ω) is a norm defined in the Sobolev space H3(Ω). … Thus, the overall objective function to be minimized is … where βα is a weighting coefficient chosen to reflect the degree of importance given to JST. The minimization of JSM is performed over an appropriate finite-dimensional subspace of H3(Ω), the so-called space of approximants, which can be spanned by cubic spline functions.” Lee reference provides historical context for the spline smoothing function and its evolution out of least squares fitting. The disclosure “a nonlinear optimization problem of minimizing the sum of squares of differences between the observed and predicted pressures subject to the constraint of the reservoir model” corresponds to claim element “one or more initial models”, based on this piecewise polynomial function is performed.
Further, it has been disclosed in page 530 heading ‘Conclusion’: “On the basis of the optimal spline, approximation, the optimal regularization parameters are βΦ=0.1 to 1 atm2 … we can suggest a history-matching strategy as follows … 2. Find a uniform initial guess of a parameter to be estimated that minimizes JLS and calculate JLS/JST at convergence. 3. Choose the regularization parameter value about the same as JLS/JST above and find a set of spline coefficients that minimizes JSM. 4. Step 3 can be repeated to evaluate the result for the different regularization parameter values around the JLS/JST value determined in Step 2, so that we can find the optimum value of regularization parameter …”. Therefore, the above disclosures by Lee reads the claim limitation).
Wilson and Lee are analogous art because they are related to have spline coefficients defined in splines to which the spline nodes correspond. Before the effective filing date of the claimed invention, it would have been obvious to one of ordinary skill in the art, having the teachings of Wilson and Lee before him or her, to modify the forward model operation to perform optimization in geological formation of Wilson, to include performing forward model operation using piecewise polynomial equivalent to “spline smoothing” of Lee. The suggestion/motivation for doing so would have been obvious by Lee because “In this study, we have developed an automatic history-matching algorithm is and tested for estimating spatially varying porosity and permeability in a single-phase areal reservoir. The algorithm is based on spline approximations of the parameters and a regularization formulation. In the regularization approach to parameter estimation by introduction of the stabilizing functional as a measure of non-smoothness, one can control the properties of the parameter estimates as well as the history match.” (Lee disclosed in page 529 heading ‘Conclusions).
Neither Wilson nor Lee explicitly teaches the limitations “generate an inversion model based on a piecewise polynomial model (PPM) comprising a series of polynomial segments, wherein generating the inversion model comprises: identifying one or more inversion controls to be used as hyper-parameters; wherein the only unknown variables in the PPM are one or more coefficients of each polynomial segment in the series of polynomial segments;
Furrer teaches generate an inversion model based on a piecewise polynomial model (PPM) comprising a series of polynomial segments, (According to the conventional meaning in the art, Examiner would construe the claim element “series of polynomial segments” as piecewise polynomials or splines, consists of individual polynomial functions defined over specific intervals or segments”.
Furrer disclosed in page 2 (1st and 2nd para of section 1): “The main contribution of this paper is the identification of a functional form approximating ω for Kriging estimators that is derived from the spatial process covariance function and is a reproducing kernel. … As an introduction and to fix ideas, we start by discussing the structure of the classic smoothing spline problem, … Also, we will outline the equivalence between a Kriging estimator and a spline estimator.” In page 2-3 section 1.1: “the parameter λ controls the degree of smoothness via the penalty term, which in this case penalizes roughness of the estimated function using its total curvature. The solution to this minimization is the standard cubic smoothing spline although the actual form as a piecewise cubic polynomial is not important to a general discussion. The form of the roughness penalty using second derivatives implies that linear functions will result in a penalty of zero. … H is a space containing all functions that have square integrable second derivatives on [0, 1] with f (0) = f ′ (0) = 0. … The full estimator can be derived by first minimizing over H and then over β, this results in a generalized least squares estimate for the null space parameters. We now identify the penalty term above with an inner product on H … and we can express the minimization criterion over f in (3) … (5)”. In page 3 under heading ‘Lemma 1.1’: “(Generalized smoothing spline). If H is a Hilbert space with reproducing kernel k then the solution ˆg of the minimization problem (5) is of the form … or i = 1, . . . , n and coefficients θi obtained by minimizing …”. This disclosure corresponds to the claim limitation “a piecewise polynomial model (PPM) comprising a series of polynomial segments” (e.g., Eq. (6) under Lemma 1.1). Further, in page 14 section 3.3 (last para), it has been discussed that one of the advantages of the use of Fourier transforms is that the mean squared
error can be evaluated without actually calculating the inverse transform in order to obtain a closed form for the reproducing kernel G. Moreover, in page 6 section 2.1 disclosed: “Our first objective is to define an inner product on a Hilbert space of functions having the correlation function k as reproducing kernel. If one has a positive definite kernel then one can always formally define an inner product such that the kernel is the reproducing kernel and also extend this to a Hilbert space.”
Therefore, it is understood from the disclosure above that a Hilbert space of functions having the correlation function k as reproducing kernel, and with an inner product on H (Hilbert space) the penalty term regarding to degree of smoothness in spline curve is identified, which is eventually piecewise polynomial. Since inverse transform is calculated to obtain a closed form for the reproducing kernel, therefore, Furrer teaches generate an inversion model based on a piecewise polynomial model (PPM) comprising a series of polynomial segments).
wherein Furrer teaches generating the inversion model comprises: identifying one or more inversion controls to be used as hyper-parameters; (Examiner would construe the claim element “hyper-parameters” as “initial solution for optimization, and/or regularization coefficients” according to the Specification of current Application para [0044]).
Furrer disclosed in page 3 under heading ‘Lemma 1.1’: “(Generalized smoothing spline). If H is a Hilbert space with reproducing kernel k then the solution ˆg of the minimization problem (5) is of the form … or i = 1, . . . , n and coefficients θi obtained by minimizing …”. In page 14 section 3.3 (last para), it has been discussed that one of the advantages of the use of Fourier transforms is that the mean squared
error can be evaluated without actually calculating the inverse transform in order to obtain a closed form for the reproducing kernel G. Further, in page 6 section 2.1 disclosed: “Our first objective is to define an inner product on a Hilbert space of functions having the correlation function k as reproducing kernel. If one has a positive definite kernel then one can always formally define an inner product such that the kernel is the reproducing kernel and also extend this to a Hilbert space.” Therefore, it is understood from the disclosure above that inversion controls to be used as hyper-parameters, as an example the disclosure above coefficients θi is obtained by minimizing Eq. (6) corresponds to “solution for optimization or hyper-parameter).
wherein Furrer teaches the only unknown variables in the PPM are one or more coefficients of each polynomial segment in the series of polynomial segments; (Furrer disclosed in page 1 section: “A common method in the analysis of spatial data is a geostatistical estimator known as Kriging. … it is of interest to understand Kriging in terms of the large sample properties such as the asymptotic variance and bias that are well established for kernel estimators. The key idea developed in this work is that Kriging estimators can be interpreted as generalized splines … The problem one is faced with in nonparametric regression is to estimate an unknown function, g, on [0, 1], for which the observations yi are supposed to depend on the “locations” xi … we use the interval [0, 1] without loss of generality. The solution to this problem by either spline or kernel methods …”. In page 3 under heading ‘Lemma 1.1’: “(Generalized smoothing spline). If H is a Hilbert space with reproducing kernel k then the solution ˆg of the minimization problem (5) is of the form … or i = 1, . . . , n and coefficients θi obtained by minimizing …”. This disclosure corresponds to the claim limitation “a piecewise polynomial model (PPM) comprising a series of polynomial segments” (e.g., Eq. (6) under Lemma 1.1).
The disclosure above “to estimate an unknown function, g, on [0, 1], for which the observations yi are supposed to depend on the “locations” xi” corresponds to claim element “unknown variables in the PPM”, which is eventually “generalized splines in Kriging estimators”, thus Kriging estimators are derived from the spatial process covariance function and is a reproducing kernel. Further, kernel is reproduced in the solution in minimization problem (in Eq. 5). Therefore, the limitation “unknown variables in the PPM are one or more coefficients of each polynomial segment in the series of polynomial segments” is taught by Furrer, as discussed)).
Wilson, Lee and Furrer are analogous art because they are related to have spline coefficients defined in splines to which the spline nodes correspond. Before the effective filing date of the claimed invention, it would have been obvious to one of ordinary skill in the art, having the teachings of Wilson, Lee and Furrer, to modify cubic splines applied on the boundary of reservoir in Wilson and Lee’s teaching, to include performing spline smoothing formulated in linear functions result in a penalty of zero by Furrer. The suggestion/motivation for doing so would have been obvious by Furrer because Furrer discussed the structure of the classic smoothing spline problem; the parameter λ (in Eq. 2) controls the degree of smoothness via the penalty term, which in this case penalizes roughness of the estimated function using its total curvature. The form of the roughness penalty using second derivatives implies that linear functions will result in a penalty of zero. Further, restating the minimization problem in matrix notation in Eq. (6) is straightforward using the reproducing property of k to simplify the penalty term. (Furrer disclosed in page 3).
Regarding Claim 5, Wilson, Lee and Furrer teach the method of claim 1, however, Wilson doesn’t explicitly teach the limitation “the optimization uses a cost function”.
wherein Lee teaches the optimization uses a cost function. (Lee disclosed in page 522 heading ‘History Matching by Regularization’: “The problem of history matching may be viewed in a general way by expressing the reservoir model, or simulator … The conventional history-matching problem can be viewed therefore as a nonlinear optimization problem of minimizing the sum of squares of differences between the observed and predicted pressures subject to the constraint of the reservoir model (Eqs. 2 through 4). In the regularization approach, we minimize an augmented objective function, called the smoothing functional, denoted by JSM, that consists of the sum of the least-squares term, JLS, and a stabilizing functional, JST. The stabilizing functional for a parameter α … is of the form …”. In page 523: “H3(Ω) is a norm defined in the Sobolev space H3(Ω). … Thus, the overall objective function to be minimized is … where βα is a weighting coefficient chosen to reflect the degree of importance given to JST. The minimization of JSM is performed over an appropriate finite-dimensional subspace of H3(Ω), the so-called space of approximants, which can be spanned by cubic spline functions.” Lee reference provides historical context for the spline smoothing function and its evolution out of least squares fitting. The disclosure above “objective function to be minimized” corresponds to claim limitation “the optimization uses a cost function”).
Wilson and Lee are analogous art because they are related to have spline coefficients defined in splines to which the spline nodes correspond. Before the effective filing date of the claimed invention, it would have been obvious to one of ordinary skill in the art, having the teachings of Wilson and Lee before him or her, to modify the forward model operation to perform optimization in geological formation of Wilson, to include performing forward model operation using piecewise polynomial equivalent to “spline smoothing” of Lee. The suggestion/motivation for doing so would have been obvious by Lee because “In this study, we have developed an automatic history-matching algorithm is and tested for estimating spatially varying porosity and permeability in a single-phase areal reservoir. The algorithm is based on spline approximations of the parameters and a regularization formulation. In the regularization approach to parameter estimation by introduction of the stabilizing functional as a measure of non-smoothness, one can control the properties of the parameter estimates as well as the history match.” (Lee disclosed in page 529 heading ‘Conclusions).
Regarding Claim 6, Wilson, Lee and Furrer teach the method of claim 5, however, Wilson doesn’t explicitly teach the limitation “the cost function is:
PNG
media_image1.png
204
703
media_image1.png
Greyscale
wherein Lee teaches the cost function is:
PNG
media_image1.png
204
703
media_image1.png
Greyscale
Lee reference provides historical context for the spline smoothing function and its evolution out of least squares fitting. Lee disclosed in starting at the bottom of Lee page 522 (near equation (6)) and continues to page 524 line 2. Most importantly, the equation (7) in Lee’s disclosure shows the basic structure of the equation. In Lee’s equation (7) the term “Beta (β)” the “weighting coefficient” corresponds with the claimed “regularization coefficient” mu (μ). The claim swaps the order of the two terms by writing the stabilizing function (with _mu_) first, and the least square portion section. The equation (7) is the same as claim 6.
Further, the prior art Furrer shows this same spline smoothing formulated in a notation closer to claim 6. Furrer’s disclosure in page 3 (Lemma 1.1) equation (6) and the associated definitions of terms teaches claim 6.
Wilson, Lee and Furrer are analogous art because they are related to have spline coefficients defined in splines to which the spline nodes correspond. Before the effective filing date of the claimed invention, it would have been obvious to one of ordinary skill in the art, having the teachings of Wilson, Lee and Furrer, to modify cubic splines applied on the boundary of reservoir in Wilson and Lee’s teaching, to include performing spline smoothing formulated in linear functions result in a penalty of zero by Furrer. The suggestion/motivation for doing so would have been obvious by Furrer because Furrer discussed the structure of the classic smoothing spline problem; the parameter λ (in Eq. 2) controls the degree of smoothness via the penalty term, which in this case penalizes roughness of the estimated function using its total curvature. The form of the roughness penalty using second derivatives implies that linear functions will result in a penalty of zero. Further, restating the minimization problem in matrix notation in Eq. (6) is straightforward using the reproducing property of k to simplify the penalty term. (Furrer disclosed in page 3).
Regarding Claim 8, Wilson, Lee and Furrer teach the method of claim 1, further Wilson teaches identifying one or more sensitivities from the forward model operation. (Wilson disclosed in page 4 para [0032-0033]: “The spline coefficients may define, in part, the splines to which the spline nodes correspond. In certain embodiments, the spline coefficients may be determined from the inversion of measurements generated … With respect to the model 400 in FIG. 4, the value of a spline surface at any lateral position (which corresponds to the value of the formation characteristic of interest at that lateral position) may be determined as the weighted sum of the four adjacent spline coefficients using Equation (1) … The spline weights Wpk (x) may be a function only of the lateral position of spline nodes, therefore remaining constant during an inversion. The sensitivities (e.g., Frechet derivatives or Jacobians) of a given spline with respect to the spline coefficients are shown in Equation (2): …”. This disclosure teaches the limitation “identifying one or more sensitivities from the forward model operation” (e.g., sensitivities such as, Frechet derivatives or Jacobians of a given spline with respect to the spline coefficients are shown)).
Regarding Claim 10, Wilson, Lee and Furrer teach the method of claim 1, wherein Wilson teaches the forward model operation uses a Jacobian process. (Wilson disclosed in page 4 para [0032-0033]: “The spline coefficients may define, in part, the splines to which the spline nodes correspond. In certain embodiments, the spline coefficients may be determined from the inversion of measurements generated … With respect to the model 400 in FIG. 4, the value of a spline surface at any lateral position (which corresponds to the value of the formation characteristic of interest at that lateral position) may be determined as the weighted sum of the four adjacent spline coefficients using Equation (1) … The spline weights Wpk (x) may be a function only of the lateral position of spline nodes, therefore remaining constant during an inversion. The sensitivities (e.g., Frechet derivatives or Jacobians) of a given spline with respect to the spline coefficients are shown in Equation (2): …”. This disclosure teaches the limitation “the forward model operation uses a Jacobian process”).
Regarding Claim 11, the same ground of rejection is made as discussed in claim 1 for substantially similar rationale, therefore claim 11 is rejected under 35 U.S.C. 103 as being unpatentable over Wilson, Lee and Furrer as discussed above for substantially similar rationale. In addition, claim 11 recites following limitations:
Wilson teaches a system comprising: a downhole tool comprising: a transmitter disposed on the downhole tool and configured to transmit an electromagnetic field; (Wilson disclosed in page 2 para [0020]: “The drilling system 80 comprises … A drill bit 14 may be coupled to the drill string 8 and driven by a downhole motor …”. In page 1 para [0003]: “Measurements of the geological formation may be made throughout the operations using electromagnetic logging techniques … Generally, at discrete measurement points within the borehole, a transmitter of the induction logging tool transmits an electromagnetic signal that passes through the geological formation around the borehole …”).
and Wilson teaches a receiver disposed on the downhole tool and configured to take one or more downhole measurements; and an information handling system communicatively connected to the downhole tool (Wilson disclosed in page 2 para [0023-0024]: “In certain embodiments, the surface control unit 32 may comprise a plurality of information handling systems arranged in a serial or parallel architecture to receive and process downhole measurement data. In the embodiment shown, the surface control unit 32 is communicably coupled to the surface receiver 30 to receive measurements from the tool 26 and/or transmit commands to the tool 26 though the surface receiver 30.”).
Regarding Claims 15, 16,18 and 20, Wilson, Lee and Furrer teach the system of claim 11, are incorporating the rejections of claims 5,6,8 and 10, because claims 15,16,18 and 20 have substantially similar claim language as claims 5,6,8 and 10, therefore claims 15,16,18 and 20 are rejected under 35 U.S.C. 103 as being unpatentable over Wilson, Lee and Furrer as discussed above for substantially similar rationale.
Regarding Claim 21, Wilson, Lee and Furrer teach the system of claim 11, wherein Wilson teaches the forward model operation uses the PPM to predict a physical property of the geological formation. (Wilson disclosed in page 3 para [0030]: “In the embodiment shown, each of the continuous functions comprises a separate spline. As used herein, a spline may comprise a numeric function that is piecewise defined by polynomial functions. Example splines include, but at not limited to, linear, bilinear, cubic, and B-splines … Similarly, the spline 414 corresponding to boundary 410e comprises polynomial segments joined at spline knots or nodes 414a - d, located at similar locations along the x - axis of the model 400 as the nodes 412a - d, and spaced apart equal distances from the trajectory 406 of the tool 408 on the y-axis of the model 400. The number and placement of spline nodes may be selected based, at least in part, on the length of expected variations within the formation and the measurement range of the resistivity logging tool 408.” In page 6 para [0045]: “In certain embodiments, the method further includes steering a drilling assembly based, at least in part, on the determined characteristic of geological formation. In certain embodiments, the at least one characteristic of the geological formation comprises at least one of distance to bed boundary, resistivity … In certain embodiments, the at least one continuous spatial function comprises at least one of a spline, polynomial function, and power series.”
The disclosures above “a spline may comprise a numeric function that is piecewise defined by polynomial functions; the spline 414 corresponding to boundary 410e comprises polynomial segments joined at spline knots or nodes; number and placement of spline nodes may be selected based, at least in part, on the length of expected variations within the formation; one characteristic of the geological formation comprises at least one of distance to bed boundary, resistivity” correspond to claim limitation “the PPM to predict a physical property of the geological formation”).
Regarding Claim 22, Wilson, Lee and Furrer teach the system of claim 11, wherein Wilson teaches the PPM defines the physical property, via the series of polynomial segments, as a function of depth such that each polynomial segment in the series of polynomial segments corresponds to a depth of the geological formation. (Wilson disclosed in page 3 para [0030]: “In the embodiment shown, each of the continuous functions comprises a separate spline. As used herein, a spline may comprise a numeric function that is piecewise defined by polynomial functions. Example splines include, but at not limited to, linear, bilinear, cubic, and B-splines … Similarly, the spline 414 corresponding to boundary 410e comprises polynomial segments joined at spline knots or nodes 414a - d, located at similar locations along the x - axis of the model 400 as the nodes 412a - d, and spaced apart equal distances from the trajectory 406 of the tool 408 on the y-axis of the model 400. The number and placement of spline nodes may be selected based, at least in part, on the length of expected variations within the formation and the measurement range of the resistivity logging tool 408.” In page 6 para [0045]: “In certain embodiments, the method further includes steering a drilling assembly based, at least in part, on the determined characteristic of geological formation. In certain embodiments, the at least one characteristic of the geological formation comprises at least one of distance to bed boundary, resistivity … In certain embodiments, the at least one continuous spatial function comprises at least one of a spline, polynomial function, and power series.”
The disclosures above “a spline may comprise a numeric function that is piecewise defined by polynomial functions; the spline 414 corresponding to boundary 410e comprises polynomial segments joined at spline knots or nodes 414a - d; and spaced apart equal distances from the trajectory 406 of the tool 408 on the y-axis of the model 400; one characteristic of the geological formation comprises at least one of distance to bed boundary, resistivity; correspond to claim limitation “PPM defines the physical property, via the series of polynomial segments(e.g., spline knots or nodes), as a function of depth (e.g., spline knots or nodes 414a - d spaced apart equal distances) such that each polynomial segment in the series of polynomial segments corresponds to a depth of the geological formation”
Claims 3,4,9,13,14, and 19 are rejected under 35 U.S.C. 103 as being unpatentable over Wilson, Lee and Furrer and further in view of journal “Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling” by Jiaxin Zhang et al. (hereinafter Zhang, available online 9 August 2020).
Regarding Claim 3, Wilson, Lee and Furrer teach the method of claim 1, however Wilson, Lee and Furrer do not explicitly teach the claim limitation “the model parameters are determined by deterministic optimization or global optimization”.
wherein Zhang teaches the model parameters are determined by deterministic optimization or global optimization. (According to the conventional meaning in the art, Examiner would construe the claim term “global optimization” as “numerical analysis that attempts to find the global minimum or maximum of a function”. Zhang disclosed in page 5-6 section 3. (cited 1st and last para of page 6): “Methods for global sensitivity analysis, … employ samples that are drawn from a known probability density. … Multimodel inference, … involves two components: 1. Model selection, and 2. Parameter estimation. When selecting a probability distribution to represent a dataset, the model selection problem is simply stated … Given a collection of Np candidate models (probability distributions) … data ds, identify the model Mi that ‘‘best” fits the data. ... In this work, we employ Bayesian posterior probabilities as the measure of best fit … this process yields an infinite set of parametrized probability models (i.e. a finite set of probability models, each with continuous joint parameter distributions). For practical purposes, it is necessary to reduce this to a finite, but statistically representative, set of Nc probability models, … from which we can perform imprecise GSA. This is achieved by Monte Carlo sampling from the infinite set of probability models. Each model, … is identified by randomly selecting a model family from M with probabilities ... and randomly selecting its parameters from the joint parameter probability density …”. This the claim limitation “model parameters are determined by deterministic optimization or global optimization”).
Wilson, Lee, Furrer and Zhang are analogous art because they are related to have sensitivity analysis to minimize the impact of uncertainties in performing optimization algorithm. Before the effective filing date of the claimed invention, it would have been obvious to one of ordinary skill in the art, having the teachings of Wilson, Lee, Furrer and Zhang before him or her, to modify performing optimization using model parameters of Wilson, Lee and Furrer, to include performing optimization (e.g., global optimization) by determining model parameters of Zhang. The suggestion/motivation for doing so would have been obvious by Zhang because “This work investigates the effect of uncertainties associated with small data sets for quantifying model inputs on the global sensitivity analysis of engineering systems. We systematically investigate the performance of the approach for estimating the imprecise sensitivity indices for increasing data set sizes. It is shown that a fully probabilistic description of the sensitivity indices is obtained and while the Sobol’ indices have large variation (uncertainty) given initially small data sets, they gradually converge to the true (deterministic) estimates when a large number of data are collected. (Zhang disclosed in page 23-24 section 7).
Regarding Claim 4, Wilson, Lee and Furrer teach the method of claim 3, however Wilson, Lee and Furrer do not explicitly teach the claim limitation “the model parameters are determined by deterministic optimization or global optimization”.
wherein Zhang teaches the one or more initial models are a multi-layer formation model generated by randomly sampling different sets of formation parameters. (Zhang disclosed in page 5-6 section 3. (cited 1st and last para of page 6): “Methods for global sensitivity analysis, … employ samples that are drawn from a known probability density. … Multimodel inference, … involves two components: 1. Model selection, and 2. Parameter estimation. When selecting a probability distribution to represent a dataset, the model selection problem is simply stated … Given a collection of Np candidate models (probability distributions) … data ds, identify the model Mi that ‘‘best” fits the data. ... In this work, we employ Bayesian posterior probabilities as the measure of best fit … this process yields an infinite set of parametrized probability models (i.e. a finite set of probability models, each with continuous joint parameter distributions). For practical purposes, it is necessary to reduce this to a finite, but statistically representative, set of Nc probability models, … from which we can perform imprecise GSA. This is achieved by Monte Carlo sampling from the infinite set of probability models. Each model, … is identified by randomly selecting a model family from M with probabilities ... and randomly selecting its parameters from the joint parameter probability density …”.
The disclosure above teaches the claim element “multi-layer formation model” e.g., “Multi-model inference” involves Parameter estimation. The disclosure “Bayesian posterior probabilities employed as the measure of best fit, this process yields an infinite set of parametrized probability models, further by performing GSA where Monte Carlo sampling from the infinite set of probability models is achieved. Each model is identified by randomly selecting a model family with probabilities and randomly selecting its parameters from the joint parameter probability density” teaches the whole claim limitation).
Wilson, Lee, Furrer and Zhang are analogous art because they are related to have sensitivity analysis to minimize the impact of uncertainties in performing optimization algorithm. Before the effective filing date of the claimed invention, it would have been obvious to one of ordinary skill in the art, having the teachings of Wilson, Lee, Furrer and Zhang before him or her, to modify performing optimization using model parameters of Wilson, Lee and Furrer, to include performing optimization (e.g., global optimization) by determining model parameters of Zhang. The suggestion/motivation for doing so would have been obvious by Zhang because “This work investigates the effect of uncertainties associated with small data sets for quantifying model inputs on the global sensitivity analysis of engineering systems. We systematically investigate the performance of the approach for estimating the imprecise sensitivity indices for increasing data set sizes. It is shown that a fully probabilistic description of the sensitivity indices is obtained and while the Sobol’ indices have large variation (uncertainty) given initially small data sets, they gradually converge to the true (deterministic) estimates when a large number of data are collected. (Zhang disclosed in page 23-24 section 7).
Regarding Claim 9, Wilson, Lee and Furrer teach the method of claim 1, further Wilson teaches identifying one or more model constraints from the one or more inversion controls (Wilson disclosed in page 4 para [0032-0033]: “The spline coefficients may define, in part, the splines to which the spline nodes correspond. In certain embodiments, the spline coefficients may be determined from the inversion of measurements generated … With respect to the model 400 in FIG. 4, the value of a spline surface at any lateral position (which corresponds to the value of the formation characteristic of interest at that lateral position) may be determined as the weighted sum of the four adjacent spline coefficients using Equation (1) … The spline weights Wpk (x) may be a function only of the lateral position of spline nodes, therefore remaining constant during an inversion. The sensitivities (e.g., Frechet derivatives or Jacobians) of a given spline with respect to the spline coefficients are shown in Equation (2): …”. The disclosure “spline coefficients may be determined from the inversion of measurements generated; spline weights a function lateral position of spline nodes, therefore constant during an inversion” corresponds to the claim limitation “identifying one or more model constraints from the one or more inversion controls”).
However, Wilson, Lee and Furrer do not explicitly teach the claim limitation “identifying the one or more model parameters”.
and Zhang teaches identifying the one or more model parameters. (Zhang disclosed in page 6 section 3. (cited 1st and last para of page 6): “Multimodel inference, … involves two components: 1. Model selection, and 2. Parameter estimation. … Given a collection of Np candidate models (probability distributions) … data ds, identify the model Mi that ‘‘best” fits the data. ... In this work, we employ Bayesian posterior probabilities as the measure of best fit … this process yields an infinite set of parametrized probability models (i.e. a finite set of probability models, each with continuous joint parameter distributions). For practical purposes, it is necessary to reduce this to a finite, but statistically representative, set of Nc probability models, … from which we can perform imprecise GSA. This is achieved by Monte Carlo sampling from the infinite set of probability models. Each model, … is identified by randomly selecting a model family from M with probabilities ... and randomly selecting its parameters from the joint parameter probability density …”. This the claim limitation “model parameters are identified by global optimization” or GSA).
Wilson, Lee, Furrer and Zhang are analogous art because they are related to have sensitivity analysis to minimize the impact of uncertainties in performing optimization algorithm. Before the effective filing date of the claimed invention, it would have been obvious to one of ordinary skill in the art, having the teachings of Wilson, Lee, Furrer and Zhang before him or her, to modify performing optimization using model parameters of Wilson, Lee and Furrer, to include performing optimization (e.g., global optimization) by determining model parameters of Zhang. The suggestion/motivation for doing so would have been obvious by Zhang because “This work investigates the effect of uncertainties associated with small data sets for quantifying model inputs on the global sensitivity analysis of engineering systems. We systematically investigate the performance of the approach for estimating the imprecise sensitivity indices for increasing data set sizes. It is shown that a fully probabilistic description of the sensitivity indices is obtained and while the Sobol’ indices have large variation (uncertainty) given initially small data sets, they gradually converge to the true (deterministic) estimates when a large number of data are collected. (Zhang disclosed in page 23-24 section 7).
Regarding Claims 13,14, and 19, Wilson, Lee and Furrer teach the system of claim 11, are incorporating the rejections of claims 3,4 and 9, because claims 13,14 and 19 have substantially similar claim language as claims 3,4 and 9, therefore claims 13,14 and 19 are rejected under 35 U.S.C. 103 as being unpatentable over Wilson, Lee, Furrer and further in view of Zhang as discussed above for substantially similar rationale.
Allowable Subject Matter
12. Claims 7 and 17 are objected to as being dependent upon a rejected base claim, but would be allowable, if rewritten in independent form including all of the limitations of the base claim and any intervening claims and overcomes the rejections 101 and 112 (b) below. The following is an Examiner’s statement of reasons for allowance: When reading the claims in light of the specification, none of the references of record alone or in combination disclose or suggest the combination of limitations specified in the claims 7 and 17, either taken by itself or in any combination, would have anticipated or made obvious the abovementioned subject matter of the present application at or before the time it was filed. The indication of allowability is not solely on the basis of the quoted limitation but instead based upon the totality of the claim and is based on limitations, context and environment not explicitly recited in the quotes or expounded upon in the reasons for allowance.
The prior arts made of record and not relied upon is considered pertinent to applicant's disclosure.
The prior art Lee et al. (Journal “History Matching by Spline Approximation and Regularization in Single-Phase Areal Reservoirs”) disclosed an automatic history-matching algorithm is developed from bicubic spline approximations of permeability and porosity distributions and from the theory of regularization to estimate permeability or porosity in a single-phase, two-dimensional (2D) areal reservoir from well pressure data. A quasi-optimal regularization parameter is determined without requiring a priori information on the statistical properties of the observations. In this study an automatic history-matching algorithm is developed and tested for estimating spatially varying porosity and permeability in a single-phase areal reservoir. The algorithm is based on spline approximations of the parameters and a regularization formulation. In the regularization approach to parameter estimation by introduction of the stabilizing functional as a measure of non-smoothness, one can control the properties of the parameter estimates as well as the history match.
The prior art Furrer disclosed (please see pages 1 and 2 section 1 and 1.1), the structure of the classic smoothing spline problem, focusing on the details which will be important for further developments. Also, the equivalence between a Kriging estimator and a spline estimator is outlined. The large sample behavior for the mean squared error of Kriging estimators is conjectured/assumed and also a key condition is verified that will allow the rigorous theory that has been applied to one dimensional splines to be extended to these more general estimators. The parameter λ (in Eq. 2) controls the degree of smoothness via the penalty term, which in this case penalizes roughness of the estimated function using its total curvature. The form of the roughness penalty using second derivatives implies that linear functions will result in a penalty of zero.
However, none of the prior arts teaches the claimed limitation: specifically: _alpha(α) regularization coefficient and Ns a number of sections in the model in claim limitation of claims 7 and 17, (in combination with the remaining claimed limitations), either taken by itself or in any combination, would have anticipated or made obvious the abovementioned subject matter of the present application at or before the time it was filed.
Conclusion
13. Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
The prior arts made of record and not relied upon is considered pertinent to applicant's disclosure. An NPL "Polynomial-Chaos-Expansion Based Integrated Dynamic Modelling Workflow for Computationally Efficient Reservoir Characterization: A Field Case Study" by Patel et al. disclosed a unique approach for computationally efficient dynamic data integration is presented which includes construction of a proxy model that can replace reservoir simulator. Realizations are first parameterized using Karhunen-Loeve (KL) transformation and represented in terms of few uncorrelated random variables. Considering these random variables as input and production parameters as output, a mathematical model based on Polynomial Chaos Expansion (PCE) is constructed using deterministic coefficients and orthogonal polynomials which is further employed in assisted history matching instead of computationally expensive reservoir simulator. The computing cost of assisted history matching is reduced by almost 95% as training of PCE needs only few full physics simulations. Finally, proposed surrogate-accelerated integrated dynamic modelling can be used in greenfield closed-loop optimization workflows and uncertainty assessment with minimal use of numerical simulator which ultimately maximize the benefit in monetary terms.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to NUPUR DEBNATH whose telephone number is (571)272-8161. The examiner can normally be reached M-F 8:00 am -4:30 pm.
Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice.
If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Renee D Chavez can be reached on (571)270-1104. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/NUPUR DEBNATH/Examiner, Art Unit 2186
/RENEE D CHAVEZ/Supervisory Patent Examiner, Art Unit 2186
Prosecution Insights