WO2015124960A1

WO2015124960A1 - Systems and methods for improved inversion analysis of seismic data

Info

Publication number: WO2015124960A1
Application number: PCT/IB2014/003134
Authority: WO
Inventors: Nuno VIEIRA DA SILVA; Andrew Ratcliffe; Vetle Vinje
Original assignee: Cgg Services Sa
Priority date: 2014-02-21
Filing date: 2014-12-19
Publication date: 2015-08-27

Abstract

A method and system for improved analysis of seismic data is provided. The method includes obtaining a recorded seismic data set, generating a synthetic seismic data set using a model of a subsurface, and computing a misfit between the recorded seismic data set and the synthetic seismic data set. The method further includes updating the model of the subsurface to reduce the misfit by modifying a selected pair of parameters. The selected pair of parameters is based on analyzing a first degree of orthogonality of a first pair of parameters, analyzing a second degree of orthogonality of a second pair of parameters, and based on the first degree of orthogonality or the second degree of orthogonality being greater, selecting the first pair of parameters or the second pair of parameters

Description

SYSTEMS AND METHODS FOR

IMPROVED INVERSION ANALYSIS OF SEISMIC DATA

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit under 35 U.S.C. § 119(e) of United States Provisional Application Serial No. 61/942,701 filed on February 21, 2014, which is incorporated by reference in its entirety for all purposes.

TECHNICAL FIELD

[0002] The present disclosure relates generally to seismic exploration and, more particularly, to improved inversion analysis of seismic data.

BACKGROUND

[0003] Seismic surveying or seismic exploration, whether on land or at sea, is accomplished by generating a seismic energy signal that propagates into the earth. Propagating seismic energy is partially reflected, refracted, diffracted and otherwise affected by one or more geologic structures within the earth, for example, by interfaces, also referred to as reflectors, between underground formations having varying acoustic impedances and velocities, and other elastic properties.

[0004] Various sources of seismic energy are used to impart the seismic waves into the earth. The seismic signal is emitted from the source in the form of a wave that is reflected off interfaces between geological layers. The reflected waves are received by an array of seismic detectors, or "receivers," placed at or near the earth's surface, in a body of water, downhole in a wellbore, or on a sea floor, which convert the displacement of the ground resulting from the propagation of the waves into an electrical signal recorded by means of a computing system. The resulting signals are recorded and processed to generate information relating to the physical properties of subsurface formations.

[0005] Receivers may be arranged in a cable-based receiver network or array where receivers are connected to each other via a cable ("strings"), or a wireless system. The distance, or offset, between a particular source and receiver is measured and stored to enable the measurement of the time required for a signal to travel to a particular receiver. The receivers typically receive data during the source's energy emission and during a subsequent "listening" interval. Data received by the receivers is transmitted to a computing system. The computing system records the time at which each reflected wave is received. The travel- time from source to receiver, along with the velocity of the source wave, can be used to reconstruct the path of the waves to create an image of the subsurface. Travel-time is considered to be the time necessary for an emitted wave to travel from the source to a reflector and back to a receiver.

[0006] A large amount of data may be recorded by the computing system and the recorded signals may be subjected to signal processing before the data is ready for interpretation. The recorded seismic data may be processed to yield information relating to the location of the subsurface reflectors and the physical properties of the subsurface formations. That information is then used to generate an image of the subsurface.

[0007] During seismic data processing, models may be used to enhance the subsurface image. Simulations are performed to create models of the subsurface. Simulations involve estimating physical parameters of the subsurface and generating synthetic data that approximates the recorded data that is recorded by receivers during a seismic survey. The misfit, or difference, between the synthetic data and the recorded data can be determined. For example, velocity models are commonly generated to characterize the discontinuous velocities across interfaces. The velocity of waves changes at each subsurface interface. Recorded seismic data may be compared to synthetic seismic data generated based on a synthetic velocity model to determine the misfit. The model may then be iteratively updated to minimize the misfit.

[0008] To generate accurate models, physical parameters that characterize the subsurface are estimated and used to create the models. Thus, accurate estimates of subsurface physical parameters can improve the models. Examples of physical parameters that characterize the subsurface include v (P-wave velocity), δ and ε (Thomsen's parameters, also referred to as "anisotropic parameters"), dipl and dip2 (deviations relative to the plane perpendicular to the symmetry axis), and p (mass density). Thomsen parameters are dimensionless combinations of elastic moduli that characterize transversely isotropic materials. Transversely isotropic materials have physical properties that are the same about an axis that is normal to the plane of symmetry. For example, vertical transverse isotropic (VTI) media is characterized by generally horizontal subsurface layers. However, because the subsurface is anisotropic, or has different physical characteristics (for example, seismic wave velocity) in different directions, the physical parameters used in modeling may vary and be difficult to estimate or characterize.

[0009] Full waveform inversion (FWI) is a technique to generate high resolution models and is used to analyze seismic data and minimize the misfit between recorded data and synthetic data. An inverse method is generally a method for determining the values of physical properties by comparing measurements with predictions obtained from the physical properties. FWI is based on the premise that a model describing the subsurface, for example, velocity, density, and anisotropy, can be obtained by minimizing the difference (misfit) between data generated by seismic sources and receivers and the synthetic data generated using the same source and receiver locations and producing the data with computers. Equations are utilized to simulate the propagation of waves in the subsurface to generate the synthetic data. Based on the equations, a model is assumed and synthetic data is generated based on what the receivers should record.

[0010] FWI is an iterative process where physical parameters of the subsurface are adjusted at each iteration to progressively get better agreement between the simulation and the recorded data, or in other words, progressively minimize the misfit. However, when updating physical parameters to generate a more accurate model, a trade-off exists related to the dependence or correlation of the different physical parameters. For example, when estimating v, δ, and ε in a combined updating process— updating parameters concurrently— an update to one parameter affects a different parameter. This trade-off is referred to as "cross-talk" and relates to the lack of orthogonality between the physical parameters. Orthogonality is the mathematical relation that describes non-overlapping, uncorrelated, or independent parameters.

[0011] In part to minimize cross-talk, some FWI algorithms update for vertical velocity only, keeping the anisotropic parameters fixed during the calculations. An advantage of such an approach is mitigating the sensitivity of the data to the different parameters. Nonetheless, keeping the anisotropic parameters fixed imposes a constraint on the update model and fails to represent the kinematics of all the waves, potentially leading to a less accurate solution. [0012] Further, FWI is difficult to perform, in part, because of the large quantities of data that must be simulated and the large amount of processing required to achieve a final model. Noise and artifacts in the seismic data further complicate the analysis. Cross-talk additionally complicates the analysis and may require significantly more iterations of the model to achieve a useful approximation of the recorded data or may result in a bias in the final result.

[0013] Additionally, some seismic processing steps experience difficulty when processing data with abrupt velocity variations. Smoothing of the seismic data is often required. In conventional smoothing (such as root-mean-square (RMS) smoothing), a side effect is that signals in the smoothed model are shifted in comparison to the unsmoothed model at velocity changes, or in other words, the travel-times between sources and receivers are not maintained. Preserved Travel-time Smoothing (PTS) discussed in Vetle Vinje et al., Preserved-Traveltime Smoothing, Geophysical Prospecting 61 (Suppl. 1), 380-90 (2013) incorporated in material part herein by reference, introduces an algorithm that preserves travel-times at velocity discontinuities. PTS generates kinematically equivalent velocity models, meaning that travel-time parameters are equivalent in both the smoothed and unsmoothed models. Kinematically equivalent media is discussed in Alexey Stovas, Kinematically Equivalent Velocity Distributions, Geophysics 73 No. 5, VE369-75 (2008) incorporated in material part herein by reference. Using PTS, the travel-time parameters for the depth interval from depth 0 to z, where z is a reflector (or interface) depth, are computed from velocity moments, m.\, m\, and m^. The velocity moments for VTI media are integrals from 0 to z as follows:

where ν(ζ') is the vertical velocity profile as a function of depth z ', and δ( ') and ε(ζ ') are the profiles for the Thomsen's parameters. In the smoothing method of Vinje et al., the following composite parameters of the PTS model are selected to be smoothed to preserve (i.e., not change) the velocity moments:

n_x {z) = i?(z) [l + 25(z)]

n₃(z) = v³(z) [l + 25(z)][l + 8ε(ζ) - 65(z)]

[0014] Seismic modeling that minimizes parameter cross-talk, accurately reflects the parameters that characterize the subsurface formation and minimizes the misfit between the simulated data and the recorded data would be useful.

SUMMARY

[0015] In accordance with some embodiments of the present disclosure, a method for improved analysis of seismic data is provided. The method includes obtaining a recorded seismic data set, generating a synthetic seismic data set using a model of a subsurface, and computing a misfit between the recorded seismic data set and the synthetic seismic data set. The method further includes updating the model of the subsurface to reduce the misfit by modifying a selected pair of parameters. The selected pair of parameters is based on analyzing a first degree of orthogonality of a first pair of parameters, analyzing a second degree of orthogonality of a second pair of parameters, and based on the first degree of orthogonality or the second degree of orthogonality being greater, selecting the first pair of parameters or the second pair of parameters.

[0016] In accordance with another embodiment of the present disclosure, a seismic processing system includes a computing system. The computing system is configured to configured to obtain a recorded seismic data set, generate a synthetic seismic data set using a model of a subsurface, and compute a misfit between the recorded seismic data set and the synthetic seismic data set. The computing system is further configured to update the model of the subsurface to reduce the misfit by modifying a selected pair of parameters. The selected pair of parameters is based on analyzing a first degree of orthogonality of a first pair of parameters, analyzing a second degree of orthogonality of a second pair of parameters, and based on the first degree of orthogonality or the second degree of orthogonality being greater, selecting the first pair of parameters or the second pair of parameters.

[0017] In accordance with another embodiment of the present disclosure, a non -transitory computer-readable medium includes instructions that, when executed by a processor, cause the processor to obtain a recorded seismic data set, generate a synthetic seismic data set using a model of a subsurface, and compute a misfit between the recorded seismic data set and the synthetic seismic data set. The processor is further caused to update the model of the subsurface to reduce the misfit by modifying a selected pair of parameters. The selected pair of parameters is based on analyzing a first degree of orthogonality of a first pair of parameters, analyzing a second degree of orthogonality of a second pair of parameters, and based on the first degree of orthogonality or the second degree of orthogonality being greater, selecting the first pair of parameters or the second pair of parameters.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] For a more complete understanding of the present disclosure and its features and advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which:

[0019] FIGURE 1 illustrates a test system used to generate synthetic data to illustrate the degree of orthogonality of physical parameters of the subsurface in accordance with some embodiments of the present disclosure;

[0020] FIGURES 2A-2E illustrate plots of travel-time misfit ranges as a function of pairs of parameters in accordance with some embodiments of the present disclosure;

[0021] FIGURE 3 A illustrates an exemplary synthetic velocity (v) model used to generate synthetic data in accordance with some embodiments of the present disclosure;

[0022] FIGURES 3B-3D illustrate synthetic velocity (v) models obtained by inverting the synthetic data generated with the model of FIGURE 3 A using different parameterizations built in an inversion algorithm in accordance with some embodiments of the present disclosure;

[0023] FIGURE 4A illustrates an exemplary synthetic epsilon (ε) model used to generate synthetic data in accordance with some embodiments of the present disclosure;

[0024] FIGURES 4B-4D illustrate synthetic epsilon (ε) models obtained by inverting the synthetic data generated with the model of FIGURE 4A using different parameterizations built in an inversion algorithm in accordance with some embodiments of the present disclosure;

[0025] FIGURE 5 illustrates an exemplary step function velocity profile for the velocity models of FIGURES 3A-3D in accordance with some embodiments of the present disclosure;

[0026] FIGURE 6 illustrates an exemplary step function ε profile for the ε models of FIGURES 4A-4D in accordance with some embodiments of the present disclosure;

[0027] FIGURE 7 illustrates a flow chart of an example method for improved inversion analysis for seismic data in accordance with some embodiments of the present disclosure; and

[0028] FIGURE 8 illustrates an elevation view of an example seismic exploration system to acquire seismic data in accordance with some embodiments of the present disclosure. DETAILED DESCRIPTION

[0029] As hydrocarbons are being extracted from increasingly complex settings, sophisticated imaging techniques depend upon a correct estimation of the physical parameters that characterize the subsurface. The estimation of these parameters is important for imaging the subsurface, allowing detection and imaging of reservoirs, and also to quantitatively and qualitatively characterize the fluid content of the rocks of geological formations. However, anisotropy in the subsurface may complicate data processing and imaging because it may produce a more complex wave travelling through the subsurface that requires an estimate of more physical parameters to accurately describe the recorded data. As discussed above, when estimating physical parameters to create models, such as velocity models or anisotropic models, concurrent multi-parameter estimation leads to trade-offs between the parameters. The trade-off is based on cross-talk resulting from non- orthogonality between the parameters being estimated. Multi-parameter estimation increases the ambiguity in the model significantly. In embodiments of the present disclosure, the trade-off between the parameters is mitigated by estimating physical or composite parameters that have a higher degree of orthogonality compared to other parameters. As such, in some embodiments, methods are discussed for determining parameters with a higher degree of orthogonality. Additionally, according to some embodiments, a method is discussed that simulates seismic data using a model, compares the simulated model to the recorded seismic data, and based on the comparison, generates an improved model by improving the match between the simulated and recorded data. The improved model is based on updating parameters that exhibit a higher degree of orthogonality.

[0030] Embodiments of the present invention and its advantages are best understood by referring to FIGURES 1-8 of the drawings, like numerals being used for like and corresponding parts of the various drawings.

[0031 ] FIGURE 1 illustrates test system 100 used to generate synthetic data to illustrate the degree of orthogonality of physical parameters of the subsurface in accordance with some embodiments of the present disclosure. In test system 100, source 104 emits a seismic wave to be reflected from subsurface interface 106 and recorded by receiver 102. Interface 106 may be set at any suitable distance below surface 108. For example, interface 106 may be located at a distance of approximately one kilometer below surface 108. Offset 110 between source 104 and receiver 102, which is used to calculate travel times, can vary in the generation of synthetic data. For example, offset 110 used to generate plots shown in FIGURES 2A-2E (discussed below) ranged from approximately zero meters (for example, source 104 and receiver 102 at the same location) to approximately five kilometers. Further, the velocity (v), δ, and ε may be specified. For the current example, v is specified at approximately 2,000 meters per second (m/s), δ is set at approximately 0.12, and ε is set at approximately 0.15. In addition to v, δ, and ε, any other appropriate parameter of the subsurface may be specified and analyzed in accordance with embodiments of the present disclosure. For example, anelliptic velocity (V_ane), vertical slowness (Vy¹), and horizontal slowness (VY¹) may also be specified.

[0032] Further, additional composite parameters can be derived as functions of physical parameters that characterize the subsurface. Composite parameters may be associated with any suitable algorithm or process. For example, the composite parameter η is referred to as the anelliptic anisotropy parameter and is a function of both δ and ε, η = (ε - δ) / (1 + 2 δ). As another example, composite parameters based on PTS, also referred to as "kinematically consistent parameters" because these composites preserve the kinematic aspects of the model (such as travel-time), may be defined as follows: η__χ = ^ (also referred to as "slowness"); r = 17(1 + 26); and r|₃ = v³(l + 2δ)(1 + 8ε - 6δ).

[0033] In some embodiments, a model can be generated based on the configuration of test system 100 and the selected parameters can be varied (or perturbed) individually to determine the effect of the particular varied parameter on the model. Pairs of parameters can be identified and a travel-time misfit calculation is plotted as a function of the pairs of parameters. The travel-time misfit function is calculated as follows:

N_traces

E_p = ^ (tp-to)²

i-1

where:

t_p = travel-time for the perturbed model; and

to = travel time for the reference model.

[0034] In some embodiments, the degree of orthogonality (or independence) of selected parameters can be determined based on the plots of the travel-time misfit as a function of the pairs of parameters. The travel-time misfit may be segmented into ranges for ease of analysis. Accordingly, in some embodiments, identification of parameters with a high degree of orthogonality may enable seismic model updates that focus on minimization of the misfit between simulated data and recorded data while reducing the effects on the data of cross-talk between parameters.

[0035] FIGURES 2A-2E illustrate plots 200a-200e of travel-time misfit ranges as a function of pairs of parameters in accordance with some embodiments of the present disclosure. To determine the degree of orthogonality (or independence) of selected parameters, travel-time misfit is graphed as a function of pairs of parameters. For each plot, the pairs of parameters were normalized by separately varying a preset value from -4% to +4%. For example, to create plot 200a shown in FIGURE 2A, velocity, v (along the x-axis), was varied from -4% to +4% based on the preset value (vo) of 2,000 m/s, and ε was varied from -4% to +4% based on the preset value (ε₀) of 0.15. Multiple pairs of parameters were simulated and plotted.

[0036] In analysis of plots 200a-200e, the degree of orthogonality can be illustrated by how correlated each approximately elliptical travel-time misfit ranges 202a-202e appear to be with the x-axis and -axis. In addition, the circularity of ranges 202a-202e indicates the relative scaling of a pair of parameters. For example, a more circular shape may indicate improved relative scaling of the parameters over a less circular shape. For simplicity, the discussion focuses on the innermost travel-time misfit range for each plot 200a-200e, although the same principles discussed hold for corresponding additional travel-time misfit ranges. For example, FIGURE 2A illustrates a plot of the relative change in the parameter pair ε and v (m/s). Travel-time misfit range 202a is approximately elliptically shaped indicating that a change in v results, at least somewhat, in a change in ε. As such, ε and v are somewhat correlated and although they exhibit some orthogonality, it is not a high degree of orthogonality.

[0037] FIGURE 2B is another example that plots travel-time misfit ranges as a function of the relative change in the parameter pair η and v. Travel-time misfit range 202b appears approximately vertical indicating that for a given velocity there is a multitude of η values, which when combined with the given value of v, results in approximately the same traveltime. As such, parameters η and v have a high degree of orthogonality with respect to each other, but are poorly scaled because a given value of v results from a wide range of values of η.

[0038] FIGURE 2C is an example that plots travel-time misfit ranges as a function of the relative change in the parameter pair V_ane and v. Travel-time misfit range 202c appears approximately elliptically shaped indicating that a change in v results, at least somewhat, in a change in V_ane- Hence, V_ane and v are somewhat correlated and they do not exhibit high degree of orthogonality.

[0039] FIGURE 2D is an example that plots travel-time misfit ranges as a function of the relative change in the composite parameter pair r|3 and η.ι. Travel -time misfit range 202d appears approximately circular shaped indicating that changes in r|3 and η.ι are essentially independent, as well as being scaled with respect to one another. Thus, these composite parameters exhibit a high degree of orthogonality with respect to each other. [0040] As a further example, FIGURE 2E plots travel-time misfit ranges as a function of the relative change in the parameter pair V_v ^_1and Vh^"1. Travel-time misfit range 202b appears approximately linear indicating that a change in V ^"1 results, at least somewhat, in a change in Vy^"1. As such, parameters V_v and V ^"1 have a low degree of orthogonality with respect to each other.

[0041 ] Based on analysis of plots 200a-200e in FIGURES 2A-2E, respectively, the parameter pair with 1) the highest degree of orthogonality, and thus independence; 2) and a degree of circularity, and thus high relative scaling of the parameters, is parameter pair r|3 and T|-i. Accordingly, updating a seismic model by varying parameter pair r| 3 and η.ι, which are derived from the PTS concept of Vinje et al., allows the effects of cross-talk to be mitigated or eliminated. Although specific parameters were selected for analysis in the foregoing examples, any suitable parameter pair may be analyzed in embodiments of the present disclosure. Further, although analyzed with a particular test system 100 and preset values of parameters, any suitable test system and preset values of parameters may be used in embodiments of the present disclosure.

[0042] In some embodiments, parameters that exhibit a high degree of orthogonality are utilized in algorithms to develop seismic models. For example, a velocity model may be developed that is dependent on the PTS parameters. Determination of velocity models begins with a wave equation. The following equations are discussed, for simplicity, with regard to the terminology and structure of a VTI media. However, the embodiments are not limited to the VTI media or model, but may be applied to other media and models, for example, tilted transverse isotropy (TTI) or structural transverse isotropy (STI), or any other suitable media or model. A wave equation in VTI media is given by:

Ap = d_ttp— v²pQLp = s

where:

d_ttp = the double partial derivative of the wavefield, p, with respect to travel- time (tt);

V = (Ph Pv)^T with ph and p_v being horizontal and vertical stress components of the wavefield;

1 + 2e VI + 26Y

VI + 2δ 1 ^' / where a_z = ;

Λ· = source term.

[0043] In FWI, the misfit function for the wave equation in VTI media is given by:

1 f

d)^TW(u - d)dt

£- ^Jo

where u represents the simulated data (or a processed version of the simulated data), d represents the recorded data (or a processed version of the recorded data), and T represents time. The gradients of the misfit function are given by the partial derivatives based on v, δ, and ε illustrated as follows:

C^T dA

d = - SdA^*— pdt

Jo ^dv

C^T dA

d = - SdA^*— pdt

Jo ^d£

C^T dA

dsJ = - \ SdA^*— pdt

Jo ⁹⁵

where Sd = (u— d)^TW and Wis a weight function (for example, a standard deviation or any other suitable measure), and A^* is the adjoint or some inverse operator.

[0044] From these equations, the basis for a misfit function that is dependent on the PTS parameters is developed as follows:

J(n_₁, n₁, n₃) = I (u— d)^TW(u— d)dt.

Jo

[0045] The gradients for each of these parameters is given by:

dA

SdA^* - pdt dA

d_nJ = - f SdA^*— pdt

Jo "ⁿi w ⁼ -

[0046] To generate the gradients based on PTS, a determination of the following quantities is needed:

dA dA dA

and

dn_₁ ' dn_x dn₃

These quantities can be determined by the following equations:

dA dA dv dA de dA dS

+ +^■

dn_₁ dv dn_₁ de dn_₁ dS dn_₁

dA dA dv dA ds dA dS

dn_x dv dn_x de dn_x dS dn_x (1)

dA dA dv dA de dA dS

— +^■

dn dv dn de dn₃ dS dn^

[0047] In some embodiments, Equations (1) may be expressed in matrix form as:

\ dn₃ / dri , dri .

[0048] Mapping between the PTS composite parameters and the physical parameters is as follows:

1

η_ - η = v(l + 25)

[0049] Solving for v, 5 and e yields:

l

δ = - (n₁n_₁ - l) (3)

[0050] Accordingly, in place of physical parameters v, δ and ε, the subsurface may be described by composite parameters n.\, and m. The additional parameter p completes the parameterization for the VTI case, while parameters dipl and dip2 are also needed for the TTI and STI cases.. These composite parameters can be updated in cascade (i.e., one after the other), all concurrently, or in subsets. Updating composite parameters to update the synthetic model, allows for a subsequent estimation of the velocity and anisotropic parameters that characterize the subsurface using Equations (3). Utilizing the composite parameters leads to a solution comparable to or improved on estimating v, δ and ε in a cascaded scheme, however decreasing the computational cost and time significantly based in part on the orthogonality of the composite parameters. Further, using composite parameters, n.\, n\ and «3, reduces ambiguity related to cross-talk because the composite parameter orthogonality is higher in comparison to orthogonality of other parameters.

[0051] FIGURE 3 A illustrates an exemplary synthetic velocity (v) model used to generate synthetic data in accordance with some embodiments of the present disclosure. Velocity models are cross-sections of the subsurface and, by colors or shading, show the change in velocity as a function of subsurface depth. In FIGURE 3 A, the true velocity model 300a is shown that demonstrates a sharp velocity change at interface 302a at a depth of approximately 2,000 meters. Another sharp velocity change is visible at interface 304a at a depth of approximately 2,300 meters.

[0052] FIGURES 3B-3D illustrate synthetic velocity (v) models obtained by inverting the synthetic data generated with the model of FIGURE 3A using different parameterizations built in an inversion algorithm in accordance with some embodiments of the present disclosure. For each of FIGURES 3B, 3C and 3D, different methods were utilized to attempt to generate a model that approximates the true velocity model 300a.

[0053] FIGURE 3B illustrates alternated update velocity model 300b. For model 300b, the parameters v and ε were optimized sequentially allowing the effects of cross-talk. Such sequential optimization may require significant resources of both time and computing power. FIGURE 3C illustrates joint update (with slownesses) velocity model 300c. For model 300c, ε and vertical velocity, V_v were both updated iteratively. FIGURE 3D illustrates PTS parameter update model 300d. For model 300d, the PTS parameters were updated concurrently. Analysis of FIGURES 3B-3D illustrate that approximately equivalent models are generated using different updating schemes. However, PTS parameter model update 300d required significantly less computational power and computing time, and thus less expense, to generate approximately equivalent models to alternated update velocity model 300b.

[0054] FIGURE 4A illustrates an exemplary synthetic epsilon (ε) model used to generate synthetic data in accordance with some embodiments of the present disclosure;

[0055] Epsilon models are cross-sections of the subsurface and, by colors or shading, illustrate the change in epsilon as a function of subsurface depth. In FIGURE 4A, the true ε model 400a is shown that demonstrates a sharp epsilon change at interface 402a at a depth of approximately 2,000 meters. Another sharp epsilon change is visible at interface 404a at a depth of approximately 2,300 meters.

[0056] FIGURES 4B-4D illustrate synthetic epsilon (ε) models obtained by inverting the synthetic data generated with the model of FIGURE 4A using different parameterizations built in an inversion algorithm in accordance with some embodiments of the present disclosure. For each of FIGURES 4B, 4C and 4D, different methods were utilized to attempt to generate a model that approximates the true ε model 400a.

[0057] FIGURE 4B illustrates alternated update ε model 400b. For model 400b, each of the parameters v and ε were optimized sequentially. Such sequential optimization may require significant resources of both time and computing power. FIGURE 4C illustrates joint update (with slownesses) ε model 400c. For model 400c, ε and vertical velocity, V_v were both updated iteratively. FIGURE 4D illustrates the ε model resulting from PTS parameter update ε model 400d. For model 400d, the PTS parameters were updated concurrently. Analysis of FIGURES 4B-4D illustrate that approximately equivalent epsilon models are generated using different updating schemes. However, analysis of FIGURES 4B-4D illustrate the PTS parameter update ε model 400d allowed the best reconstruction of the true ε model 400a. Even though the sequential approach, alternated update ε model 400b, also approximated relatively well the true ε model 400a, model 400b required approximately twice the computational effort of the PTS parameter update ε model 400d. Thus, the parameterization with PTS may have advantages in terms of both the quality of the reconstruction and computational load. [0058] FIGURE 5 illustrates an exemplary step function velocity profile 500 for the velocity models of FIGURES 3A-3D in accordance with some embodiments of the present disclosure. Profile 500 includes plots for true model 502a from FIGURE 3A, alternated updated model 502b from FIGURE 3B, joint update (with slownesses) model 502c from FIGURE 3C, and PTS parameter update model 502d from FIGURE 3C. As can be seen from profile 500, each of the update models 502b, 502c and 502d approximate true model 502a.

[0059] FIGURE 6 illustrates an exemplary step function ε profile for the ε models of FIGURES 4A-4D in accordance with some embodiments of the present disclosure. Profile 600 includes plots for the true ε model 602a from FIGURE 4A, alternated update ε model 602b from FIGURE 4B, joint update ε model 602c (obtained with slownesses), and PTS update ε model 602d. As can be seen from profile 600, the alternated update and the PTS parameterization lead to similar results and present the best reconstruction of the true ε model. However, PTS update ε model 602d may utilize only half the computational effort of the alternated update ε model 602b. Thus, PTS update ε model 602d may be the optimum overall solution.

[0060] In some embodiments, both the velocity analysis, discussed with reference to FIGURES 3A-3D and 5, and the ε analysis, discussed with reference to FIGURES 4A-4D and 6, may be performed. In analysis of both velocity and ε, the PTS update model may recover ε better than the alternated update models (especially in the region of the anomaly) and the PTS update may model the velocity better than the alternated update, with approximately half the computational effort. When the PTS update model is compared with the joint update model, the velocity models are similar but the PTS update model may recover ε with higher accuracy. Thus, the PTS update may be the optimum solution among the alternatives.

[0061] FIGURE 7 illustrates a flow chart of an example method 700 for improved inversion analysis for seismic data in accordance with some embodiments of the present disclosure. The steps of method 700 are performed by a user, various computer programs, models configured to process or analyze seismic data, and combinations thereof. The programs and models include instructions stored on a computer readable medium and operable to perform, when executed, one or more of the steps described below. The computer readable media includes any system, apparatus or device configured to store and retrieve programs or instructions such as a hard disk drive, a compact disc, flash memory, or any other suitable device. The programs and models are configured to direct a processor or other suitable unit to retrieve and execute the instructions from the computer readable media. Collectively, the user or computer programs and models used to process and analyze seismic data may be referred to as a "computing system." For illustrative purposes, method 700 is described with respect to data based on system 800 of FIGURE 8; however, method 700 may be used for improved inversion analysis of any set of seismic data.

[0062] Method 700 begins, and at step 702, the computing system obtains seismic data from a seismic exploration or survey. For example, a seismic data set is generated by signals received by receivers 802 shown in FIGURE 8 below.

[0063] At step 704, the computing system generates synthetic seismic data from a model of the subsurface. The model may be an existing model, or a generated model based on current understanding of the subsurface formations.

[0064] At step 706, the computing system computes the difference, or misfit, between the obtained seismic data and the synthetic seismic data. The misfit may be measured by any measure of the data misfit using a norm defined in a vector space; cross-correlating synthetic and real data; comparing seismic travel-times, for instance when performing travel-time tomography or using a measure of focusing in the image space, as in migration velocity analysis; differential semblance optimization; using a migration/demigration sequence for velocity analysis; or computing the difference, as in FWI.

[0065] At step 708, the computing system selects a parameter to perform an update to the model based on orthogonality analysis. The update to the model may assist in minimizing the misfit or difference. In some embodiments, the selected parameter may be a parameter from a pair of parameters that has a greater degree of orthogonality than other pairs of parameters. For example, as discussed with reference to FIGURE 2A-2E, analysis may be performed on pairs of parameters to determine a degree of orthogonality of the pairs. A comparison of the degree of orthogonality of each pair of parameters may be made. The parameter pairs with a higher degree of orthogonality may be identified. One or more parameters from the identified orthogonal parameters may be selected to update, such as a PTS parameter n.\, n\ and «3. In some embodiments, other or additional parameters may be selected based upon orthogonality analysis. In some embodiments, parameters may be selected to preserve velocities or travel-times between the synthetic data and the acquired data. For example, PTS parameters may be kinematically consistent such that travel-times are preserved during modeling.

[0066] At step 710, the computing system updates the model using the selected parameter. In some embodiments, the model may be iteratively updated until misfit between the synthetic data and the acquired data meets a predefined minimum, or some other specified quality measure is satisfied. At step 712, the computing system generates an improved model of the subsurface based on the updated model.

[0067] Additionally, modifications, additions, or omissions may be made to method 700 without departing from the scope of the present disclosure. For example, the order of the steps may be performed in a different manner than that described and some steps may be performed at the same time. Additionally, each individual step may include additional steps without departing from the scope of the present disclosure.

[0068] FIGURE 8 illustrates an elevation view of an example seismic exploration system 800 to acquire seismic data in accordance with some embodiments of the present disclosure. System 800 is configured to produce imaging of the earth's subsurface geological formations. System 800 includes one or more seismic energy sources 804 and one or more receivers 802 located within an exploration area. The exploration area is any defined area selected for seismic survey or exploration.

[0069] Receiver 802 may be located on or proximate to surface 808 of the earth within an exploration area. Receiver 802 may be any type of instrument that is operable to transform seismic energy or vibrations into a voltage signal. For example, receiver 802 may be a vertical, horizontal, or multicomponent geophone, accelerometers, or optical fiber with wire or wireless data transmission, such as a three component (3C) geophone, a 3C accelerometer, or a 3C Digital Sensor Unit (DSU). Multiple receivers 802 may be utilized within an exploration area to provide data related to multiple locations and distances from sources 804. Receivers 802 may be positioned in multiple configurations, such as linear, grid, array, or any other suitable configuration. In some embodiments, receivers 802 may be positioned along one or more strings 810. Each receiver 802 is typically spaced apart from adjacent receivers 802 in the string 810. Spacing between receivers 802 in string 810 may be approximately the same preselected distance, or span, or the spacing may vary depending on a particular application, exploration area topology, or any other suitable parameter.

[0070] In some embodiments, system 800 includes one or more seismic energy sources 804. Seismic energy source 804 may be referred to as an acoustic source, seismic source, energy source, or source 804. In some embodiments, for example seismic surveys on land, source 804 is located on or proximate to the surface of the earth within the exploration area. In other embodiments, such as seismic surveys at sea, source 804 is towed behind a vessel. A particular source 804 is spaced apart from other adjacent sources 804. Source 804 are typically operated by a central controller that coordinates the operation of several sources 804. Further, a positioning system, such as a global positioning system (GPS), may be utilized to locate or time-correlate sources 804 and receivers 802.

[0071] Source 804 is any type of seismic device that generates controlled seismic energy used to perform reflection or refraction seismic surveys, such as dynamite, an air gun, a thumper truck, a seismic vibrator, vibroseis, or any other suitable seismic energy source. For example, source 804 may be an impulsive energy source such as an air gun. With an impulsive energy source, a large amount of energy is injected into the surrounding media in a very short period of time.

[0072] Seismic exploration system 800 may include monitoring device 812 that operates to record reflected energy rays 832, 834, and 836, as well as other forms of seismic energy waves from, for example, transmission or prism waves. Monitoring device 812 may include one or more receivers 802, network 816, recording unit 818, and processing unit 820. In some embodiments, monitoring device 812 may be located remotely from source 804 and receiver 802.

[0073] One or more receivers 802 transmit raw seismic data of the recorded seismic energy via network 816 to recording unit 818. Recording unit 818 transmits raw seismic data to processing unit 820 via network 816. Processing unit 820 performs seismic data processing on the raw seismic data to prepare the data for interpretation. For example, processing unit 820 may perform the techniques described in FIGURES 1 -7. Although discussed separately, recording unit 818 and processing unit 820 may be configured as separate units or as a single unit. Recording unit 818 or processing unit 820 may include any instrumentality or aggregation of instrumentalities operable to compute, classify, process, transmit, receive, store, display, record, or utilize any form of information, intelligence, or data. For example, recording unit 818 and processing unit 820 may include one or more personal computers, storage devices, servers, or any other suitable device and may vary in size, shape, performance, functionality, and price. Recording unit 818 and processing unit 820 may include random access memory (RAM), one or more processing resources, such as a central processing unit (CPU) or hardware or software control logic, or other types of volatile or non-volatile memory. Additional components of recording unit 818 and processing unit 820 may include one or more disk drives, one or more network ports for communicating with external devices, one or more input/output (I/O) devices, such as a keyboard, a mouse, or a video display. Recording unit 818 or processing unit 820 may be located in a station truck or any other suitable enclosure.

[0074] Network 816 may be configured to communicatively couple one or more components of monitoring device 812 with any other component of monitoring device 812. For example, network 816 may communicatively couple receivers 802 with recording unit 818 and processing unit 820. Further, network 814 may communicatively couple a particular receiver 814 with other receivers 814. Network 814 may be any type of network that provides communication, such as one or more of a wireless network, a local area network (LAN), or a wide area network (WAN), such as the Internet.

[0075] The seismic survey emitted by source 804 may be repeated at various time intervals to determine changes in target reservoir 830. The time intervals may be months or years apart. Data may be collected and organized based on offset distances, such as the distance between a particular source 804 and a particular receiver 802 and the amount of time it takes for rays 832 and 834 from a source 804 to reach a particular receiver 802. Data collected during a survey by receivers 802 may be result in traces that may be gathered, processed, and utilized to generate a model of the subsurface structure or variations of the structure.

[0076] Although discussed with reference to a land implementation, embodiments of the present disclosure are also useful in marine applications. In a marine application, monitoring device 812 may include hydrophones or accelerometers contained inside buoyant streamers, which may be towed behind a vessel. Source 804 and monitoring device 812 may be towed behind the same or a different vessel. Embodiments of the present disclosure may also be used in a seabed acquisition application. In a seabed acquisition application, where receiver 802 is placed on the seabed, monitoring device 812 may include 3C geophone and hydrophones.

[0077] Herein, "or" is inclusive and not exclusive, unless expressly indicated otherwise or indicated otherwise by context. Therefore, herein, "A or B" means "A, B, or both," unless expressly indicated otherwise or indicated otherwise by context. Moreover, "and" is both joint and several, unless expressly indicated otherwise or indicated otherwise by context. Therefore, herein, "A and B" means "A and B, jointly or severally," unless expressly indicated otherwise or indicated otherwise by context.

[0078] This disclosure encompasses all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. Similarly, where appropriate, the appended claims encompass all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. Moreover, reference in the appended claims to an apparatus or system or a component of an apparatus or system being adapted to, arranged to, capable of, configured to, enabled to, operable to, or operative to perform a particular function encompasses that apparatus, system, component, whether or not it or that particular function is activated, turned on, or unlocked, as long as that apparatus, system, or component is so adapted, arranged, capable, configured, enabled, operable, or operative.

[0079] Any of the steps, operations, or processes described herein may be performed or implemented with one or more hardware or software modules, alone or in combination with other devices. In one embodiment, a software module is implemented with a computer program product comprising a computer-readable medium containing computer program code, which can be executed by a computer processor for performing any or all of the steps, operations, or processes described.

[0080] Embodiments of the disclosure may also relate to an apparatus for performing the operations herein. This apparatus may be specially constructed for the required purposes, and/or it may comprise a general-purpose computing device selectively activated or reconfigured by a computer program stored in the computer. Such a computer program may be stored in a tangible computer readable storage medium or any type of media suitable for storing electronic instructions, and coupled to a computer system bus. Furthermore, any computing systems referred to in the specification may include a single processor or may be architectures employing multiple processor designs for increased computing capability.

[0081] Although the present disclosure has been described with several embodiments, a myriad of changes, variations, alterations, transformations, and modifications may be suggested to one skilled in the art, and it is intended that the present disclosure encompass such changes, variations, alterations, transformations, and modifications as fall within the scope of the appended claims. Moreover, while the present disclosure has been described with respect to various embodiments, it is fully expected that the teachings of the present disclosure may be combined in a single embodiment as appropriate.

[0082] Reference throughout the specification to "one embodiment," "some embodiments," or "an embodiment" means that a particular feature, structure or characteristic described in connection with an embodiment is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases "in one embodiment," "in some embodiments," or "in an embodiment" in various places throughout the specification is not necessarily referring to the same embodiment. Further, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments.

Claims

WHAT IS CLAIMED IS:

1. A method for improved analysis of seismic data, the method comprising: obtaining a recorded seismic data set;

generating a synthetic seismic data set using a model of a subsurface;

computing a misfit between the recorded seismic data set and the synthetic seismic data set; and

updating the model of the subsurface to reduce the misfit by modifying a selected pair of parameters, wherein the selected pair of parameters is based on:

analyzing a first degree of orthogonality of a first pair of parameters;

analyzing a second degree of orthogonality of a second pair of parameters; and

based on the first degree of orthogonality or the second degree of orthogonality being greater, selecting the first pair of parameters or the second pair of parameters.

2. The method of Claim 1, wherein the selected pair of parameters comprises a composite parameter.

3. The method of Claim 2, wherein the composite parameter is a function of a velocity and an anisotropic parameter.

4. The method of Claim 1, wherein the recorded seismic data set and the synthetic seismic data set comprise processed data.

5. The method of Claim 1, wherein the update of the model of the subsurface is based on a full wave inversion (FWI) algorithm.

6. The method of Claim 1, wherein the first degree of orthogonality is analyzed by plotting a misfit range as a function of the first pair of parameters.

7. The method of Claim 1, wherein the selected parameter is a preserved travel- time smoothing (PTS) parameter.

8. The method of Claim 1 further comprising generating an image of the subsurface using the updated model.

9. A seismic processing system, comprising:

a computing system configured to:

obtain a recorded seismic data set;

generate a synthetic seismic data set using a model of a subsurface;

compute a misfit between the recorded seismic data set and the synthetic seismic data set; and

update the model of the subsurface to reduce the misfit by modifying a selected pair of parameters, wherein the selected pair of parameters is based on:

analyzing a first degree of orthogonality of a first pair of parameters; analyzing a second degree of orthogonality of a second pair of parameters; and

10. The system of Claim 9, wherein the selected pair of parameters comprises a composite parameter.

11. The system of Claim 10, wherein the composite parameter is a function of a velocity and an anisotropic parameter.

12. The system of Claim 9, wherein the recorded seismic data set and the synthetic seismic data set comprise processed data.

13. The system of Claim 9, wherein the update of the model of the subsurface is based on a full wave inversion (FWI) algorithm.

14. The system of Claim 9, wherein the first degree of orthogonality is analyzed by plotting a misfit range as a function of the first pair of parameters.

15. The system of Claim 9, wherein the selected parameter is a preserved travel- time smoothing (PTS) parameter.

16. The system of Claim 9, wherein the computing system is further configured to generate an image of the subsurface using the updated model.

17. A non-transitory computer-readable medium, comprising:

computer-executable instructions carried on the computer-readable medium, the instructions, when executed, causing a processor to:

obtain a recorded seismic data set;

generate a synthetic seismic data set using a model of a subsurface;

18. The non-transitory computer-readable medium of Claim 17, wherein the selected pair of parameters comprises a composite parameter.

19. The non-transitory computer-readable medium of Claim 18, wherein the composite parameter is a function of a velocity and an anisotropic parameter.

20. The non-transitory computer-readable medium of Claim 17, wherein the recorded seismic data set and the synthetic seismic data set comprise processed data.