Data-driven method for inverting formation anisotropy constants using borehole acoustic data

Abstract

A method is proposed in which formation anisotropy constants are inverted using wellbore sonic data.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to U.S. Provisional Patent Application 62 / 909429, filed October 2, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0003] This disclosure relates to the manipulation of acoustic data. More specifically, this disclosure relates to methods for inverting formation anisotropy constants using acoustic data. Background Technology

[0004] Traditionally, acoustic waveform processing workflows primarily consist of assessments of formation compression (dtc) and shear (dts) slowness or P&S. These two logging records can be extracted using equipment from Schlumberger Technology Corporation via waveforms from monopole, dipole, or quadrupole transmitters. However, most sedimentary rocks exhibit some degree of anisotropy, particularly in shale-containing geological deposits. This anisotropy plays a significant role in geomechanical studies. The most commonly observed type of anisotropy in shale is known as vertical-to-lateral isotropy (VTI), which requires five parameters to describe the elastic constants. Using the notation commonly used in the field, this type of anisotropy can be described by two vertical slownesses (i.e., dtc and dts, or by two velocities, VP0 and VS0) and three dimensionless (so-called "Thomsen") parameters ∈, γ, and δ, which are reduced to zero for isotropic formations. These three parameters are necessary for establishing a mechanical geomechanical model (MEM) for geomechanical analysis, such as estimating rock hardness, strength, stress, sand production prediction, wellbore stability, and hydraulic fracturing design.

[0005] The three Thomson parameters mentioned above cannot be directly measured by a wellbore sonic logging tool along a single orientation at a given depth. A model-based inversion method is used to estimate these anisotropy constants. This model-based inversion method is not robust and can produce unreliable results because several local minima exist in the cost function, defined by the mismatch between the measured and theoretical wellbore models. Furthermore, the mud properties in the downhole environment are required to compute the model-based inversion. However, these mud properties are often not measured. In some cases, these mud property values ​​can have a significant impact on wellbore dispersion models.

[0006] Therefore, it is necessary to accurately estimate the anisotropy parameters, including the three Thomson parameters.

[0007] It is also necessary to accurately estimate the anisotropy parameters that serve as a depth function.

[0008] These anisotropic parameters also need to be accurately estimated using data-driven methods with physical constraints. Summary of the Invention

[0009] Therefore, a more detailed description of the features of this disclosure can be obtained by referring to the embodiments, some of which are illustrated in the figures. It should be noted that the figures only illustrate typical embodiments of this disclosure and should not be considered as limiting its scope, as this disclosure allows for other equally effective embodiments without specific description. Therefore, the following overview provides only a few aspects and should not be used to limit the described embodiments to a single concept.

[0010] In one non-limiting embodiment, a method is disclosed. This method may include...

[0011] The method involves acquiring and processing a waveform to obtain at least one of Stoneley dispersion, bending dispersion, quadrupole dispersion, and pseudo-Rayleigh dispersion. The method may further include performing calculations of interpolated theoretical dispersions of the Stoneley dispersion, bending dispersion, quadrupole dispersion, and pseudo-Rayleigh dispersion, and obtaining at least one library calculation. The method may also include performing an initial estimate of mud slowness using the processing of the acquired waveform and the interpolation of the theoretical dispersion, and calculating a mismatch between the processed waveform obtaining at least one Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersion and the theoretical dispersion of the Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersion. The method may further include estimating at least one DTMud value as a vertical depth profile and using the at least one estimated DTMud value to calculate a second mismatch between the theoretical dispersion and the processed waveform. The method may further include calculating at least one parameter at multiple depths by minimizing the second mismatch and estimating at least one parameter using regression. The method may further include updating the value of at least one parameter based on regression, and calculating a third mismatch between the theoretical dispersion and the measured dispersion based on the updated value of the at least one parameter based on regression. The method may also include estimating the final value of at least one parameter by minimizing the mismatch between theoretical dispersion and measured dispersion.

[0012] In another example embodiment, a method may be performed. The method may include obtaining a waveform from an acoustic wellbore device in the formation. The method may also include processing the waveform obtained from the acoustic wellbore device to obtain at least one value for Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersions. The method may further include performing calculations to generate theoretical dispersions of the Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersions of the waveform. The method may also include performing an initial estimate of mud slowness using the processed and theoretical dispersions of the obtained waveform. The method may also include calculating a first mismatch between the processed waveform, which yields at least one Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersion, and the theoretical dispersions of the Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersions. The method may further include estimating at least one DTmud value as a vertical depth profile and using at least one estimated DTmud value to calculate a second mismatch between the theoretical dispersion and the processed waveform. The method may also calculate at least one modified Thomson parameter at multiple depths by minimizing the second mismatch and estimating at least one Thomson parameter of the formation using regression. The method may further include calculating a third mismatch between the theoretical dispersion and the measured dispersion based on updated values ​​of regression-based Thomson parameters. The method may also include estimating the final value of at least one Thomson parameter by minimizing the mismatch between the theoretical and measured dispersions. Attached Figure Description

[0013] Therefore, a more detailed understanding of the above-described features of this disclosure, and a more specific description of this disclosure, which has been briefly summarized above, can be obtained by referring to the embodiments, some of which are illustrated in the accompanying drawings. However, it should be noted that the drawings only illustrate typical embodiments of this disclosure and should not be considered as limiting its scope, as this disclosure allows for other equally effective embodiments.

[0014] Figure 1 This is a composite monopole Stoneley and dipole bending dispersion curve of the North Sea Shale A1 core.

[0015] Figure 2A These are the synthetic monopole Stoneley and dipole bending dispersion curves of the hard shale G32 core.

[0016] Figure 2B yes Figure 2A Pseudo-Rayleigh dispersion curve of hard shale G32 core.

[0017] Figure 3A This is a sensitivity plot of the unipolar Stoneley frequency to mud slowness in the A1 core sample of the Beihai Shale.

[0018] Figure 3B yes Figure 3ASensitivity plots of the single-pole Stoneley frequency of the core sample to the Thomson parameters ∈, γ, and δ.

[0019] Figure 4A This is a sensitivity diagram of frequency dipole bending dispersion to mud slowness in the A1 core sample of the Beihai Shale.

[0020] Figure 4B yes Figure 4A Sensitivity plot of dipole bending dispersion frequency of core sample to Thomson parameters ∈, γ, and δ.

[0021] Figure 5A This is a sensitivity plot of the unipolar Stoneley frequency to mud slowness in a core sample of hard shale G32.

[0022] Figure 5B yes Figure 5A Sensitivity plots of the single-pole Stoneley frequency of the core sample to the Thomson parameters ∈, γ, and δ.

[0023] Figure 6A This is a sensitivity plot of dipole bending frequency and mud slowness for a core sample from hard shale G32.

[0024] Figure 6B yes Figure 6A Sensitivity plot of dipole bending frequencies of Thomson parameters ∈, γ, and δ for core samples.

[0025] Figure 7A This is a sensitivity plot of pseudo Rayleigh frequencies to mud slowness in a hard shale G32 core sample.

[0026] Figure 7B It shows Figure 7A Sensitivity plots of pseudo Rayleigh frequencies of core samples against Thomson parameters for ∈, γ, and δ.

[0027] Figure 8A This is a correlation diagram using the data in Table 1 for γ and ∈.

[0028] Figure 8B This is a correlation graph of ∈ and δ using the data in Table 1.

[0029] Figure 9 This is the local correlation of the core data reported in Table 1, where the symbols with "X" and "O" represent two different local lithologies.

[0030] Figure 10 This describes a method for a data-driven inversion process in a non-limiting example embodiment of the present invention.

[0031] Figure 11This is a depiction of a synthetic test using eight synthetic core data sets and assuming a linear mud slowness profile. From left to right: borehole diameter (track 1), formation density (track 2), compression slowness (track 3), shear slowness (track 4), dipole curvature and Stoneley dispersion at frequencies from 1 to 8 kHz (track 5), mismatch plots for different values ​​of dtmud (track 6), mismatch plots for different values ​​of γ (track 7); mismatch plots for different values ​​of ∈ (track 8); mismatch plots for different values ​​of δ (track 9). The inverted mud slowness, represented by dots, and the actual mud slowness, represented by solid lines, overlap in track 5.

[0032] Figure 12 This is a description of a synthetic test using eight synthetic core data sets and assuming a linear mud slowness profile, with inverted mud slowness mean and depth gradient. Inverted values ​​are shown in "o", while true values ​​are shown in "x".

[0033] Figures 13A to 13C This is a description of the second synthetic test, in which... Figure 13A In (a), the inversion results are presented using five synthetic core data sets and assuming a constant mud slowness profile. From left to right: borehole diameter (channel 1), formation density (channel 2), compression slowness (channel 3), shear slowness (channel 4), dipole curvature and Stoneley dispersion at frequencies from 1 to 8 kHz (channel 5), mismatch plots for different values ​​of dtmud (channel 6), mismatch plots for different γ values ​​(channel 7); mismatch plots for different ∈ values ​​(channel 8); mismatch plots for different δ values ​​(channel 9); the red dots in channels 6 to 8 represent peaks in the mismatch plots. At certain depths, multiple peaks can be observed, representing multiple local minima in the constructed mismatch plots. Figure 13B The text describes the variation of superimposed mud slowness with depth. Figure 13C The second-step inversion is illustrated using a stacked mud slowness of 196 μS / ft, with mismatch plots from left to right: different γ values ​​(Track 1); different γ values ​​(Track 2); and different δ values ​​(Track 3). Note that the dashed lines represent uncertainties calculated from mismatch values ​​less than 1 μS / ft. Because the mud slowness stack is 196 μS / ft, the Thomson parameter estimates in Step 2 now have less uncertainty compared to Step 1.

[0034] Figures 14A to 14D The results of the second synthesis test are shown. Figure 14A In this context, the initial correlation range is between ∈ and γ. Figure 14B In this study, five synthetic core data sets are used, assuming a constant mud slowness profile, to illustrate the results of the second inversion. From left to right, mismatch plots for different γ values ​​(track 1); mismatch plots for different γ values ​​(track 2); mismatch plots for different δ values ​​(track 3). Figure 14CThe diagram shows the new correlation range between ∈ and γ after the second inversion. Figure 14D The results of the third inversion are shown in the figure, where the new correlation range was used. Note that the dashed lines represent uncertainties, which are calculated from mismatch values ​​less than 1 μS / ft. As the correlation ranges for γ and ∈ decrease, the estimates of the Thomson parameters in step 3 now have less uncertainty compared to step 2.

[0035] For ease of understanding, the same reference numerals have been used to denote the same elements in the figures (“Figures”) where possible. It is contemplated that elements disclosed in one embodiment may be advantageously used in other embodiments without specific description. Detailed Implementation

[0036] In the following text, embodiments of the invention are referenced. However, it should be understood that this disclosure is not limited to the specifically described embodiments. Rather, any combination of the following features and elements, whether or not associated with different embodiments, is considered to be able to implement and practice this disclosure. Furthermore, while embodiments of this disclosure may achieve advantages over other possible solutions and / or prior art, whether a particular advantage is achieved by a given embodiment does not limit this disclosure. Therefore, the following aspects, features, embodiments, and advantages are merely illustrative and are not to be considered elements or limitations of the claims unless expressly stated in the claims. Similarly, references to “this disclosure” should not be construed as a generalization of the inventive subject matter disclosed herein and should not be considered elements or limitations of the claims unless expressly stated in the claims.

[0037] While the terms first, second, third, etc., may be used herein to describe various elements, components, regions, layers, and / or portions, these elements, components, regions, layers, and / or portions should not be limited by these terms. These terms are used only to distinguish one element, component, region, layer, or portion from another. Terms such as “first,” “second,” and other numerical terms, when used herein, do not imply order or sequence unless the context clearly indicates otherwise. Therefore, without departing from the teachings of the exemplary embodiments, the first element, component, region, layer, or portion discussed herein may be referred to as the second element, component, region, layer, or portion.

[0038] When an element or layer is referred to as being "located on," "joined to," "connected to," or "attached to" another element or layer, it may be directly located on, joined to, connected to, or attached to the other element or layer, or there may be interleaved elements or layers. Conversely, when an element is referred to as being "directly on," "directly joined to," "directly connected to," or "directly attached to" another element or layer, there may not be interleaved elements or layers. Other terms used to describe relationships between elements should be interpreted in a similar manner. As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed terms.

[0039] Some embodiments will now be described with reference to the accompanying drawings. For consistency, similar elements in the figures will be indicated by similar numbers. In the following description, numerous details are set forth to provide an understanding of various embodiments and / or features. However, those skilled in the art will understand that some embodiments may be practiced without these details, and many variations or modifications to the described embodiments are possible. As used herein, the terms “above” and “below”, “upper” and “lower”, “upper part” and “lower part”, “upward” and “downward”, and other similar terms indicating relative positions above or below a given point are used in this specification to more clearly describe certain embodiments.

[0040] The described aspects are applicable to the field of wellbore acoustic waveform processing. The application of the method can provide quantification of the magnitude and uncertainty of anisotropic elastic constants (e.g., the three Thomson parameters in vertically and laterally isotropic (VTI) formations), as well as wellbore mud slowness as a function of depth. The described method can be used with acoustic logging tools equipped with single-mode or multi-mode transmitters. The presented embodiments are applicable to wireline and logging-while-drilling tools. The obtained anisotropic elastic constants can be used for rock physics and geomechanical applications.

[0041] The objective of various aspects of this invention is to provide estimates of anisotropic parameters (e.g., three Thomson parameters) and wellbore mud slowness as a function of depth using a physically constrained data-driven approach. The overall workflow / method may include three steps. First, a comprehensive random or grid search algorithm is performed to match all possible theoretical wellbore dispersion profiles with the measured wellbore pattern of the sonic logging tool. The search range is constrained based on some initial physical or empirical correlations. The first step may provide a coarse estimate of mud slowness as a linear, multilinear, or nonlinear profile at depth. Then, in the second step, the same dispersion matching process is repeated using the linear, multilinear, or nonlinear mud slowness profile obtained from the first step. The second step may provide estimates of the anisotropic parameters (e.g., Thomson parameters). Because anisotropic parameters are often observed to follow some strong correlation with a given formation, linear or nonlinear regression methods can be applied to obtain a locally correlated model using the inversion results from the second step. Finally, as a third step, the search process is repeated to match the measured wellbore pattern dispersion, and the correlation of the new constraints is applied to define the search range of the anisotropy parameters, thereby obtaining a more reliable estimate of the anisotropy parameters.

[0042] Note that the above workflow / method is one possible example; in application, we can use more or fewer than 3 steps in the inversion workflow. The order of the steps can be changed. Also note that in the first step, the regressed DTM profile may be associated with some uncertainties, which can also be carried over to the second step.

[0043] Sensitivity of wellbore dispersion mode to mud slowness and anisotropic elastic constants

[0044] Several modeling examples are provided to illustrate the sensitivity of wellbore models to formation and mud properties, and to explain how to estimate Thomson parameters and mud slowness based on these observations.

[0045] Consider cable-operated open-hole sonic logging tools with different parameters in fast or slow formations, as listed in Table 1, where c 11 ,c 33 ,c 44 ,c 13 ,c 66 There are five independent VTI elastic constants, where ρ is the volume density and ∈, γ, δ are the anisotropic Thomson parameters.

[0046] Table 1: Linear elastic constants of rock samples from [3][4] and [5] measured in the laboratory.

[0047]

[0048]

[0049] Of all these core samples, two representative samples (North Sea Shale A1 and Hard Shale G32) were selected to study their dispersion sensitivity to mud slowness and VTI parameters.

[0050] Figure 1 Synthetic dispersion of the Stoneley and bending modes of formation lithomorphic properties using North Sea Shale A1 core data from Table 1 is presented. In the synthetic modeling, the wellbore diameter was 7 inches. The mud slowness was 200 microseconds / foot (μs / ft). The mud density was 1000 kg / m³. 3 . Figure 2A This illustrates the synthetic monopole Stoneley and dipole bending dispersion maps of the hard shale G32 core sample. Figure 2B The synthetic pseudo Rayleigh dispersion map of the G32 hard shale core sample is presented.

[0051] To study the sensitivity, in this embodiment, the following expressions are used to calculate the sensitivity to mud slowness, Thomson γ,∈,δ, respectively:

[0052] Sensitivity

[0053] Sensitivity

[0054] Sensitivity

[0055] Sensitivity

[0056] The superscript "mode" can represent different wellbore modes, such as Stoneley, dipole bending, pseudo Rayleigh, or quadrupole, etc. dtm,∈,γ,δ represents mud slowness and Thomson parameters (∈,γ,δ), respectively. S0 represents the dispersion curve under the reference state, and S(Δdtm), S(Δ∈), S(Δγ), and S(Δδ) represent the dispersion curves caused by small disturbances in dtm,∈,γ,δ, respectively.

[0057] Figures 3 and 4 show the sensitivity analysis of Stoneley dispersion and dipole dispersion of the North Sea Shale A1 core data to different input parameters. Figures 5, 6, and 7 show the sensitivity analysis of Stoneley dispersion, dipole dispersion, and pseudo-Rayleigh dispersion of the hard shale G32 core sample to different input parameters.

[0058] Note that the sensitivity is a nonlinear function of the perturbations in dtm,∈,γ,δ. In the sensitivity analysis, we present small perturbations to these parameters. For example, in Figure 3A , Figure 4A , Figure 5A , Figure 6A and Figure 7AIn this study, the sensitivity to mud slowness was calculated by perturbing the mud slowness by 5%. On the other hand, in... Figure 3B , Figure 4B , Figure 5B , Figure 6B and Figure 7B In this study, the slowness sensitivity to the Thomson parameter was calculated by perturbing the Thomson parameter by 5%.

[0059] These sensitivity analyses reveal that all four unknowns (i.e., mud slowness, γ, δ, and δ) can have very different effects on the dispersion curve, depending on the specific circumstances. Therefore, these values ​​cannot be ignored in the inversion workflow. In one embodiment, as a general rule, all four parameters are inverted (for the VTI case) and the uncertainty is quantified. Furthermore, since the sensitivity behavior can vary significantly between different models, all available wellbore models are used for inversion to improve its stability.

[0060] Correlation between VTI parameters

[0061] As discussed in the previous section, all anisotropic parameters and mud slowness (i.e., dtm, γ, ∈, δ) need to be treated as unknowns in the inversion. However, even when we use all available dispersion modes from monopole, dipole, and quadrupole emitters, such an inversion can be highly ill-conditioned. To overcome this challenge, we use physical or empirical correlations between the Thomson parameters and other known parameters to constrain and stabilize our inversion. For example, Figure 8A The correlation between ∈ and γ was plotted using all the core data in Table 1. Figure 8B The correlation between ∈ and δ was plotted. We can see from... Figure 8A Figure 8 shows the empirical bounds for 0.5γ < ∈ < 2γ, and Figure 9 shows the empirical bounds for δ < ∈. These bounds can be used for stability inversion. Furthermore, these bounds can be updated during the inversion process. For example, Figure 9 The core data listed in Table 1 are plotted, and we can see that these data can be divided into two groups: one group is ∈>γ, and the other group is ∈<γ. This new relationship can be obtained during the inversion process using a data-driven approach, which will be discussed in the next section.

[0062] Methods for inverting Thomson parameters and mud slowness using Stoneley scattering, dipole scattering, and / or pseudo-Rayleigh scattering

[0063] This section outlines an inversion method for VTI formations, where the theoretical dispersion can be written as:

[0064]

[0065] There are 11 input parameters a, ρb , ρ m dtc, dts, dtm, ∈, γ, δ, well_devi, and tool_azim represent the wellbore radius, formation density, mud density, formation compression and shear vertical slowness, mud slowness, Thomson parameters (∈, γ, δ), well inclination, and tool azimuth direction in the well, respectively. The superscript "mode" represents different modes, such as Stoneley (ST), Dipole Curvature (FL), Pseudo Rayleigh (PR), or Quadrupole (QD).

[0066] If multi-mode acquisition is available in the tool, the theoretical dispersion can be combined as follows:

[0067]

[0068] The inversion process can be accomplished by matching the theoretical dispersion with the measured dispersion. The matching process is done by uniformly or randomly sampling the unknown parameters within a given range. Based on the above discussion of physical or empirical correlations, we can define the ranges of ∈ and δ as...

[0069] k min γ < ∈ < k max γ (3),

[0070] l min ∈<δ<l max ∈. (4)

[0071] These two conditions help us narrow down the search range during the matching process, thereby improving performance and stability. Finally, the mismatch between the measured dispersion and the theoretical dispersion can be calculated as follows:

[0072] E = ||D theory -D measured || (5)

[0073] The inversion workflow consists of several steps. Figure 10 For example, in the first step, the inversion is run by minimizing Equation 5, where minimization can be achieved by random search or grid search on the initial guess of dtm and the initial ranges of ∈, γ, and δ constrained by Equations 3 and 4.

[0074] Next, based on the fact that the mud slowness gradually changes over two consecutive logging depths (e.g., 0.5 feet, which is commonly used in industry), after the first step, linear regression, nonlinear regression, or visual methods can be used to optimize the mud slowness as a linear, multilinear, or nonlinear profile over the logging depth. The mud slowness depth profile can be correlated with the uncertainty obtained from the regression method.

[0075] Then, the inversion can be run again as a second step, where the range of dtm is narrowed using the regression profile from the first step, with or without uncertainty. Because dtm now has a narrower range or a single value, the inverted Thomson parameters can be more stable than in the first step. Therefore, linear regression, nonlinear regression, or visual estimation is applied to optimize the range between ∈, γ, and δ in the formats of Equations 3 and 4. The regression can give k min k max , l min , and l max The new reduced range.

[0076] Finally, as the third step, we use the newly regressed k min ,k max ,l min , and l max The range is then inverted again to obtain the final result of the Thomson parameters, which may or may not have uncertainty.

[0077] It is important to note that physical or empirical constraints, such as Equations 3 and 4, can be directly extended to incorporate more correlations with other known (e.g., other rock physics inputs) or unknown parameters based on data availability. Furthermore, theoretical and measurement data can be extended to add other patterns, such as casing dispersion and tool bending patterns in logging-while-drilling or cased-well logging scenarios.

[0078] Illustrative example

[0079] Comprehensive Situation Test #1

[0080] Figures 11 to 1 4 illustrates a synthetic example of this data-driven, physically constrained inversion method. Figure 11 In this study, data from eight core samples were used to generate synthetic Stoneley and bending dispersions (Track 5). As an illustrative example, a linear mud slowness profile was assumed when generating these synthetic dispersions; however, mud slowness can also be assumed to be nonlinear. Tracks 1 through 4 plot borehole diameter, formation density, compression, and shear slowness, respectively. The calculated mismatch was projected onto the mud slowness axis and plotted in Track 6. Based on the mismatch values, linear mud slowness can be regressed using two parameters of the linear curve: the mud slowness value at the midpoint of the logging interval and the mud slowness depth gradient, such as... Figure 12 As shown, the regressed mud slowness profile matches the true profile very well. However, we can also see that minimizing the Thomson parameter is not well defined in this step. As mentioned earlier, a second inversion using the regressed mud slowness is therefore necessary.

[0081] Comprehensive Situation Test #2

[0082] Figure 13 illustrates how the regression of mud slowness contributes to improving the stability of the VTI parameters. In this case, five core samples are selected as input. These five core samples are taken from the same site, so the correlation between the Thomson parameters can represent a local range. In this case, it is assumed that the mud slowness profile remains constant. Figure 13A The first step of the inversion is shown, from which it can be seen that although there may be mismatch plots for the three Thomson parameters from Dow 7 to Dow 9, their minimum values ​​have a great deal of uncertainty.

[0083] exist Figure 13B In the process, the mud slowness values ​​are stacked to obtain an average value across five depths, and this average value is applied to the second inversion step, such as... Figure 13C As shown. Note that the dashed lines in the track represent uncertainties, which are calculated by finding mismatches less than 1 μS / ft. Since the mud slowness superposition is 196 μS / ft, the Thomson parameter estimate in step 2 now has less uncertainty compared to step 1.

[0084] Figure 14 illustrates how the update correlation between Thomson parameters helps to further stabilize the inversion. Figure 14A The initial correlation between ∈ and γ is shown. The second inversion step is performed in... Figure 14B As shown in channels 1 to 3, the midpoint is the mismatch peak. Figure 14C In the sample, the peaks overlapped at five depths and were then plotted as a cross plot. In this comprehensive test, core samples from the same site were used, allowing for the regression of a new, simplified correlation between ∈ and γ. For example, this localized relationship could be obtained using linear regression, yielding 1.0γ < ∈ < 1.6γ, as shown below. Figure 14C As shown by the dashed line. Finally, in Figure 14D In the third step of the inversion shown in steps 1 to 3, the application is from... Figure 14C The new correlations obtained are 1.0γ < ∈ < 1.6γ. As the correlation ranges for γ and ∈ decrease, the estimates of the Thomson parameters in step 3 now have less uncertainty compared to step 2. Note that the dashed lines represent uncertainty, calculated by finding mismatches less than 1 µS / ft.

[0085] At 1002, monopole and / or dipole and / or quadrupole waveforms are acquired. At 1004, the monopole and / or dipole and / or quadrupole waveforms are processed to obtain Stoneley, bending, quadrupole, and / or pseudo-Rayleigh dispersions. Different methods, such as TKO, SPI, and SDICE, can be used at 1004. TKO is described in "Dispersion Estimation from Borehole Acoustic Arrays Using a Modified Matrix Pencil Algorithm," 29th Asilomar Conf. Signals Systems and Computing, Pacific Grove, CA, October 31, 1995, Ekstrom, ME. At 1005, calculations can be performed or libraries can be used to interpolate the theoretical Stoneley, bending, quadrupole, and / or pseudo-Rayleigh dispersions. At 1006, using the data from 1004 and 1005, the method continues to perform initial estimates of the mud slowness range and initial estimates of the Thomson parameter correlation. At 1008, the method continues to calculate the mismatch between theoretical and measured dispersion. In 1008, the value DTmud can be estimated as a vertical depth profile by minimizing the mismatch between theoretical and measured dispersion. At 1010, a second calculation of the mismatch between theoretical and measured dispersion is performed using the DTmud vertical depth profile. In 1010, the Thomson parameter can be estimated by minimizing the mismatch calculated in step 1010. At 1012, the Thomson parameter is calculated at multiple depths using regression. The Thomson parameter values ​​can be updated from the regression. At 1014, the mismatch between theoretical and measured dispersion is calculated using the regression parameters obtained in 1012. At 1014, the Thomson parameter can be estimated by minimizing the mismatch to a final logging result with uncertainty.

[0086] Example embodiments are now disclosed. These example embodiments should not be considered limiting. In one non-limiting embodiment, a method is disclosed. The method may include obtaining a waveform and processing the obtained waveform to obtain at least one of Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersions. The method may also include performing at least one of calculations of interpolated theoretical dispersions of Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersions and obtaining library calculations. The method may also include performing an initial estimate of mud slowness using the processing of the obtained waveform and the interpolation of the theoretical dispersions, and calculating a mismatch between the processed waveform obtaining at least one Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersion and the theoretical dispersion of Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersion. The method may also include estimating at least one DTMud value as a vertical depth profile and using the at least one estimated DTMud value to calculate a second mismatch between the theoretical dispersion and the processed waveform. The method may also include calculating at least one parameter at multiple depths by minimizing the second mismatch and estimating at least one parameter using regression. The method may further include updating the value of at least one parameter based on regression, and calculating a third mismatch between theoretical dispersion and measured dispersion based on the updated value of the at least one parameter based on regression. The method may also include estimating the final value of at least one parameter by minimizing the mismatch between theoretical dispersion and measured dispersion.

[0087] In another example embodiment, the method can be performed where the waveform is generated by a wellbore acoustic device.

[0088] In another exemplary embodiment, the method may be performed, wherein the waveform is at least one of a unipolar, a dipole, and a quadrupole waveform.

[0089] In another exemplary embodiment, the method may be performed in which the obtained waveform is processed to obtain at least one of Stoneley, bending, quadrupole, and pseudo Rayleigh dispersion, using one of the TKO, SPI, and SDICE methods.

[0090] In another example embodiment, the method can be performed in which the DTmud value is estimated by minimizing the mismatch between the theoretical dispersion and the measured dispersion.

[0091] In another example embodiment, the method can be performed where at least one parameter of the second mismatch estimate is a Thomson parameter.

[0092] In another example embodiment, the method can be performed, where the Thomson parameter is three Thomson parameters.

[0093] In another example embodiment, the method can be performed where the final value is the Thomson parameter.

[0094] In another example embodiment, a method may be performed. The method may include obtaining a waveform from an acoustic wellbore device in the formation. The method may also include processing the waveform obtained from the acoustic wellbore device to obtain at least one value for Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersions. The method may further include performing calculations to generate theoretical dispersions of the Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersions of the waveform. The method may also include performing an initial estimate of mud slowness using the processed and theoretical dispersions of the obtained waveform. The method may also include calculating a first mismatch between the processed waveform, which yields at least one Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersion, and the theoretical dispersions of the Stoneley, bending, quadrupole, and pseudo-Rayleigh dispersions. The method may further include estimating at least one DTmud value as a vertical depth profile and using at least one estimated DTmud value to calculate a second mismatch between the theoretical dispersion and the processed waveform. The method may also calculate at least one modified Thomson parameter at multiple depths by minimizing the second mismatch and estimating at least one Thomson parameter of the formation using regression. The method may further include calculating a third mismatch between the theoretical dispersion and the measured dispersion based on updated values ​​of regression-based Thomson parameters. The method may also include estimating the final value of at least one Thomson parameter by minimizing the mismatch between the theoretical and measured dispersions.

[0095] In another exemplary embodiment, the method may be implemented where the formation is anisotropic.

[0096] In another exemplary embodiment, the method may be performed, wherein the waveform is at least one of a unipolar, a dipole, and a quadrupole waveform.

[0097] In another exemplary embodiment, the method may be performed in which the obtained waveform is processed to obtain at least one of Stoneley, bending, quadrupole, and pseudo Rayleigh dispersion, using one of the TKO, SPI, and SDICE methods.

[0098] In another example embodiment, the method can be performed in which the DTmud value is estimated by minimizing the mismatch between the theoretical dispersion and the measured dispersion.

[0099] In another exemplary embodiment, the method may be performed where the Thomson value is three values.

[0100] The foregoing description of embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or limiting of this disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but are interchangeable and may be used in selected embodiments where applicable, even if not specifically shown or described. Similarly, many different ways are possible. Such variations should not be considered as departing from this disclosure, and all such modifications are intended to be included within the scope of this disclosure.

Claims

1. A method for inverting formation anisotropy constants using sonic data, comprising: obtaining waveforms from a borehole sonic device in a formation; processing the obtained waveforms to obtain at least one of a Stoneley, a Bending, a Quadrupole, and a Pseudo-Rayleigh dispersion; performing at least one of a calculation and obtaining a library calculation of an interpolated theoretical dispersion for the Stoneley, the Bending, the Quadrupole, and the Pseudo-Rayleigh dispersion; performing an initial estimate of a mud slowness using the processing of the obtained waveforms and the interpolated theoretical dispersion; calculating a first misfit between the processed waveforms obtained for at least one of the Stoneley, the Bending, the Quadrupole, and the Pseudo-Rayleigh dispersion and the theoretical dispersion for the Stoneley, the Bending, the Quadrupole, and the Pseudo-Rayleigh dispersion; estimating at least one DTmud value by minimizing the misfit between the theoretical dispersion and the measured dispersion, the at least one DTmud value estimated as a vertical depth profile of the mud slowness; calculating a second misfit between the theoretical dispersion and the processed waveforms using the at least one estimated DTmud value; estimating at least one anisotropy parameter by minimizing the second misfit; calculating the at least one anisotropy parameter over a plurality of depths using regression; updating a value of the at least one anisotropy parameter based on the regression; calculating a third misfit between the theoretical dispersion and the measured dispersion based on the updated value of the at least one anisotropy parameter based on the regression; and estimating a final value of the at least one anisotropy parameter by minimizing the misfit between the theoretical dispersion and the measured dispersion, the final value used to establish a more accurate geomechanical model for geomechanical analysis.

2. The method of claim 1, wherein, the waveforms are at least one of monopole, dipole, and quadrupole waveforms.

3. The method of claim 1, wherein, the processing of the obtained waveforms to obtain at least one of a Stoneley, a Bending, a Quadrupole, and a Pseudo-Rayleigh dispersion uses one of a TKO, a SPI, and a SDICE method.

4. The method of claim 1, wherein, the at least one anisotropy parameter estimated by minimizing the second misfit is a Thomsen parameter.

5. The method of claim 4, wherein, the Thomsen parameter is three Thomsen parameters.

6. The method of claim 1, wherein, the final value is a Thomsen parameter.

7. A method for inverting formation anisotropy constants using sonic data, comprising: obtaining waveforms from a sonic borehole device in a formation; processing the waveforms obtained from the sonic borehole device to obtain at least one value of a Stoneley, a Bending, a Quadrupole, and a Pseudo-Rayleigh dispersion; performing a calculation to produce a theoretical dispersion of the Stoneley, the Bending, the Quadrupole, and the Pseudo-Rayleigh dispersion of the waveforms; performing an initial estimate of a mud slowness using the processing of the obtained waveforms and the theoretical dispersion; calculating a first misfit between the processed waveforms obtained for at least one of the Stoneley, the Bending, the Quadrupole, and the Pseudo-Rayleigh dispersion and the theoretical dispersion for the Stoneley, the Bending, the Quadrupole, and the Pseudo-Rayleigh dispersion; estimating DTmud values by minimizing the misfit between the theoretical dispersion and the measured dispersion, the at least one DTmud value estimated as a vertical depth profile of the mud slowness; calculating a second misfit between the theoretical dispersion and the processed waveforms using the at least one estimated DTmud value; estimating at least one Thomsen parameter of the formation by minimizing the second misfit; calculating the at least one corrected Thomsen parameter over a plurality of depths using regression; calculating a third misfit between the theoretical dispersion and the measured dispersion based on the updated value of the Thomsen parameter based on the regression; and The final values of the at least one Thomson parameter are estimated by minimizing the mismatch between the theoretical dispersion and the measured dispersion, a more accurate geomechanical model is built using the final values, for geomechanical analysis.

8. The method of claim 7, wherein, The waveforms are at least one of monopole, dipole and quadrupole waveforms.

9. The method of claim 7, wherein, The processing of the obtained waveforms to obtain at least one of Stoneley, Bending, Quadrupole and Pseudo-Rayleigh dispersion uses one of TKO, SPI and SDICE methods.

10. The method of claim 7, wherein, The values of the Thomson parameters are three values.

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