Prosecution Insights
Last updated: July 17, 2026
Application No. 18/476,017

Robust Stochastic Seismic Inversion with New Error Term Specification

Non-Final OA §103
Filed
Sep 27, 2023
Priority
Oct 10, 2022 — provisional 63/378,963
Examiner
SULTANA, DILARA
Art Unit
2858
Tech Center
2800 — Semiconductors & Electrical Systems
Assignee
BP plc
OA Round
2 (Non-Final)
80%
Grant Probability
Favorable
2-3
OA Rounds
0m
Est. Remaining
97%
With Interview

Examiner Intelligence

Grants 80% — above average
80%
Career Allowance Rate
106 granted / 132 resolved
+12.3% vs TC avg
Strong +17% interview lift
Without
With
+16.8%
Interview Lift
resolved cases with interview
Typical timeline
2y 9m
Avg Prosecution
22 currently pending
Career history
179
Total Applications
across all art units

Statute-Specific Performance

§101
2.7%
-37.3% vs TC avg
§103
82.5%
+42.5% vs TC avg
§102
12.2%
-27.8% vs TC avg
§112
2.4%
-37.6% vs TC avg
Black line = Tech Center average estimate • Based on career data from 132 resolved cases

Office Action

§103
DETAILED ACTIONS 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 . Response to Amendment This office action is in response to the amendments/arguments submitted by the Applicant(s) on 03/16/2026. Status of the Claims Claims 1-20 are pending. Claims 1, 8, and 15 are amended. Response to Arguments Rejections Under 35 U.S.C.§102(a)(1) Applicant's arguments, see remarks page 7-13, filed 03/16/2026. with respect to the rejection(s) of Claims under §102(a)(1 ) has been considered, and are moot because the amendment has necessitated a new ground of rejections. The new rejections are set forth below. Claim Rejections - 35 USC § 103 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. Claims 1-20 are rejected under 35 U.S.C. 103 as being unpatentable over Douglas Spencer Sassen (US 2016/0116620 A1, hereinafter Sassen) and in view of Jianhua YU, (US 2023/0184974 A1, hereinafter Yu, Prov. Application Filed on Dec 10, 2021). Regarding Claim 1, Sassen teaches, A method, (Sassen, Figure 3) comprising: receiving observed seismic data (Sassen, Figure 3, Step 310, Inputs: Seismic data); generating a variable noise term based in part upon the first observed value; utilizing the variable noise term to determine a likelihood function of a stochastic inversion operation (Figure 3-4, [0091] In both FIGS. 3 and 4, noise is estimated from the mean squared residuals from differences between the observed seismic gathers and the modeled seismic gathers at each iteration of the loops (in FIGS. 3 and 4). These updated noise levels may be used to adapt the thresholding. The estimation of the noise is done separately on each gather and can be windowed in time); utilizing the likelihood function to generate a posterior probability distribution in conjunction with the stochastic inversion operation; and applying the posterior probability distribution to characterize a subsurface region of Earth. (Figure 3, [0057] Some embodiments of the present disclosure may use a Bayesian estimation framework for estimating seismic properties (perturbations in Vp, Vs, and p or just P for properties) and their associated uncertainty from reflection seismic sparse-spike inversion results. The posterior p.d.f. of the properties (P) as a function of reflection seismic angle gathers (S) may be given by, p(PIS)=Np(SIP)p(P), where N is the normalization factor, p(SIP) is the likelihood function relating the conditional probability of the reflection seismic angle gathers (S) given the properties, and p(P) is the prior probability of the property of interest”). Sassen teaches processing seismic data and estimate wavelet based on seismic data see. ([0126], equation 1, [0016], Claim 1) Sassen is silent on determining an envelope or magnitude of the observed seismic data as a first observed value; the envelope or magnitude of the observed seismic data representing a phase-independent amplitude of the observed seismic data. However, Yu teaches determining an envelope or magnitude of the observed seismic data as a first observed value (Yu, Figure 4, step 422, [0059] After the shifting of the seismic data in operation 422, seismic attributes are calculated in operation 424. As discussed above, examples of seismic attributes include amplitude envelope); the envelope or magnitude of the observed seismic data representing a phase-independent amplitude of the observed seismic data (Yu, Figure 4, [0040] Examples of seismic attributes include amplitude envelope, amplitude weighted frequency, amplitude weighted phase, average frequency, apparent polarity, cosine instantaneous phase, derivative of seismic data, derivative instantaneous amplitude, dominant frequency, instantaneous frequency, instantaneous phase, and integrated absolute amplitude, etc. One or more seismic attributes may be selected by a user” NOTE: Phase-independent seismic data envelope is known as measure of instantaneous amplitude). It would have been obvious to a person of ordinary skill before the effective filing date to modify Sassen method to include Yu method of using observe data and generate seismic attributes such as amplitude generate prior model as taught by Yu in order to apply inversion and constructing posterior density function with a Bayesian theorem using likelihood function. (Yu, [figure 4, [0012] [0018]). Regarding Claim 2, combination of Sassen and Yu teaches the method of claim 1, Sassen further teaches comprising generating the variable noise term (Figure 3, 310, estimate noise, [0016], equation 1, n(t) noise) based at least in part upon a signal to noise ratio of the observed seismic data. (Sassen, [0048], “(a hybrid approach may be to use ISTA, or FISTA, to get the model close to optimal, and then a small number of IHI iterations may be applied to allow the expansion of the overly shrunken coefficients. This approach may still truncate coefficients that are dominated by noise and fits with our philosophy of parsimony. This ISTA/IHT approach may be used when the signal to noise ratio is large, but further improvements can be made by including a temporal co-location constraint that assumes that the 'gradient' reflection coefficients are associated with 'intercept' (or 15t principal eigenvalue) coefficients that are above the noise level and apply hard-thresholding”). Regarding Claim 3, combination of Sassen and Yu teaches the method of claim 2, Sassen further teaches comprising generating the variable noise term by dividing a smoothed envelope or magnitude of the observed seismic data as the first observed value by a square root of the signal to noise ratio of the observed seismic data (Sassen, [0071], [0070] Least-squares may be used to find a solution to inconsistent linear equations ( e.g. noisy systems) of m equations and n unknowns-with the requirement that its columns of M are independent and the rank is equal ton. If the system is rank deficient or if the columns are not independent, then the problem may have no solution or may be indeterminate (infinite solutions). This issue arises in seismic inversion when one tries to estimate the 3rd 'Far' component of Zeoppritz' Rpp equation at typical offsets. Usually this component is below noise and is largely degenerate with the 2nd component at angles less than 40 degrees. The method of Singular Value Decomposition (SYD) may thus be used to find solutions to such problems”) Regarding Claim 4, combination of Sassen and Yu teaches the method of claim 1, Sassen further teaches comprising determining whether a first data point of the first observed value exceeds a threshold value. (Sassen, 0052] The effectiveness of hard thresholding for estimating sparse spike peaks may be explained from a Bayesian perspective. The typical soft-thresholding rule is equivalent to placing a double exponential, or Laplacian, prior probability distribution function (p.d.f.) model on the inversion problem. This 'long tailed' distribution provides for high probability of wavelet ( or reflection) coefficients at zero-as well as a significant probability of large coefficients. Hard-thresholds are equivalent to an improper prior, where the prior p.d.f. is uniform everywhere except below the threshold-where all of the density falls on zero. This essentially means that all possible outcomes are equally likely except below the threshold where only zero is a possible solution. This is equivalent to a general form of penalized least-squares inversion”). Regarding Claim 5, combination of Sassen and Yu teaches the method of claim 4, Sassen further teaches, comprising setting the threshold value based upon the observed seismic data. (Sassen, Figure 3, [0029] A soft-threshold SYD inversion algorithm for these problems may be equivalent to regularization with a Ll norm that enforces a parsimonious model. SYD utilizes the calculation of eigenvalues and eigenvectors to both orthogonalize the system of equations and to find zero valued or nearly zero singular values (singular values=square root of eigenvalues). Regarding Claim 6, combination of Sassen and Yu teaches the method of claim 4, Sassen further teaches, comprising utilizing the variable noise term to determine the likelihood function when the first data point exceeds the threshold value. (Sassen, [0022] “This technique uses a soft thresholding rule F(g) to eliminate wavelet coefficients (i.e. spikes) that fall below noise levels while iterating towards a sparse set of coefficients that fit observed seismic data. The end result may be a model that has preserved reflections resolvable by the bandwidth of the seismic above noise and without smoothing” [0053] “The posterior probability distribution is the product of both the likelihood function, which for our case is described by a multivariate Gaussian distribution, and the prior p.d.f., which for soft-thresholding is a Laplacian. When the likelihood function is not very informative with respect to the 'gradient' component (i.e.: a very small eigenvalue just above noise) the product of the prior with the likelihood may be strongly dominated by the prior. Therefore, in iterative optimization techniques such as ISTA or FI STA, there may be a tendency to converge towards, but not to, the global solution because of the restraint placed by the prior. However, the benefit of the soft-thresholding is to help make the inversion more robust-to help prevent the inversion from becoming overly sensitive to outliers or noise”). Regarding Claim 7, combination of Sassen and Yu teaches the method of claim 4, Sassen further teaches utilizing the threshold value as the variable noise term to determine the likelihood function when the first data point is below the threshold value (Sassen, [0022] “This technique uses a soft thresholding rule F(g) to eliminate wavelet coefficients (i.e. spikes) that fall below noise levels while iterating towards a sparse set of coefficients that fit observed seismic data. The end result may be a model that has preserved reflections resolvable by the bandwidth of the seismic above noise and without smoothing”) Regarding Claim 8, Sassen teaches, A tangible, non-transitory, machine-readable media, comprising instructions configured to cause a processor (Sassen, Figure 9) to: receiving observed seismic data (Figure 3, Step 310, Inputs: Seismic data); generating a variable noise term based in part upon the first observed value; utilizing the variable noise term to determine a likelihood function of a stochastic inversion operation (Figure 3-4, [0091] In both FIGS. 3 and 4, noise is estimated from the mean squared residuals from differences between the observed seismic gathers and the modeled seismic gathers at each iteration of the loops (in FIGS. 3 and 4). These updated noise levels may be used to adapt the thresholding. The estimation of the noise is done separately on each gather and can be windowed in time); utilizing the likelihood function to generate a posterior probability distribution in conjunction with the stochastic inversion operation; and applying the posterior probability distribution to characterize a subsurface region of Earth. (Figure 3, [0057] Some embodiments of the present disclosure may use a Bayesian estimation framework for estimating seismic properties (perturbations in Vp, Vs, and p or just P for properties) and their associated uncertainty from reflection seismic sparse-spike inversion results. The posterior p.d.f. of the properties (P) as a function of reflection seismic angle gathers (S) may be given by, p(PIS)=Np(SIP)p(P), where N is the normalization factor, p(SIP) is the likelihood function relating the conditional probability of the reflection seismic angle gathers (S) given the properties, and p(P) is the prior probability of the property of interest”). Sassen teaches processing seismic data and estimate wavelet based on seismic data see. ([0126], equation 1, [0016], Claim 1) Sassen is silent on determining an envelope or magnitude of the observed seismic data as a first observed value; the envelope or magnitude of the observed seismic data representing a phase-independent amplitude of the observed seismic data. However, Yu teaches determining an envelope or magnitude of the observed seismic data as a first observed value (Yu, Figure 4, step 422, [0059] After the shifting of the seismic data in operation 422, seismic attributes are calculated in operation 424. As discussed above, examples of seismic attributes include amplitude envelope); the envelope or magnitude of the observed seismic data representing a phase-independent amplitude of the observed seismic data (Yu, Figure 4, [0040] Examples of seismic attributes include amplitude envelope, amplitude weighted frequency, amplitude weighted phase, average frequency, apparent polarity, cosine instantaneous phase, derivative of seismic data, derivative instantaneous amplitude, dominant frequency, instantaneous frequency, instantaneous phase, and integrated absolute amplitude, etc. One or more seismic attributes may be selected by a user” NOTE: Phase-independent seismic data envelope is known as measure of instantaneous amplitude). It would have been obvious to a person of ordinary skill before the effective filing date to modify Sassen method to include Yu method of using observe data and generate seismic attributes such as amplitude generate prior model as taught by Yu in order to apply inversion and constructing posterior density function with a Bayesian theorem using likelihood function. (Yu, [figure 4, [0012] [0018]). Regarding Claim 9, combination of Sassen and Yu teaches the tangible, non-transitory, machine-readable media of claim 8, Sassen further teaches comprising generating the variable noise term (Figure 3, 310, estimate noise, [0016], equation 1, n(t) noise) based at least in part upon a signal to noise ratio of the observed seismic data. (Sassen, [0048], “(a hybrid approach may be to use ISTA, or FISTA, to get the model close to optimal, and then a small number of IHI iterations may be applied to allow the expansion of the overly shrunken coefficients. This approach may still truncate coefficients that are dominated by noise and fits with our philosophy of parsimony. This ISTA/IHT approach may be used when the signal to noise ratio is large, but further improvements can be made by including a temporal co-location constraint that assumes that the 'gradient' reflection coefficients are associated with 'intercept' (or 15t principal eigenvalue) coefficients that are above the noise level and apply hard-thresholding”). Regarding Claim 10, combination of Sassen and Yu teaches the tangible, non-transitory, machine-readable media of claim 9, Sassen further teaches comprising generating the variable noise term by dividing a smoothed envelope or magnitude of the observed seismic data as the first observed value by a square root of the signal to noise ratio of the observed seismic data (Sassen, [0071], [0070] Least-squares may be used to find a solution to inconsistent linear equations ( e.g. noisy systems) of m equations and n unknowns-with the requirement that its columns of M are independent and the rank is equal ton. If the system is rank deficient or if the columns are not independent, then the problem may have no solution or may be indeterminate (infinite solutions). This issue arises in seismic inversion when one tries to estimate the 3rd 'Far' component of Zeoppritz' Rpp equation at typical offsets. Usually this component is below noise and is largely degenerate with the 2nd component at angles less than 40 degrees. The method of Singular Value Decomposition (SYD) may thus be used to find solutions to such problems”). Regarding Claim 11, combination of Sassen and Yu teaches the tangible, non-transitory, machine-readable media of claim 10, Sassen further teaches comprising determining whether a first data point of the first observed value exceeds a threshold value. (Sassen, 0052] The effectiveness of hard thresholding for estimating sparse spike peaks may be explained from a Bayesian perspective. The typical soft-thresholding rule is equivalent to placing a double exponential, or Laplacian, prior probability distribution function (p.d.f.) model on the inversion problem. This 'long tailed' distribution provides for high probability of wavelet (or reflection) coefficients at zero-as well as a significant probability of large coefficients. Hard-thresholds are equivalent to an improper prior, where the prior p.d.f. is uniform everywhere except below the threshold-where all of the density falls on zero. This essentially means that all possible outcomes are equally likely except below the threshold where only zero is a possible solution. This is equivalent to a general form of penalized least-squares inversion”). Regarding Claim 12, combination of Sassen and Yu teaches the tangible, non-transitory, machine-readable media of claim 11, Sassen further teaches, comprising setting the threshold value based upon the observed seismic data. (Sassen, Figure 3, [0029] A soft-threshold SYD inversion algorithm for these problems may be equivalent to regularization with a Ll norm that enforces a parsimonious model. SYD utilizes the calculation of eigenvalues and eigenvectors to both orthogonalize the system of equations and to find zero valued or nearly zero singular values (singular values=square root of eigenvalues). Regarding Claim 13, combination of Sassen and Yu teaches the tangible, non-transitory, machine-readable media of claim 12, Sassen further teaches, comprising utilizing the variable noise term to determine the likelihood function when the first data point exceeds the threshold value. (Sassen, [0022] “This technique uses a soft thresholding rule F(g) to eliminate wavelet coefficients (i.e. spikes) that fall below noise levels while iterating towards a sparse set of coefficients that fit observed seismic data. The end result may be a model that has preserved reflections resolvable by the bandwidth of the seismic above noise and without smoothing” [0053] “The posterior probability distribution is the product of both the likelihood function, which for our case is described by a multivariate Gaussian distribution, and the prior p.d.f., which for soft-thresholding is a Laplacian. When the likelihood function is not very informative with respect to the 'gradient' component (i.e.: a very small eigenvalue just above noise) the product of the prior with the likelihood may be strongly dominated by the prior. Therefore, in iterative optimization techniques such as ISTA or FI STA, there may be a tendency to converge towards, but not to, the global solution because of the restraint placed by the prior. However, the benefit of the soft-thresholding is to help make the inversion more robust-to help prevent the inversion from becoming overly sensitive to outliers or noise”). Regarding Claim 14, combination of Sassen and Yu teaches the tangible, non-transitory, machine-readable media of claim 13, Sassen further teaches utilizing the threshold value as the variable noise term to determine the likelihood function when the first data point is below the threshold value (Sassen, [0022] “This technique uses a soft thresholding rule F(g) to eliminate wavelet coefficients (i.e. spikes) that fall below noise levels while iterating towards a sparse set of coefficients that fit observed seismic data. The end result may be a model that has preserved reflections resolvable by the bandwidth of the seismic above noise and without smoothing”). Regarding Claim 15, Sassen teaches, A method, (Sassen, Figure 3) comprising: receiving observed seismic data (Figure 3, Step 310, Inputs: Seismic data) ; determining whether a value of the variable noise term is above a threshold value; utilizing the variable noise term to determine a likelihood function of a stochastic inversion operation when the value of the variable noise term is determined to be above the threshold value; (Sassen, [0022] “This technique uses a soft thresholding rule F(g) to eliminate wavelet coefficients (i.e. spikes) that fall below noise levels while iterating towards a sparse set of coefficients that fit observed seismic data. The end result may be a model that has preserved reflections resolvable by the bandwidth of the seismic above noise and without smoothing” [0053] “The posterior probability distribution is the product of both the likelihood function, which for our case is described by a multivariate Gaussian distribution, and the prior p.d.f., which for soft-thresholding is a Laplacian. When the likelihood function is not very informative with respect to the 'gradient' component (i.e.: a very small eigenvalue just above noise) the product of the prior with the likelihood may be strongly dominated by the prior. Therefore, in iterative optimization techniques such as ISTA or FI STA, there may be a tendency to converge towards, but not to, the global solution because of the restraint placed by the prior. However, the benefit of the soft-thresholding is to help make the inversion more robust-to help prevent the inversion from becoming overly sensitive to outliers or noise”). utilizing the likelihood function to generate a posterior probability distribution in conjunction with the stochastic inversion operation; and applying the posterior probability distribution to characterize a subsurface region of Earth. (Figure 3, [0057] Some embodiments of the present disclosure may use a Bayesian estimation framework for estimating seismic properties (perturbations in Vp, Vs, and p or just P for properties) and their associated uncertainty from reflection seismic sparse-spike inversion results. The posterior p.d.f. of the properties (P) as a function of reflection seismic angle gathers (S) may be given by, p(PIS)=Np(SIP)p(P), where N is the normalization factor, p(SIP) is the likelihood function relating the conditional probability of the reflection seismic angle gathers (S) given the properties, and p(P) is the prior probability of the property of interest”). Sassen teaches processing seismic data and estimate wavelet based on seismic data see. ([0126], equation 1, [0016], Claim 1) Sassen is silent on determining an envelope or magnitude of the observed seismic data as a first observed value; the envelope or magnitude of the observed seismic data representing a phase-independent amplitude of the observed seismic data. However, Yu teaches determining an envelope or magnitude of the observed seismic data as a first observed value (Yu, Figure 4, step 422, [0059] After the shifting of the seismic data in operation 422, seismic attributes are calculated in operation 424. As discussed above, examples of seismic attributes include amplitude envelope); the envelope or magnitude of the observed seismic data representing a phase-independent amplitude of the observed seismic data (Yu, Figure 4, [0040] Examples of seismic attributes include amplitude envelope, amplitude weighted frequency, amplitude weighted phase, average frequency, apparent polarity, cosine instantaneous phase, derivative of seismic data, derivative instantaneous amplitude, dominant frequency, instantaneous frequency, instantaneous phase, and integrated absolute amplitude, etc. One or more seismic attributes may be selected by a user” NOTE: Phase-independent seismic data envelope is known as measure of instantaneous amplitude). It would have been obvious to a person of ordinary skill before the effective filing date to modify Sassen method to include Yu method of using observe data and generate seismic attributes such as amplitude generate prior model as taught by Yu in order to apply inversion and constructing posterior density function with a Bayesian theorem using likelihood function. (Yu, [figure 4, [0012] [0018]). Regarding Claim 16, combination of Sassen and Yu teaches the method of claim 15, Sassen further teaches utilizing the threshold value as the variable noise term to determine the likelihood function when the first data point is below the threshold value (Sassen, [0022] “This technique uses a soft thresholding rule F(g) to eliminate wavelet coefficients (i.e. spikes) that fall below noise levels while iterating towards a sparse set of coefficients that fit observed seismic data. The end result may be a model that has preserved reflections resolvable by the bandwidth of the seismic above noise and without smoothing”). Regarding Claim 17, combination of Sassen and Yu teaches the method of claim 16, Sassen further teaches comprising generating the variable noise term (Figure 3, 310, estimate noise, [0016], equation 1, n(t) noise) based at least in part upon a signal to noise ratio of the observed seismic data. (Sassen, [0048], “(a hybrid approach may be to use ISTA, or FISTA, to get the model close to optimal, and then a small number of IHI iterations may be applied to allow the expansion of the overly shrunken coefficients. This approach may still truncate coefficients that are dominated by noise and fits with our philosophy of parsimony. This ISTA/IHT approach may be used when the signal to noise ratio is large, but further improvements can be made by including a temporal co-location constraint that assumes that the 'gradient' reflection coefficients are associated with 'intercept' (or 15t principal eigenvalue) coefficients that are above the noise level and apply hard-thresholding”). Regarding Claim 18, combination of Sassen and Yu teaches the method of claim 17, Sassen further teaches comprising generating the variable noise term by dividing a smoothed envelope or magnitude of the observed seismic data as the first observed value by a square root of the signal to noise ratio of the observed seismic data (Sassen, [0071], [0070] Least-squares may be used to find a solution to inconsistent linear equations ( e.g. noisy systems) of m equations and n unknowns-with the requirement that its columns of M are independent and the rank is equal ton. If the system is rank deficient or if the columns are not independent, then the problem may have no solution or may be indeterminate (infinite solutions). This issue arises in seismic inversion when one tries to estimate the 3rd 'Far' component of Zeoppritz' Rpp equation at typical offsets. Usually this component is below noise and is largely degenerate with the 2nd component at angles less than 40 degrees. The method of Singular Value Decomposition (SYD) may thus be used to find solutions to such problems”). Regarding Claim 19, combination of Sassen and Yu teaches the method of claim 15, Sassen further teaches wherein determining an envelope of the observed seismic data comprises filtering the envelope of the observed seismic data to generate a smoothed envelope as envelope of the observed seismic data. (Sassen, [0059] The seismic model used in the present disclosure may assume a weak interaction between reflectors that may allow us to express seismic data and reflectivity with a convolutional model expressed as, S(0,t)= W(0,tJ* R(0,t)+n(0,t). (1) where S(8,t) is the seismic signal at multiple angles 8, W(8,t) is the seismic wavelet, R(8,t) is the reflectivity series for each angle 8, and n(8,t) is the noise. The inverse problem is to recover R( 8, t) from the seismic and source wavelet by searching for models of R(8,t) that minimize the norm of the observed seismic and the proposed synthetic seismic. For an inconsistent set of linear equations, which arise when a system is noisy or poorly conditioned, regularization may be needed to find a stable solution to the inverse. In the typical L2 nonn case, the minimization function becomes, /= I W(0,tJ* R(0,t)-S(0,t)2 +/,,IRI 2 , (2) where A is the weighting term for the regularization. In a Bayesian sense, the L2 regularization term implies a Gaussian model covariance, and may be equivalent to a prior smoothing constraint that essentially removes any sharp discontinuities from the resulting inversion as A increases to allow convergence to norm”). Regarding Claim 20, combination of Sassen and Yu teaches the method of claim 19, Sassen further teaches comprising determining whether a first data point of the first observed value exceeds a threshold value. (Sassen, 0052] The effectiveness of hard thresholding for estimating sparse spike peaks may be explained from a Bayesian perspective. The typical soft-thresholding rule is equivalent to placing a double exponential, or Laplacian, prior probability distribution function (p.d.f.) model on the inversion problem. This 'long tailed' distribution provides for high probability of wavelet ( or reflection) coefficients at zero-as well as a significant probability of large coefficients. Hard-thresholds are equivalent to an improper prior, where the prior p.d.f. is uniform everywhere except below the threshold-where all of the density falls on zero. This essentially means that all possible outcomes are equally likely except below the threshold where only zero is a possible solution. This is equivalent to a general form of penalized least-squares inversion”). Conclusion Citation of Pertinent Prior Art The prior art made of record and not relied upon is considered pertinent to applicant's disclosure. Ray et al. (US 2019/0011583 A1) recites “A method is described for full waveform inversion using a tree-based Bayesian approach which automatically selects the model complexity, thereby reducing the computational cost. The method may be executed by a computer system.” GRIFFITH et al. (WO 2021/092201 A1) recites “A method of for computing a high frequency envelope attribute from seismic data involves selecting a 1D trace of the seismic data and computing an envelope for the 1D trace. A high frequency envelope attribute is computed by adding the envelope to any quantity derived from the 1D trace”. 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. Any inquiry concerning this communication or earlier communications from the examiner should be directed to DILARA SULTANA whose telephone number is (571)272-3861. The examiner can normally be reached Mon-Fri, 9 AM-5:30 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, EMAN ALKAFAWI can be reached on (571) 272-4448. 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. /DILARA SULTANA/Examiner, Art Unit 2858 05/01/2026 /EMAN A ALKAFAWI/Supervisory Patent Examiner, Art Unit 2858 5/6/2026
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Prosecution Timeline

Sep 27, 2023
Application Filed
Dec 22, 2025
Non-Final Rejection mailed — §103
Mar 16, 2026
Response Filed
May 08, 2026
Final Rejection mailed — §103
Jun 10, 2026
Response after Non-Final Action

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