阅读说明：本技术 将正交化滤波应用于波场分离 (Applying orthogonalization filtering to wavefield separation ) 是由 郑宇敦 康斯坦丁诺斯·钦戈斯 金永成 于 2018-11-06 设计创作，主要内容包括：本公开描述了用于将正交化滤波应用于波场分离的方法和系统,包括计算机实现的方法、计算机程序产品和计算机系统。一种计算机实现的方法包括：获得多分量波场；对多分量波场执行波场分离以获得分离的波场；以及将局部正交化权重(LOW)滤波应用于经分离的波场以获得经滤波的波场。(The present disclosure describes methods and systems, including computer-implemented methods, computer program products, and computer systems, for applying orthogonalization filtering to wavefield separation. A computer-implemented method comprising: obtaining a multi-component wavefield; performing a wavefield separation on the multi-component wavefield to obtain a separated wavefield; and applying a Local Orthogonalization Weight (LOW) filter to the separated wavefields to obtain filtered wavefields.)

1. A method, comprising:

obtaining a multi-component wavefield;

performing a wavefield separation on the multi-component wavefield to obtain a separated wavefield; and

local orthogonalization weight LOW filtering is applied to the separated wavefields to obtain filtered wavefields.

2. The method of claim 1, further comprising: a depth image is calculated based on the filtered wavefield.

3. The method of claim 1, wherein the multi-component wavefield is formed using a time-domain elastic wave propagation model based on a first-order two-dimensional elastic wave equation, and comprises a horizontal component and a vertical component.

4. The method of claim 3, wherein the separated wavefield includes at least one of the horizontal component P wavefield, the vertical component P wavefield, the horizontal component S wavefield, or the vertical component S wavefield.

5. The method of claim 3, wherein performing wavefield separation comprises:

decoupling the first-order two-dimensional elastic wave equation into a P-wave component and an S-wave component which are separated; and

separating the multi-component wavefield based on the decoupled first-order two-dimensional elastic wave equation.

6. The method of claim 5, wherein a first order two dimensional elastic wave equation is written in terms of stress and particle velocity formulas and is decoupled using a set of equations associated with a compressional wave component that provides P-wave stress and particle velocity for both horizontal and vertical components.

7. The method of claim 3, wherein applying the LOW filter comprises:

for each of the separated wavefields:

calculating local orthogonalization weights; and

obtaining a filtered wavefield by applying the calculated local orthogonalization weights to corresponding components of the multi-component wavefield.

8. The method of claim 1, wherein the wavefield separation is performed using a P-wavefield and an S-wavefield separation method.

9. An apparatus, comprising:

a memory; and

a processing unit arranged to perform operations comprising:

obtaining a multi-component wavefield;

performing a wavefield separation on the multi-component wavefield to obtain a separated wavefield; and

local orthogonalization weight LOW filtering is applied to the separated wavefields to obtain filtered wavefields.

10. The apparatus of claim 9, the operations further comprising: a depth image is calculated based on the filtered wavefield.

11. The apparatus of claim 9, wherein the multi-component wavefield is formed using a time-domain elastic wave propagation model based on a first-order two-dimensional elastic wave equation, and comprises a horizontal component and a vertical component.

12. The apparatus of claim 11, wherein the separated wavefield includes at least one of the horizontal component P wavefield, the vertical component P wavefield, the horizontal component S wavefield, or the vertical component S wavefield.

13. The apparatus of claim 11, wherein performing wavefield separation comprises:

decoupling the first-order two-dimensional elastic wave equation into a P-wave component and an S-wave component which are separated; and

separating the multi-component wavefield based on the decoupled first-order two-dimensional elastic wave equation.

14. The apparatus of claim 13, wherein a first order two dimensional elastic wave equation is written in terms of stress and particle velocity formulas and is decoupled using a set of equations associated with a compressional wave component that provides P-wave stress and particle velocity for both horizontal and vertical components.

15. The apparatus of claim 11, wherein applying the LOW filtering comprises:

for each of the separated wavefields:

calculating local orthogonalization weights; and

obtaining a filtered wavefield by applying the calculated local orthogonalization weights to corresponding components of the multi-component wavefield.

16. The apparatus of claim 9, wherein the wavefield separation is performed using a P-wavefield and an S-wavefield separation method.

17. A non-transitory computer-readable medium storing instructions executable by a computer system to perform operations comprising:

obtaining a multi-component wavefield;

performing a wavefield separation on the multi-component wavefield to obtain a separated wavefield; and

local orthogonalization weight LOW filtering is applied to the separated wavefields to obtain filtered wavefields.

18. The medium of claim 17, the operations further comprising: a depth image is calculated based on the filtered wavefield.

19. The medium of claim 17, wherein the multi-component wavefield is formed using a time-domain elastic wave propagation model based on a first-order two-dimensional elastic wave equation, and comprises a horizontal component and a vertical component.

20. The medium of claim 19, wherein the separated wavefield includes at least one of the horizontal component P wavefield, the vertical component P wavefield, the horizontal component S wavefield, or the vertical component S wavefield.

Technical Field

The present disclosure relates to seismic data processing, and more particularly to applying orthogonalization filtering to wavefield separation.

Background

P-wavefield and S-wavefield separation have been used to separate elastic multi-component wavefields in the time and space domains. However, considerable residual energy remains in the decomposed wavefield.

Disclosure of Invention

The present disclosure describes methods and systems, including computer-implemented methods, computer program products, and computer systems, for applying orthogonalization filtering to wavefield separation. A computer-implemented method comprising: obtaining a multi-component wavefield; performing a wavefield separation on the multi-component wavefield to obtain a separated wavefield; and applying a Local Orthogonalization Weight (LOW) filter to the separated wavefield to obtain a filtered wavefield.

Other embodiments of this aspect include: corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods. The system of one or more computers may be configured to: certain operations or actions may be performed by software, firmware, or hardware, or a combination of software, firmware, or hardware, that when installed in operation causes the system to perform the actions. The one or more computer programs may be configured to: certain operations or actions are performed by virtue of including instructions that, when executed by a data processing apparatus, cause the apparatus to perform the actions.

The foregoing and other embodiments may each optionally include, alone or in combination, one or more of the following features:

a first aspect combinable with the general embodiment comprises: generating a depth image based on the filtered wavefield.

A second aspect combinable with any of the preceding aspects, wherein the multi-component wavefield is formed using a time-domain elastic wave propagation model based on a first-order two-dimensional elastic wave equation, and the multi-component wavefield includes a horizontal component and a vertical component.

A third aspect combinable with any of the preceding aspects, wherein the separated wavefield includes at least one of the horizontal component P wavefield, the vertical component P wavefield, the horizontal component S wavefield, or the vertical component S wavefield.

A fourth aspect combinable with any of the preceding aspects, comprising: decoupling a first-order two-dimensional elastic wave equation into a P-wave component and an S-wave component which are separated; and separating the multi-component wavefield based on the decoupled first-order two-dimensional elastic wave equation.

A fifth aspect combinable with any of the preceding aspects, wherein a first order two-dimensional elastic wave equation is written in stress and particle velocity formulas and is decoupled using a set of equations associated with the compressional wave component that provides P-wave stress and particle velocity for both horizontal and vertical components.

A sixth aspect combinable with any of the preceding aspects, wherein applying LOW filtering comprises: for each of the separated wavefields: calculating local orthogonalization weights; and obtaining a filtered wavefield by applying the calculated local orthogonalization weights to corresponding components of the multi-component wavefield.

A seventh aspect combinable with any of the preceding aspects, wherein the wavefield separation is performed using a P-wavefield and an S-wavefield separation method.

Although generally described as computer-implemented software implemented on a tangible medium that processes and converts corresponding data, some or all of the aspects may be computer-implemented methods or also included in corresponding systems or other apparatus for performing the described functions. The details of these and other aspects and implementations of the disclosure are set forth in the accompanying drawings and the description below. Other features and advantages of the disclosure will be apparent from the description and drawings, and from the claims.

Drawings

FIG. 1 illustrates an example snapshot of horizontal and vertical wavefields, according to some embodiments.

FIG. 2 illustrates an example snapshot of separated P and S wavefields, according to some embodiments.

Fig. 3 is a diagram illustrating example orthogonality between signals and noise, according to some embodiments.

FIG. 4 illustrates example snapshots of filtered P and S wavefields, according to some embodiments.

FIG. 5 is a flow diagram illustrating an example method of applying orthogonalization filtering to wavefield separation according to some embodiments.

Fig. 6 illustrates an example snapshot of normalized gradient directions, according to some embodiments.

Fig. 7 is a block diagram illustrating an example computer system for providing computing functionality associated with algorithms, methods, functions, processes, flows and processes as described in this disclosure, in accordance with some embodiments.

Like reference numbers and designations in the various drawings indicate like elements.

Detailed Description

The following detailed description describes the application of orthogonalization filtering to wavefield separation and is presented to enable any person skilled in the art to make and use the subject matter disclosed in the context of one or more specific embodiments. Various modifications, changes, and substitutions to the disclosed embodiments may be made and will be apparent to those skilled in the art, and the general principles defined may be applied to other embodiments and applications without departing from the scope of the disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown or described, but is to be accorded the widest scope consistent with the principles and features disclosed.

In elastic wave propagation modeling, complex simultaneous propagation of elastic wave modes (e.g., P-wave fields and S-wave fields) interfere with each other and can cause artifacts during multi-component seismic imaging and velocity modeling. Thus, P-wavefield and S-wavefield separation have been used to separate elastic multi-component wavefields in the time and space domains.

Wavefield separation based on decoupled wave equations (i.e., decoupled propagation methods) separates P-wave equations and S-wave equations during numerical modeling. The decoupled propagation method shows competitive performance in terms of computational cost, memory usage and numerical stability compared to other wavefield separation methods (e.g., selective attenuation methods). In addition, since the decoupling of the two modes (i.e., the P-wave field and the S-wave field) is performed implicitly during numerical modeling, the decoupled propagation method is easier and more efficient to implement than other methods that use elastic wave propagation modeling. Although the decoupled wave equation separates the P-wave field and the S-wave field, artifacts, for example, generated by S-wave transitions and reflections, are observed in the separated wave fields. Therefore, decoupled propagation methods are not widely used in, for example, velocity modeling and depth imaging.

The described method provides a wavefield separation and filtering method (also referred to as a filtered wavefield separation method). The described wavefield separation and filtering method combines an elastic wavefield separation method based on a decoupled wave equation with a Local Orthogonalization Weight (LOW) filtering method. For example, LOW filtering is applied after the wavefield separation process to improve the signal-to-noise ratio to compensate for signal leakage in each separated wavefield component. The decoupled wave equations are used in a wavefield separation process to efficiently and accurately separate P and S wavefields during elasticity numerical modeling. In addition, LOW filtering is applied to the separated wavefield to eliminate artifacts (false artifacts) generated during elasticity numerical modeling. Because artifacts are eliminated, the above-described wavefield separation and filtering methods can be used, for example, in elastic wavefield modeling, Elastic Full Waveform Inversion (EFWI), and elastic inverse time migration (ERTM) to obtain sharper images.

Wavefield separation using decoupled wave equations

In general, for elastically isotropic media, the first-order two-dimensional elastic wave equation using the stress and particle velocity (particle-velocity) formula is expressed as:

D_tv_x＝b(D_xτ_xx+D_zτ_xz) (1)

D_tv_z＝b(D_xτ_xz+D_zτ_zz) (2)

for the particle velocity component, an

D_tτ_xx＝(λ+2μ)D_xv_x+λD_zv_z(3)

D_tτ_zz＝(λ+2μ)D_zv_z+λD_xv_x(4)

D_tτ_xz＝μ(D_xv_x+D_zv_z) (5)

For a stress component, wherein

Accordingly, (x, z) represents a two-dimensional spatial coordinate, t represents time, b is buoyancy (i.e., the inverse of density ρ), and λ and μ represent the lame coefficient. v and τ are the particle velocity component and the stress component, respectively. Although this disclosure references, for purposes of example, a first-order two-dimensional elastic wave equation that employs stress and particle velocity equations, the subject matter of this document may be applied to other types of wave equations.

A decoupled propagation method may be used to rewrite the elastic wave equation (i.e., equations (1) through (6)) into separate P-wave and S-wave components. For example, additional equations related to the compressional wave component may be used to decouple the elastic wave equation and provide P-wave stress and particle velocity for both the horizontal and vertical components. Thus, by decomposing the elastic wave equations (i.e., equations (1) through (6)), the following P-wave stresses and particle velocities for both the horizontal and vertical components can be obtained:

D_tv_xP＝b D_xτ_P(7)

D_tv_zp＝b D_zτ_P(8)

D_tτ_P＝(λ+2μ)(D_xv_x+D_zv_z) (9)

where the lower subscript denotes the P-mode. v. of_xPAnd v_zPThe P-wave particle velocity horizontal and vertical components, respectively. Tau is_PIs the P-wave stress component. Therefore, the stress and particle velocity of the S wavefield may be calculated by subtracting the P wavefield obtained in equations (7) through (9) from the original (or normal) wavefield obtained in equations (1) through (6):

v_xS＝v_x-v_xP(10)

v_zS＝v_z-v_zP(11)

wherein the subscript S represents an S mode. v. of_xSAnd v_zSThe horizontal and vertical components of the S-wave particle velocity, respectively.

FIG. 1 illustrates an example snapshot 100 of horizontal and vertical wavefields, according to some embodiments. For example, a four-layer velocity model with three interfaces simulates both P-wave and S-wave velocities. The density model is fixed to a constant. FIG. 1 shows a snapshot of the horizontal wavefield 105 and a snapshot of the vertical wavefield 110, both obtained using, for example, elastic wave equations (i.e., equations (1) through (6)). In fig. 1 and fig. 2, 4, and 6 described later, xline (x-line) and depth represent an x-axis and a z-axis, respectively. The snapshot image is generated, for example, using the tool XIMAGE of sessmicunix.

FIG. 2 illustrates an example snapshot 200 of separated P and S wavefields, according to some embodiments. In FIG. 2, the horizontal wavefield 105 in FIG. 1 is decomposed into horizontal P wavefields 205 and horizontal S wavefields 215 using, for example, decoupled elastic wave equations (i.e., equation (7) through equation (11)). The vertical wavefield 110 in FIG. 1 is decomposed into vertical P wavefields 210 and vertical S wavefields 220 using, for example, decoupled elastic wave equations (i.e., equation (7) through equation (11)). Artifacts at the locations identified by the arrows are shown in the horizontal P-wavefield 205 and the vertical P-wavefield 210. The positions identified by the arrows are the positions where the P-to-S conversion and S-wave reflection occur. In some embodiments, the artifacts may be suppressed when a smoother velocity model with smoother interfaces is used instead of the four-layer velocity model with three interfaces described in fig. 1. However, when performing Reverse Time Migration (RTM) and Full Waveform Inversion (FWI) with more complex velocity models, artifacts may not be suppressed.

Local Orthogonalization Weight (LOW) calculation

Fig. 3 is a diagram illustrating example orthogonality 300 between signals and noise, according to some embodiments. In FIG. 3, s_obsAnd n_obsRepresenting the signal and noise, respectively, initially observed after the denoising or filtering process. s and n represent the final estimated signal and noise, respectively. w is a weighting operator that weights the observed signal. The observed signal corresponds to the signal energy remaining in the noise component. To obtain the weighting operator w, an optimization problem may be set such that the leakage signal energy and the weighting signal ws in the observed noise are equal_obsMinimization of the residual error between:

where diag (a) represents a diagonal matrix composed of the elements of the original vector a, and R is the smooth regularization operator. Note the diag(s)_obs)w＝diag(w)s_obs. The solution to the least squares problem (i.e., equation (12)) produces a local weighting vector that minimizes signal leakage in the noise component. Thus, the final estimate of the signal and noise is expressed as:

s＝s_obs+diag(w)s_obs＝s_obs+diag(s_obs)w (13)

n＝n_obs-diag(w)s_obs＝n_obs-diag(s_obs)w (14)

in the LOW calculation, one assumption is that the signal and noise are orthogonal and unlikely to correlate with each other. In addition, there are two inputs for the LOW calculation. For example, if the original wavefield and the separated wavefield are the first and second inputs, respectively, the LOW calculations (equations (12) through (14)) produce a filtered wavefield by enhancing seismic events that are common to both inputs and ignoring seismic events that are not locally correlated. The filtered wavefield may be used in many applications that use elastic wave propagation equations, such as elastic numerical modeling, computation of gradients during Elastic Full Waveform Inversion (EFWI), and Elastic Reverse Time Migration (ERTM), to provide more accurate results (e.g., sharper depth images) than using the original wavefield or the separated wavefield.

Filtering of separated wavefields by LOW

The wavefield separation and filtering method described next denoises the separated wavefield in the image domain (or spatial domain) by calculating local orthogonalization weights between the separated P and S wavefields during wave propagation modeling. From the decoupled wave equations (i.e., equation (7) through equation (11)), the corresponding horizontal and vertical components of the P and S wavefields with artifacts (also referred to as noise) are expressed as:

for P-waves; and

for the S-wave, where the superscripts t and n represent the noise-free (i.e., true) and noise components, respectively.

To apply LOW to the separated wavefield, assume the horizontal P-wave particle velocity v_xPIs the observed noise n_obsAnd horizontal particle velocity v_xIs the observed signal s in equation (12)_obs. Thus, a new least squares problem is obtained as follows:

equation (19) for the weighting operator w_PSolving is carried out, the acquisition of which stays at v_xPSignal v of_x. From equation (13) to equation (16), the final estimate of noise on the horizontal P wavefield is:

and the final estimate of the noise-free signal over the horizontal P wavefield is:

from equations (20) and (21), the final estimate of the noise-free signal over the horizontal P wavefield, representing the signal after wavefield separation and orthogonalization filtering, is:

similar processing (e.g., equation (19) through equation (22)) may be applied to the vertical P-wavefield to obtain a final estimate of the noise-free signal on the vertical P-wavefield

For the S-wave component, assume the horizontal S-wave particle velocity v_xSIs the observed noise n_obsAnd horizontal particle velocity v_xIs the observed signal s in equation (12)_obs. Thus, another least squares problem is obtained as follows:

equation (23) for the weighting operator w_SSolving is carried out, the acquisition of which stays at v_xSSignal v of_x. From equations (13) to (16), the final estimate of the noise on the horizontal S wavefield is:

and the final estimate of the noise-free signal over the horizontal S-wavefield is:

from equation (24) and equation (25), the final estimate of the noise-free signal over the horizontal S-wavefield, representing the signal after wavefield separation and orthogonalization filtering, is:

similar processing (e.g., equations (23) through (26)) may be applied to the vertical S-wavefield to obtain a final estimate of the noise-free signal on the vertical S-wavefield

FIG. 4 illustrates an example snapshot 400 of filtered P and S wavefields, according to some embodiments. In FIG. 4, the separated wavefields 205, 210, 215, and 220 in FIG. 2 are respectively filtered using, for example, LOW filtering (i.e., equations (15) through (26)) to produce a filtered horizontal P wavefield 405, a filtered vertical P wavefield 410, a filtered horizontal S wavefield 415, and a filtered vertical S wavefield 420. The filtered horizontal P wave field 405 and the filtered vertical P wave field 410 illustrate the removal of artifacts observed in the horizontal P wave field 205 and the vertical P wave field 210 in fig. 2. Fig. 4 illustrates that LOW filtering performs very well on noise suppression on the separated wavefield.

FIG. 5 is a flow diagram illustrating an example method 500 for applying orthogonalization filtering to wavefield separation according to some embodiments. For clarity of presentation, the following description generally describes the method 500 in the context of other figures of the specification. For example, the method 500 may be performed by the computer system depicted in FIG. 7. However, it should be understood that method 500 may be performed, for example, by any suitable system, environment, software, and hardware, or suitable combination of systems, environments, software, and hardware, as appropriate. In some embodiments, the steps of method 500 may be performed in parallel, in combination, in a loop, or in any order.

The method 500 begins at block 505 where a multi-component wavefield is obtained. In some embodiments, a multi-component wavefield is formed using a time-domain elastic wave propagation model based on first-order two-dimensional elastic wave equations (e.g., equations (1) through (6)). The multi-component wavefield includes a horizontal component and a vertical component. In some embodiments, the first-order two-dimensional elastic wave equation is written in terms of stress and particle velocity equations. In some implementations, the propagation model can be implemented using a staggered mesh finite difference method (e.g., a staggered pattern or a staggered mesh).

At block 510, wavefield separation is performed on the multi-component wavefield to obtain a separated wavefield. In some embodiments, the wavefield separation is performed using P-wavefield and S-wavefield separation methods (e.g., decoupled propagation methods). After wavefield separation, the separated wavefield includes at least one of a horizontal component P wavefield, a vertical component P wavefield, a horizontal component S wavefield, or a vertical component S wavefield. In some embodiments, performing wavefield separation comprises: decoupling the first order two-dimensional elastic wave equations into separate P-wave and S-wave components (e.g., equations (7) through (11)), and separating the multi-component wavefield based on the decoupled first order two-dimensional elastic wave equations. In some embodiments, the decoupling of the first-order two-dimensional elastic wave equation is performed using a set of equations associated with the compressional wave component (e.g., equations (7) through (9)) that provide the P-wave stress and particle velocity for both the horizontal and vertical components.

At block 515, Local Orthogonalization Weight (LOW) filtering is applied to the separated wavefields to obtain filtered wavefields. In some implementations, for each of the separated wavefields, local orthogonalization weights are calculated (e.g., equation (19) and equation (23)). And for each of the separated wavefields, obtaining a filtered wavefield (e.g., equation (22), equation (26)) by applying the calculated local orthogonalization weights to corresponding components (e.g., equation (20) -equation (21), equation (24) -equation (25)) of the multi-component wavefield.

The example method 500 shown in fig. 5 may be modified or reconfigured to include additional, fewer, or different steps (not shown in fig. 5), which may be performed in the order shown or in a different order. For example, after block 515, an image (e.g., a depth image of the subsurface reservoir) may be computed based on the filtered wavefield. In some embodiments, the filtered and separated wavefields are used to calculate a gradient direction for Elastic Full Waveform Inversion (EFWI), an imaging condition for Elastic Reverse Time Migration (ERTM), or a combination of both. For example, images (e.g., 625 and 630 in fig. 6 described later) may be obtained from EFWI using LOW filtering, and each image may be used to update the elasticity parameters (e.g., P-wave velocity, S-wave velocity). Additionally, the updated elasticity parameters may be used in depth imaging employing Reverse Time Migration (RTM). In some embodiments, for example, one or more of the steps shown in fig. 5 may be repeated or iterated until a termination condition is reached. In some embodiments, one or more of the individual steps shown in fig. 5 may be performed as multiple separate steps, or one or more subsets of the steps shown in fig. 5 may be combined and performed as a single step. In some embodiments, one or more of the individual steps shown in fig. 5 may also be omitted from the example method 500.

Fig. 6 illustrates an example snapshot 600 of normalized gradient directions, according to some embodiments. To investigate the applicability and effectiveness of LOW filtering in wavefield separation, for example, two-dimensional Elastic Full Waveform Inversion (EFWI) was performed on land datasets. Since the observations of the terrestrial data set have only vertical components, the P-mode dominates in forward and backward modeling. Therefore, the gradient direction for acquiring the P-wave velocity is calculated by the PP mode and the gradient direction for acquiring the S-wave velocity is calculated by the PS mode, respectively. Fig. 6 shows the gradient direction at the 6 th iteration of the P-wave velocity and S-wave velocity. In fig. 6, for example, the normalized gradient direction of the P-wave velocity 605 and the normalized gradient direction of the S-wave velocity 610 are obtained based on the conventional FWI, and are interference images according to the inherent characteristics of the conventional EFWI. As shown in fig. 6, the images with opposite polarization (oppositepolarity) are similar. For example, the normalized gradient direction 615 for P-wave velocity and the normalized gradient direction 620 for S-wave velocity are obtained based on using PP and PS related wavefield separation. Due to crosstalk and interference generated from the P-wave field and the S-wave field, the normalized gradient direction of the P-wave velocity 615 and the normalized gradient direction of the S-wave velocity 620 are contaminated by the horizontal noise band. For example, based on using PP and PS related wavefield separation (i.e., decoupling the elastic waves) in combination with LOW filtering, a normalized gradient direction 625 for P-wave velocity and a normalized gradient direction 630 for S-wave velocity are obtained. The normalized gradient direction of the P-wave velocity 625 and the normalized gradient direction of the S-wave velocity 630 indicate that the wavefield separation followed by LOW filtering can provide robust and less noisy gradient directions for both the PP and PS wavefields.

Fig. 7 is a block diagram illustrating an example computer system 700 for providing computing functionality associated with the described algorithms, methods, functions, processes, flows, and processes as described in this disclosure, according to an embodiment. The illustrated computer 702 is intended to include any computing device (e.g., a server, a desktop computer, a laptop/notebook computer, a wireless data port, a smart phone, a Personal Data Assistant (PDA), a tablet computing device), one or more processors within these devices, or any other suitable processing device, including a physical instance or a virtual instance (or both) of a computing device. Additionally, computer 702 can comprise a computer including input devices (e.g., a keypad, keyboard, touch screen, or other device) that can accept user information and output devices that communicate information associated with the operation of computer 702, including numerical data, visual or audio information (or a combination of information), or a Graphical User Interface (GUI).

The computer 702 may serve the role (or combination of roles) of a client, network component, server, database or other persistent device (persistence), or any other component of a computer system for executing the subject matter described in this disclosure. The computer 702 is shown communicatively coupled to a network 730. In some implementations, one or more components of the computer 702 can be configured to: operate within an environment (or combination of environments) that includes a cloud-based computing environment, a local environment, a global environment, or other environment.

Computer 702 is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some embodiments, computer 702 may also include, or be communicatively coupled with, an application server, an email server, a web server, a cache server, a streaming data server, or other servers (or combinations of servers).

The computer 702 may receive requests from client applications (e.g., executing on another computer) over the network 730 and respond to the received requests by processing the received requests using an appropriate software application. Additionally, requests may also be sent to computer system 702 from internal users (e.g., from a command console or through another internal access method), external or third parties, other automation applications, and any other appropriate entity, person, system, or computer.

Each of the components of the computer 702 may communicate using a system bus 703. In some implementations, any or all of the components, hardware or software (or a combination of hardware and software) of the computer 702 can interface with each other through the system bus 703 or the interface 704 (or a combination of both) using an Application Programming Interface (API)712 or a service layer 713 (or a combination of API712 and service layer 713). API712 may include specifications for routines, data structures, and object classes. API712 may be language independent or dependent on the computer and may refer to a complete interface, a single function, or even a set of APIs. Service layer 713 provides software services to computer 702 or other components communicatively coupled to computer 702 (whether shown or not). The functionality of the computer 702 may be accessible to all service consumers using the service layer. Software services (e.g., software services provided by service layer 713) provide reusable, defined functionality through defined interfaces. For example, the interface can be software written in JAVA, C + +, another computing language, or can be software written in a combination of computing languages that provide data in an extensible markup language (XML) format, another format, or a combination of formats. Although shown as an integrated component of computer 702, alternative embodiments may show API712 or service layer 713 as a separate component from other components of computer 702 or communicatively coupled to other components of computer 702 (whether shown or not). Further, any or all portions of API712 and service layer 713 may be implemented as a sub-module or sub-module of another software module, enterprise application, or hardware module without departing from the scope of this disclosure.

The computer 702 includes an interface 704. Although illustrated in fig. 7 as a single interface 704, two or more interfaces 704 may be used depending on the particular needs, desires, or particular implementations of the computer 702. Interface 704 is used by computer 702 to communicate with other systems connected to network 730 in a distributed environment (whether shown or not). In general, the interface 704 comprises logic encoded in software or hardware (or a combination of software and hardware) and operable to communicate with the network 730. More specifically, interface 704 may include software that supports one or more communication protocols associated with communication such that network 730 or the interface's hardware is operable to communicate physical signals both inside and outside of illustrated computer 702.

The computer 702 includes a processor 705. Although illustrated in fig. 7 as a single processor 705, two or more processors may be used depending on the particular needs, desires, or particular implementations of the computer 702. In general, the processor 705 executes instructions and manipulates data to perform the operations of the computer 702 and any algorithms, methods, functions, processes, flows, and processes described in this disclosure.

The computer 702 further includes: a database 706 that can hold data for the computer 702 or other components (or a combination of both) that can be connected to the network 730 (whether shown or not). For example, database 706 may be an internal memory (in-memory), a conventional or other type of database that stores data consistent with the present disclosure. In some embodiments, the database 706 can be a combination of two or more different database types (e.g., a hybrid internal memory and a traditional database) depending on the particular needs, desires, or particular embodiments of the computer 702 and the functionality described. Although shown as a single database 706 in FIG. 7, two or more databases (of the same or combined type) may be used depending on the particular needs, desires, or particular implementations of the computer 702 and the functionality described. Although database 706 is shown as an integrated component of computer 702, in alternative embodiments, database 706 may be external to computer 702. As shown, database 706 holds wavefields 716, separated wavefields 718, and filtered wavefields 720.

The computer 702 further includes: a memory 707 that holds data for the computer 702 and other components (or a combination of both) that may be connected to a network 730 (whether shown or not). For example, the memory 707 may be Random Access Memory (RAM), Read Only Memory (ROM), optical, magnetic, etc. that stores data consistent with the present disclosure. In some embodiments, the memory 707 can be a combination of two or more different types of memory (e.g., a combination of RAM and magnetic memory) depending on the particular needs, desires, or particular embodiments of the computer 702 and the functions described. Although illustrated in fig. 7 as a single memory 707, two or more memories 707 (of the same or combined type) may be used depending on the particular needs, desires, or particular implementations of the computer 702 and the functions described. While the memory 707 is shown as an integrated component of the computer 702, in alternative embodiments, the memory 707 may be external to the computer 702.

Applications 708 are algorithmic software engines that provide functionality according to particular needs, desires, or particular implementations of computer 702 (particularly with respect to the functionality described in this disclosure). For example, application 708 can function as one or more components, modules, or applications. Further, although illustrated as a single application 708, application 708 may be implemented as multiple applications 708 on computer 702. Additionally, although shown as being integrated with computer 702, in alternative embodiments, application 708 may be external to computer 702.

There may be any number of computers 702 associated with or external to the computer system containing the computer 702, each computer 702 communicating over the network 730. Moreover, the terms "client," "user," and other suitable terms may be used interchangeably, as appropriate, without departing from the scope of the present disclosure. Further, the present disclosure contemplates that many users can use one computer 702, or that one user can use multiple computers 702.

Implementations of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory computer-readable storage medium for execution by, or to control the operation of, data processing apparatus. Alternatively or additionally, program instructions may be encoded in/on an artificially generated propagated signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of computer storage media.

The terms "data processing apparatus," "computer," or "electronic computer apparatus" (or equivalents thereof as understood by those of ordinary skill in the art) refer to data processing hardware and include various apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can also be or include special purpose logic circuitry, e.g., a Central Processing Unit (CPU), an FPGA (field programmable gate array), or an ASIC (application-specific integrated circuit). In some embodiments, the data processing apparatus or dedicated logic circuitry (or a combination of the data processing apparatus or dedicated logic circuitry) may be hardware-based or software-based (or a combination of hardware-based and software-based). The apparatus can optionally include code that creates an execution environment for the computer program, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of execution environments. The present disclosure contemplates the use of data processing devices with or without a legacy operating system (e.g., LINUX, UNIX, WINDOWS, MAC OS, ANDROID, IOS, or any other suitable legacy operating system).

A computer program (which may also be referred to or described as a program, software application, module, software module, script, or code) can be written in any form of programming language, including: a compiled or interpreted language, or a declarative or procedural language, and the computer program may be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. The computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. While the portions of the program shown in the figures are illustrated as respective modules implementing the respective features and functions through various objects, methods, or other processes, the program may instead include a plurality of sub-modules, third party services, components, libraries, or the like, as appropriate. Rather, the features and functionality of the various components may be combined into a single component, as appropriate. The threshold for making the computational determination may be determined statistically, dynamically, or both.

The methods, processes, and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The methods, processes, or logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry (e.g., a CPU, FPGA, or ASIC).

A computer suitable for execution of a computer program may be based on a general purpose or special purpose microprocessor, both or any other type of CPU. Generally, a CPU will receive instructions and data from a read-only memory (ROM) or a Random Access Memory (RAM) or both. The essential elements of a computer are a CPU for executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. However, the computer need not have these devices. Further, the computer may be embedded in another device, e.g., a mobile telephone, a Personal Digital Assistant (PDA), a mobile audio or video player, a game player, a Global Positioning System (GPS) receiver, or a portable storage device (e.g., a Universal Serial Bus (USB) flash drive), to name a few.

Computer-readable media (suitable transitory or non-transitory) suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, such as erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory devices; magnetic disks (e.g., internal hard disks or removable disks); magneto-optical disks; and CD-ROM, DVD +/-R, DVD-RAM and DVD-ROM disks. The memory may store various objects or data, including: caches, classes, frames, applications, backup data, jobs, web pages, web page templates, database tables, knowledge bases storing dynamic information, and any other suitable information including any parameters, variables, algorithms, instructions, rules, constraints, references thereto. Further, the memory may include any other suitable data, such as logs, policies, security or access data, reporting files, and the like. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device (e.g., a CRT (cathode ray tube), LCD (liquid crystal display), LED (light emitting diode), or plasma monitor) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse, a trackball, or a trackpad) by which the user can provide input to the computer. Touch screens (e.g., a tablet computer surface with pressure sensitivity, a multi-touch screen using capacitive or electrical sensing, or other types of touch screens) may also be used to provide input to the computer. Other types of devices may also be used to provide for interaction with a user; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. Further, the computer may interact with the user by sending documents to and receiving documents from the device used by the user; for example, a user is interacted with by sending a web page to a web browser on a user client device in response to a request received from the web browser.

The terms "graphical user interface" or "GUI" may be used in the singular or plural to describe one or more graphical user interfaces and each display of a particular graphical user interface. Thus, the GUI may represent any graphical user interface, including but not limited to a web browser, touch screen, or Command Line Interface (CLI) that processes information and efficiently presents the results of the information to the user. In general, a GUI may include a number of User Interface (UI) elements, some or all of which are associated with a web browser, such as interactive fields, drop-down lists, and buttons. These and other UI elements may relate to or represent functionality of a web browser.

Implementations of the subject matter described in this specification can be implemented in a computing system that includes a back-end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a client computer having a graphical user interface or a web browser through which a user can interact with an implementation of the subject matter described in this specification), or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by a medium of wired or wireless digital data communication (or a combination of data communication) or any form (e.g., communication network). Examples of communication networks include a Local Area Network (LAN), a Radio Access Network (RAN), a Metropolitan Area Network (MAN), a Wide Area Network (WAN), Worldwide Interoperability for Microwave Access (WIMAX), a Wireless Local Area Network (WLAN) using, for example, 802.11a/b/g/n or 802.20 (or a combination of 802.11x and 802.20 or other protocols consistent with this disclosure), all or a portion of the internet, or any other communication system or system at one or more locations (or combination of communication networks). The network may communicate, for example, Internet Protocol (IP) packets, frame relay frames, Asynchronous Transfer Mode (ATM) cells, voice, video, data, or other suitable information (or combination of communication types) between network addresses.

The computer system may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

While this specification contains many specific implementation details, these should not be construed as limitations on the scope of the disclosure or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of the disclosure. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Furthermore, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

Specific embodiments of the present subject matter have been described. Other implementations, modifications, and substitutions of the described implementations are apparent to those of skill in the art and are within the scope of the following claims. Although operations are depicted in the drawings or claims in a particular order, this should not be understood as: it may be desirable to perform the operations in the particular order shown, or in sequential order, or to perform all of the operations shown (some of which may be considered optional) in order to achieve desirable results. In some cases, multitasking or parallel processing (or a combination of multitasking and parallel processing) may be advantageous and performed as deemed appropriate.

Moreover, the separation or integration of various system modules and components in the foregoing embodiments is not to be understood as requiring such separation or integration in all embodiments, and it is to be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

Accordingly, the example embodiments described previously do not define or limit the disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure.

Moreover, any claimed embodiments are considered at least applicable to a computer-implemented method; a non-transitory computer-readable medium storing computer-readable instructions for performing a computer-implemented method; and a computer system comprising a computer memory interoperably coupled with a hardware processor configured to perform a computer-implemented method or instructions stored on a non-transitory computer-readable medium.