Patent Application
20200088895
The present disclosure generally relates to anisotropy parameter determination and, more particularly, to generating high fidelity velocity models for acoustic vertically transverse isotropic media by taking advantage of full-waveform inversion based modeling using vertical seismic profile data.
Certain earth formations exhibit a property called “anisotropy”, where the velocity of acoustic waves polarized in one direction may be somewhat different than the velocity of acoustic waves polarized in a different direction within the same earth formation. Anisotropy may arise from intrinsic structural properties, such as grain alignment, crystallization, aligned fractures, or from unequal stresses within the formation. Anisotropy is particularly of interest in the measurement of the velocity of seismic P-waves propagating in the earth formations. Subsurface formations are often anisotropic, meaning that the acoustic wave propagation speed depends on the direction in which the wave propagates. Typically, the formations, even when anisotropic, are relatively isotropic in the horizontal plane. This particular version of anisotropy is often called vertical transverse isotropic (“VTI”). Accurate seismic imaging requires that such anisotropy be accounted for during the migration portion of seismic data processing. VTI based models represent the conventional approach for anisotropic depth imaging in many areas, and prior knowledge of a vertical velocity (Vp0) and two anisotropy Thomsen parameters ε and δ is essential to produce accurate depth image of P-wave seismic data. It may be noted here that alternative combinations of these parameters can also be used for creation of such depth images and hence Vp0, ϵ, and δ may be substituted by other parameters obtained by reformulation of the definitions of these parameters.
Over the past several decades, seismic processing has gradually developed to allow for estimation of anisotropy parameters from seismic data. One such method is vertical seismic profile (“VSP”) approach. However, conventional VSP processing methods like semblance or ray-based tomography do not exploit the full-data information and, hence, generate sub-optimal velocity models. The failure to exploit all the data is because semblance and tomography methods only utilize the kinematic information and ignore the dynamic (amplitude) information in the seismic data. This results in poor recovery of subsurface parameters which affects the reservoir characterization, modeling and, ultimately, production.
Various embodiments of the present disclosure will be understood more fully from the detailed description given below and from the accompanying drawings of various embodiments of the disclosure. In the drawings, like reference numbers may indicate identical or functionally similar elements.
Illustrative embodiments and related methods of the present disclosure are described below as they might be employed in methods and systems for generating velocity models of a subsurface formation using pseudo-acoustic formulations. In the interest of clarity, not all features of an actual implementation or method are described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure. Further aspects and advantages of the various embodiments and related methods of the disclosure will become apparent from consideration of the following description and drawings.
As described herein, illustrative embodiments and methods of the present disclosure are applied to generate high fidelity velocity models for acoustic VTI media by taking advantage of full-waveform based modeling using VSP data. The present disclosure provides a new approach to determine VTI parameters in acoustic media using a simplifying approximation for the elastic wave equation. Specifically, the illustrative methods described herein use pseudo-acoustic equations which eliminate or substantially eliminate the contribution from shear waves, and thus significantly reducing the time needed to perform inversion. Thus, the methods disclosed herein provide workflows for performing full waveform inversion, including direct P wave and reflected P wave arrivals, to provide velocity models used to generate seismic images with high quality and resolution.
In a generalized method of the present disclosure, a velocity model of a subsurface formation is generated by obtaining VSP field data, and a trial velocity model of a subsurface formation is generated. A pseudo-acoustic wave equation is applied to the trial velocity model to generate a synthetic dataset which matches an acquisition geometry of the VSP field data. Thereafter, a final velocity model is generated using the synthetic dataset. The final velocity model may then be used to produce superior images of the subsurface formation which can be used in a variety of downhole operations such as, for example, formation interpretation and monitoring producing reservoirs.
Borehole seismic surveys have the capability to record high frequency data in a low noise environment. The surveys can resolve thin layering and poorly imaged areas, such as subsalt imaging, better than surface seismic surveys. Conventional velocity model generation methods for VSP methods like semblance or ray-based tomography, for example, fail to provide high fidelity images or recover accurate subsurface parameters.
Therefore, as described herein, illustrative embodiments and methods of the present disclosure perform full-waveform modeling in order to ensure use of the all information contained in the subsurface data. Full-waveform inversion (“FWI”) is a non-linear data-fitting technique which generates high-resolution velocity models of the subsurface. FWI uses a nonlinear gradient based local optimization approach that iteratively matches the simulated data with raw field data. FWI has been successfully applied to surface seismic data for accurate parameter estimation in complex media. However, the implementation of FWI to walkaway VSP data has been focused on anisotropic elastic and viscoelastic media. The current disclosure applies a simplifying method which simulates the effect of an anisotropic media while not specifically modeling the shear wave data. As such, it is called a “pseudo-acoustic” modeling method. Thus, as used herein, pseudo-acoustic refers to those formulations which eliminate or substantially eliminate shear wave contributions. In certain pseudo-acoustic applications described herein, some weak shear wave artifacts may still be generated in non-elliptical (epsilon not equal to delta) cases. However, in isotropic and elliptical (epsilon equal to delta) cases, there are no shear wave artifacts.
In accordance with embodiments of the present disclosure, computing system 108 may be configured to acquire VSP data associated with the subterranean formation 112 from wellbore receivers 114 via some wired or wireless communications link, generate the velocity models as described herein, and perform estimation of anisotropy parameters of the subterranean formation 112. In one or more embodiments, computing system 108 may be further configured to utilize the calculated anisotropy parameters of subterranean formation 112 to generate depth images and an accurate seismic data volume associated with the subterranean formation 112. For certain embodiments, the obtained depth images and the accurate seismic data volume of subterranean formation 112 obtained by taking into account anisotropy parameters of subterranean formation 112 may be utilized in real time for drilling of wellbore 106. In general, the presented illustrative methods for generating velocity models using pseudo-acoustic modeling may be used to obtain more coherent depth images of hydrocarbon reservoirs in the subterranean formations leading to more efficient drilling of wellbores and increased hydrocarbon production.
In view of the foregoing, the theory underlying the methods herein will now be described. Wave field reconstruction in a transverse isotropic (“TI”) media, which can be either VTI, horizontal TI (“HTI”), or transverse TI (“TTI”), is provided by a system of two second-order coupled equations. If a VTI assumption is imposed and the shear waves are ignored by setting Vs0=0, the pseudo-acoustic wave propagation may be expressed as:
where Vhor=Vnmo√{square root over (1+2η)}=Vp0√{square root over (1+2ϵ)} is the P-wave horizontal velocity. Both the p- and q-components of the wave field contain a P-wave with the correct kinematics and a shear-wave “artifact” caused by setting the S-wave vertical velocity to zero. Thus, Equations 1 and 2 are the pseudo-acoustic equations in this illustrative embodiment.
The matrix form of VTI-coupled equations is:
where upand uq are the p and q forward-propagated wave field variables, and fp and fqare the p and q source terms, respectively. In certain illustrative methods of the present disclosure, the adjoint wave field can be evaluated by computing the adjoint of the above equation:
where ap and aq are the p and q adjoint wavefield variables and dp and dq are the p and q source terms for adjoint equations, respectively.
The adjoint-state method described herein may be applied in a variety of ways. The adjoint-state method provides an efficient way of computing the derivatives of an objective function with respect to the model parameters. In certain illustrative methods, the components of the adjoint-state method are the objective function, state equations, and adjoint equations. The objective function depends on the model parameters obtained using the state equations, which represent the forward-modeling equations used in the pseudo-acoustic formulations, as will be discussed below. The adjoint-state method involves four main steps: (i) computation of the state variables (i.e., forward wave field given by u) by solving the state equations; (ii) computation of the adjoint source functions (d1); (iii) computation of the adjoint-state variable (e.g., adjoint wave field given by λ) by solving the adjoint equations; and (iv) computation of the gradient of the objective function.
Thus, in certain methods, the FWI method can be posed as an optimization problem using the Lagrangian function which may be formulated as:
Λ(m,u, λ)=J−<F, λ>, Eq. 5,
where Λ is the Lagrangian function, m represents the model parameters, u is the state variable, λ is the adjoint variable, J is the objective function, and F is the state equation for the forward-modeled wavefield, and:
2J=(dobs−dpre)TWd(dobs−dpre)+(mi−mprior)TWm(mi −mprior) Eq. 6,
which is the regularization based objective function to be minimized. Equation 6, as presented above, is a measure of error between observed data and predicted synthetic data and is regularized using the second term on the right hand side of the equation involving the model m. Additional regularization is provided by the data weighting matrix Wd. It may be noted here that the objective function J could also take other forms such as a correlation between field data and simulated data. In fact a correlation objective is more useful in case of FWI since correlation places importance on matching the phase of the seismic signal. A correlation-based objective function can be written as:
The function F in Eq. 5 is the state equation for the forward-modeled wave field. The model vector for the problem may be defined as m={Vp0;ϵ; δ}. Alternatively, the model vector can be defined using rearrangements of the model parameters in m. A viable alternative is m={Vp0; Vhor; Vnmo}.
The gradient computation (i.e., sensitivity kernel) may be achieved in a variety of ways. In one illustrative method, the state-variable and adjoint-state variable calculated above in steps (i) and (iii), respectively, serve as inputs to the gradient computation. The sensitivity kernel for a particular model parameter is the response in the model space to the data perturbations for a single source and a single receiver. The sensitivity kernel describes the model areas that can provide updates for a particular receiver location. For our problem, the sensitivity kernel is the zero lag cross-correlation of the source wave field with the adjoint wave field. The data residuals are back-propagated along the “banana-doughnut” kernel to generate the sensitivity kernel.
In view of the foregoing theory, illustrative embodiments and methods of the present disclosure extend acoustic FWI from surface seismic to VSP data for VTI media using the adjoint state method. A primary focus of the adjoint state method is the efficient computation of gradients of an objective function with respect to the model parameters Vp0, ϵ, and δ or alternatively Vp0, Vhor and Vnmo. Vp0 is the P-wave velocity, while ϵ, and δ are the Thomsen parameters. Vhor and Vnmo have been defined earlier in the section on pseudo-acoustic wave equation. To demonstrate the method, synthetic data from a4 layered model is used with a VTI background while applying a reverse VSP geometry.
At block 204, computing system 108 preprocessing the VSP field data. In certain methods, the data, dobs, is prepared by performing functions such as, for example, noise removal, quality control, change of format, 3c rotation, etc. At block 206, an initial (or trial) VTI velocity model, mi, is generated. The initial velocity model may be the first in time model or some intervening iteration before the final velocity model is generated. Thus, “trial” velocity model as used herein could refer to any model except the final velocity model. However, the true first in time velocity model is generated using, for example, well log, surface seismic derived velocities, or zero offset (when the source is located near the well head) VSP velocities. As will be described below, subsequent trial velocity models are iteratively updated using the methods of the present disclosure until a desired convergence is achieved.
At block 208, forward modeling is performed using the pseudo-acoustic forward modeling Equations 1 and 2 described above. As previously stated, the pseudo-acoustic equations described herein eliminate or substantially eliminate contributions from shear waves. Using the pseudo-acoustic forward modeling formations, a set of synthetic data is created using the trial velocity model. In certain illustrative methods, the synthetic dataset matches the acquisition geometry of the field VSP dataset. Here, the equation Lus−f=0 refers to the forward modeling wave equation, and us is the source term which is composed of to both up and uq (from above).
At block 210, computer system 108 extracts synthetic VSP data (i.e., synthetic seismic traces) from the synthetic dataset. In certain methods, the extracted synthetic VSP data dprc matches the geometry of the VSP field data. At block 212, the objective function is calculated using the observed data dobs from block 204 and the predicted data dpre from block is 210. At block 218, computer system 108 first calculates the adjoint sources d1 using, the VSP field data (from block 204) and the synthetic VSP data generated at block 210. Also at block 220, adjoint modeling is used to back propagate the adjoint sources from block 218 using the trial velocity model. The equation LTas−d1=0 refers to the adjoint modeling wave equation where as is the adjoint field which is composed of both αp and αs (from above).
At block 218, the adjoint sources are used as data residuals. At block 214, the trial velocity model is deemed converged if the termination criteria has been met, such as, for example, the number of iterations has been achieved or the minimization error is small enough. Here, computer system compares the synthetic data of the trial velocity model to the VSP field datasets to determine the convergence of the two using the criteria in block 214 (i.e., the objective function of Eq. 6 or Eq. 7 above). If the criteria has been met, the results have converged, and the current trial model is saved as the final model, mf, and the iteration is stopped at block 216. If, however, the criteria of the objective function has not been met, the results have not converged, and (at block 222) computer system 108 performs gradient computations to determine the sensitivity of the results due to small changes in the trial velocity model parameters. The gradient calculations are performed using adjoint modeling of block 220, along with the pseudo-acoustic forward modeling of block 208. In certain methods, this process includes performing a zero lag correlation computation of the corresponding wave field snap shots, which are summed along the time axis, creating the gradient for each model parameter in the grid.
At block 224, computer system 108 alters the step length a which controls the amount of correction or adjustment to each model parameter as the trial model converges to the true model (for which the VSP field data and the modeled data also converge). At block 226, the initial/trial model is updated accordingly using the step length along the gradient direction. The equation mi+1=mi−αG refers to the model updating equation for each iteration, i, where m is the model parameter, alpha is the step length, and G is the gradient. Thus, blocks 224 and 226 achieves the FWI. The method then loops back to block 208, where the forward modeling on the previous model generates the predicted data and initial/trial model is iteratively updated until the desired convergence is achieved. Once the final VTI velocity model has been generated, any variety of downhole operations may be conducted accordingly, including drilling of a wellbore.
Methods of the present disclosure were tested on a four-layered VTI model, as the one illustrated in
The bus 708 collectively represents all system, peripheral, and chipset buses that communicatively connect the numerous internal devices of the computing system 700. For instance, the bus 708 communicatively connects the processing unit(s) 712 with the ROM 710, the system memory 704, and the permanent storage device 702. From these various memory units, the processing unit(s) 712 retrieves instructions to execute and data to process in order to execute the processes of the subject disclosure. The processing unit(s) can be a single processor or a multi-core processor in different implementations.
In this example, ROM 710 stores static data and instructions that are needed by the processing unit(s) 712 and other modules of the computing system 700. The permanent storage device 702, on the other hand, is a read-and-write memory device. This device is a non-volatile memory unit that stores instructions and data even when the computing system 700 is off. Some implementations of the subject disclosure use a mass-storage device (such is as a magnetic or optical disk and its corresponding disk drive) as the permanent storage device 702.
The bus 708 also connects to the input and output device interfaces 714 and 706. The input device interface 714 enables the user to communicate information and select commands to the computing system 700. Input devices used with the input device interface 714 include, for example, alphanumeric, QWERTY, or T9 keyboards, microphones, and pointing devices (also called “cursor control devices”). The output device interfaces 706 enables, for example, the display of images generated by the computing system 700. Output devices used with the output device interface 706 include, for example, printers and display devices, such as cathode ray tubes (CRT) or liquid crystal displays (LCD). Some implementations include devices such as a touchscreen that functions as both input and output devices.
Also, as shown in
Accordingly, the embodiments and methods described herein provide high resolution velocity models for vertically transverse isotropic media and subsequently generate better focused subsurface images in contrast to conventional techniques. This disclosure provides a new tool to determine the anisotropic parameters of the acoustic VTI media and subsequently characterize the reservoir. In case of thin layering or poorly illuminated areas like subsalt, where surface seismic data fails to provide satisfactory velocity models, these methods can calibrate surface seismic data.
Moreover, methods described herein apply pseudo-acoustic wave formulations which allow for much faster computation and convergence in comparison to conventional approaches. Also, use of the objective functions described herein, which has fewer local minima when compared to conventional approaches, provide a more accurate update giving a faster convergence. In addition, the use of the adjoint state method allows methods of the disclosure to compute the entire gradient in only two modeling iterations.
Embodiments described herein further relate to any one or more of the following paragraphs:
1. A method for generating a velocity model of a subsurface formation, the method comprising obtaining vertical seismic profile (“VSP”) field data; generating a trial velocity model of a subsurface formation; applying a pseudo-acoustic wave equation to the trial velocity model to thereby generate a synthetic dataset which matches an acquisition geometry of the VSP field data; and generating a final velocity model using the synthetic dataset.
2. A method as defined in paragraph 1, wherein the trial and final velocity models are vertical transverse isotropic (“VTI”) models.
3. A method as defined in paragraphs 1 or 2, wherein generating the final velocity model comprises extracting synthetic VSP data from the synthetic dataset, wherein the synthetic VSP data matches the acquisition geometry of the VSP field data; comparing the synthetic VSP data to the VSP field data; and converging the synthetic VSP data and the VSP field data, thereby generating the final velocity model.
4. A method as defined in any of paragraphs 1-3, wherein the synthetic VSP data and the VSP field data are compared using an objective function.
5. A method as defined in any of paragraphs 1-4, wherein the objective function can be a correlation based objective function or a regularization based objective function.
6. A method as defined in any of paragraphs 1-5, wherein converging the synthetic VSP data and the VSP field data comprise performing gradient computations on the trial velocity model.
7. A method as defined in any of paragraphs 1-6, further comprising updating the trial velocity model using an adjoint modeling technique.
8. A method as defined in any of paragraphs 1-7, wherein the adjoint modeling technique is applied to back propagate adjoint sources into the trial velocity model.
9. A method as defined in any of paragraphs 1-8, wherein the first velocity model is updated using a full waveform inversion (“FWI”) technique.
10. A method as defined in any of paragraphs 1-9, wherein the trial velocity model is generated using at least one of well log data, surface seismic derived velocity data, and zero offset VSP velocity data.
11. A method as defined in any of paragraphs 1-10, wherein one or more seismic sources generate acoustic waves which travel through the subsurface formation and reflect off geological features contained therein; one or more receivers are positioned adjacent the subsurface formation to collect the reflected acoustic waves and thereby generate the VSP field data which is communicated to a processor; and the processor is used to obtain the VSP is field data.
12. A system for generating a velocity model of a subsurface formation, the system comprising at least one processor; and a memory coupled to the processor having instructions stored therein, which when executed by the processor, cause the processor to perform operations comprising: obtaining vertical seismic profile (“VSP”) field data; generating a trial velocity model of a subsurface formation; applying a pseudo-acoustic wave equation to the trial velocity model to thereby generate a synthetic dataset which matches an acquisition geometry of the VSP field data; and generating a final velocity model using the synthetic dataset.
13. A system as defined in paragraph 12, wherein the trial and final velocity models are vertical transverse isotropic (“VTI”) models.
14. A system as defined in paragraphs 12 or 13, wherein generating the final velocity model comprises extracting synthetic VSP data from the synthetic dataset, wherein the synthetic VSP data matches the acquisition geometry of the VSP field data; comparing the synthetic VSP data to the VSP field data; and converging the synthetic VSP data and the VSP field data, thereby generating the final velocity model.
15. A system as defined in any of paragraphs 12-14, wherein the synthetic VSP data and the VSP field data are compared using an objective function.
16. A system as defined in any of paragraphs 12-15, wherein converging the synthetic VSP data and the VSP field data comprise performing gradient computations on the trial velocity model.
17. A system as defined in any of paragraphs 12-16, further comprising updating the trial velocity model using an adjoint modeling technique.
18. A system as defined in any of paragraphs 12-17, wherein the adjoint modeling technique is applied to back propagate adjoint sources into the trial velocity model.
19. A system as defined in any of paragraphs 12-18, wherein the first velocity model is updated using a full waveform inversion (“FWI”) technique.
20. A system as defined in any of paragraphs 12-19, wherein the trial velocity model is generated using at least one of well log data, surface seismic derived velocity data, and zero offset VSP velocity data.
21. A system as defined in any of paragraphs 12-20, comprising one or more seismic sources to generate acoustic waves which travel through the subsurface formation and reflect off geological features contained therein; and one or more receivers positioned adjacent the subsurface formation to collect the reflected acoustic waves and thereby generate the VSP field data which is communicated to the processor.
Furthermore, any the illustrative methods described herein may be implemented by a system comprising processing circuitry or a non-transitory computer readable medium comprising instructions which, when executed by at least one processor, causes the processor to perform any of the methods described herein.
Although various embodiments and methods have been shown and described, the disclosure is not limited to such embodiments and methods and will be understood to include all modifications and variations as would be apparent to one skilled in the art. Therefore, it should be understood that the disclosure is not intended to be limited to the particular forms disclosed. Rather, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the disclosure as defined by the appended claims.
The present application is a Patent Cooperation Treaty Application of U.S. National Stage Provisional Patent Application No. 62/377,235, filed on Aug. 19, 2016, the benefit of which is claimed and the disclosure of which is incorporated herein by reference in its entirety.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US2017/047428 | 8/17/2017 | WO | 00 |
| Number | Date | Country | |
|---|---|---|---|
| 62377235 | Aug 2016 | US |
