Patent Description:
The present disclosure relates generally to performing efficient modeling, and more specifically, to modeling of extended-duration moving seismic sources.

A seismic survey includes generating an image or map of a subsurface region of the Earth by sending sound energy down into the ground and recording the reflected sound energy that returns from the geological layers within the subsurface region. During a seismic survey, an energy source is placed at various locations on or above the surface region of the Earth, which may include hydrocarbon deposits or formations suitable for long-term underground fluid storage. Each time the source is activated, the source generates a seismic (e.g., sound wave) signal that travels downward through the Earth, is reflected, and, upon its return, is recorded using one or more receivers disposed on or above the subsurface region of the Earth. The seismic data recorded by the receivers may then be used to create an image or profile of the corresponding subsurface region.

Methods for modeling moving seismic sources executed by a computer system are provided according to claims <NUM> and <NUM>.

A tangible, non-transitory, machine-readable media, comprising instructions that when executed cause a processor to execute a methods for modeling moving seismic sources is provided according to claim <NUM>.

Vibratory marine seismic sources are a topic of renewed interest in seismic acquisition. Marine sources are generally moving while sourcing, so a vibratory source's "shot point" will generally be spread out along the source's path, introducing a new complication for processing compared to traditional impulsive sources. If the source signature duration is relatively short, or the data are acquired with the sources and receivers moving together (e.g. streamer acquisition), or the moving sources or receivers are densely sampled, then there are existing methods for pre-processing the data to correct for the motion. After the correction, traditional processing (which assumes the sources and receivers are stationary) will then be applied to process the seismic data.

However, data generated from extended-duration or continuous sources shooting into stationary receivers, especially when the sources are sparsely sampled, may not be amenable to the pre-processing approach outlined above. In such cases, the sources' motion may instead be included in the wavefield extrapolation step of the processing algorithm (e.g. modeling, migration, inversion, etc.). However, inclusion of the motion of the sources may cause the processing to be less efficient.

For example, if the vibratory source's signature lasts for <NUM> seconds, but the waves of interest traverse the model in <NUM> seconds, their sum (<NUM> seconds of propagation time) is modeled to capture the desired output. However, if the source were a traditional impulsive source instead of a vibratory source, modeling <NUM> seconds of propagation time would be sufficient to capture the desired result. Thus, brute-force modeling of the vibratory source's signature is <NUM> times more costly in view of the additional propagation time that is modeled.

For the case of a non-moving vibratory source, deconvolution or pulse compression can be utilized to cause the signature of the source to be more impulsive prior to injecting it into the numerical model to improve efficiency (similar to techniques for processing data from land vibratory sources). However, direct application of this technique may not yield accurate results when the seismic source is moving while sounding.

Typically, there are many more sources than receivers in seismic acquisition. The principle of seismic reciprocity states that the roles of sources and receivers can be swapped and the same data will be recorded (i.e., without affecting the recorded data). Additionally, it is possible to model one source sounding simultaneously into multiple receivers. Therefore, if there are more receivers than sources (e.g., <NUM> times as many receivers as sources), by making use of reciprocity we can process the data <NUM> times more efficiently. However, reciprocity does not directly apply if the sources and/or receivers are moving, so again, for the case of moving vibratory sources, there may be a significant penalty in computational efficiency.

In situations in which seismic data is acquired in a way that makes it difficult to use one of the existing techniques to pre-process the data to correct for the source motion, then one or more embodiments described herein can be used to more efficiently model a moving source in modeling, migration, and/or inversion algorithms. One such situation includes the source being recorded by stationary receivers where the source moves in jumps instead of continuously. By replacing the moving source with a sum of stationary ones, and noting that for each stationary source the computational techniques of deconvolution and reciprocity apply as usual, the correct generalizations and applications of the techniques described above can be determined and then applied to the case of a continuously moving source. While an accompanying computational increase occurs, by taking advantage of the linearity of the wave equation, most of the efficiency savings of the computational techniques can be maintained.

Document <CIT> describes a method for seismic exploration using moving marine vibrators, wherein effects of different position during activation of moving seismic sources are corrected with a procedure of desmearing of a seismic signal produced by the seismic sources.

Document <CIT> describes a method for generating an image of a subsurface of a geographical area using seismic data, wherein the source used to generate seismic waves is a moving, non-impulsive source.

Document <CIT> describes a method for processing reflected seismic waves to correct for motion of a ship which generated incident seismic waves.

By way of introduction, seismic data may be acquired using a variety of seismic survey systems and techniques, two of which are discussed with respect to <FIG> and <FIG>. Regardless of the seismic data gathering technique utilized, after the seismic data is acquired, a computing system may analyze the acquired seismic data and may use the results of the seismic data analysis (e.g., seismogram, map of geological formations, etc.) to perform various operations within the hydrocarbon exploration and production industries. For instance, <FIG> illustrates a flow chart of a method <NUM> that details various processes that may be undertaken based on the analysis of the acquired seismic data for the purpose of oil / gas production. Likewise, <FIG> illustrates a method <NUM> that details an alternative workflow that may be undertaken for the purpose of carbon capture and storage. Although methods <NUM> and <NUM> are described as consisting of steps that occur in a particular order, it should be noted that the steps in methods <NUM> and/or <NUM> may be performed in any suitable order.

Referring now to <FIG>, at block <NUM>, locations and properties of hydrocarbon deposits within a subsurface region of the Earth associated with the respective seismic survey may be determined based on the analyzed seismic data. In one embodiment, the seismic data acquired are analyzed to generate a map or profile that illustrates various geological formations within the subsurface region. Based on the identified locations and properties of the hydrocarbon deposits, at block <NUM>, certain positions or parts of the subsurface region may be explored. That is, hydrocarbon exploration organizations may use the locations of the hydrocarbon deposits to determine locations at the surface of the subsurface region to drill into the Earth. As such, the hydrocarbon exploration organizations may use the locations and properties of the hydrocarbon deposits and the associated overburdens to determine a path along which to drill into the Earth, how to drill into the Earth, and the like.

After exploration equipment has been placed within the subsurface region, at block <NUM>, the hydrocarbons that are stored in the hydrocarbon deposits may be produced via natural flowing wells, artificial lift wells, and the like. At block <NUM>, the produced hydrocarbons may be transported to refineries and the like via transport vehicles, pipelines, and the like. At block <NUM>, the produced hydrocarbons may be processed according to various refining procedures to develop different products using the hydrocarbons.

It should be noted that the processes discussed with regard to the method <NUM> may include other suitable processes that may be based on the locations and properties of hydrocarbon deposits as indicated in the seismic data acquired via one or more seismic survey. As such, it should be understood that the processes described above are not intended to depict an exhaustive list of processes that may be performed after determining the locations and properties of hydrocarbon deposits within the subsurface region.

Method <NUM>, as illustrated in <FIG>, is similar to method <NUM> except that the goal is not removing hydrocarbons from the Earth but safely storing unwanted fluids in the Earth. Block <NUM> is analogous to block <NUM>, except the goal is to identify locations with underground formations suitable for storage. Block <NUM> may be performed using, for example, existing data, such as, seismic data, well logs, etc. It is desirable to verify (for example, in real time) that the storage is successful, so, in block <NUM>, a baseline seismic survey is acquired. Typically block <NUM> is performed prior to the injection of any fluids into the Earth. Block <NUM> is analogous to block <NUM> of method <NUM> and block <NUM> is analogous to block <NUM> of method <NUM>, but again with the goal of injecting fluids (e.g., gasses or liquids) into an underground reservoir instead of extracting oil or gas. At block <NUM> an additional survey is conducted. This survey may be a monitoring survey over the area of the injection and, in some embodiments, may be a "4D" seismic survey that monitors the area of the injection over time.

In block <NUM>, the survey from block <NUM> is processed. This may include performing 4D processing on the seismic survey to monitor subsurface fluid motion and to determine if the motion is as expected (i.e., the data in block <NUM> is analyzed to monitor the status of the injected fluids). At block <NUM>, an operational decision is made based on the results of block <NUM> as to whether to continue the injection at the current well (e.g., return to step <NUM>), drill a new well nearby (e.g., return to step <NUM>), or cease injection in the area.

With the foregoing in mind, <FIG> is a schematic diagram of a marine survey system <NUM> (e.g., for use in conjunction with block <NUM> of <FIG> or block <NUM> of <FIG>) that may be employed to acquire seismic data (e.g., waveforms) regarding a subsurface region of the Earth in a marine environment. Generally, a marine seismic survey using the marine survey system <NUM> may be conducted in an ocean <NUM> or other body of water over a subsurface region <NUM> of the Earth that lies beneath a seafloor <NUM>. The marine survey system may be an Ocean Bottom Seismic (OBS) system that operates to generate seismic data (e.g., OBS datasets).

The marine survey system <NUM> may include a vessel <NUM>, one or more seismic sources <NUM>, an ocean-bottom cable <NUM>, one or more (seismic) receivers <NUM> along the cable <NUM>, and/or other equipment that may assist in acquiring seismic images representative of geological formations within a subsurface region <NUM> of the Earth located beneath the seafloor <NUM>. The vessel <NUM> may tow the seismic source(s) <NUM> (e.g., an air gun array) that may produce energy, such as sound waves (e.g., seismic waveforms), that is directed at a seafloor <NUM>. The ocean-bottom cable <NUM> includes one or more receivers <NUM> (e.g., hydrophones) that record seismic waveforms that represent the energy output by the seismic source(s) <NUM> subsequent to being reflected off of various geological formations (e.g., salt domes, faults, folds, etc.) within the subsurface region <NUM>. For example, data may be stored in the one or more receivers <NUM> for an extended period of time (e.g., hours, days, weeks, or longer) prior to the stored data being retrieved (either via cable <NUM> or optically, or downloaded after recovery). As illustrated, the one or more receivers <NUM> may be coupled to a vessel <NUM> (and, in some embodiments, to one another) via the cable <NUM>. The ocean-bottom cable <NUM> may be a fiber-optic cable utilizing distributed acoustic sensing techniques to synthesize receivers at arbitrary locations along its length. Moreover, data acquired via the one or more receivers <NUM> may be transmitted via the cable <NUM> to the vessel <NUM> (or, for example, optically or after recovery if the OBS system is an Ocean Bottom Node system).

Moreover, while the illustrated OBS system is an Ocean Bottom Cable (OBC) system inclusive of one or more receivers <NUM> disposed on the seafloor <NUM> coupled via a cable <NUM> to a second vessel <NUM>, other embodiments of an OBS system, such as an Ocean Bottom Node (OBN) system or any other seismic recording system may be utilized. That is, there may be no cable <NUM>, with the receivers <NUM> instead deployed individually as nodes, which may be located on the seafloor <NUM>, or tethered, floating, or actively maneuvering in the water column. In some embodiments, the cable <NUM> may be located in the water column instead of on the seafloor <NUM>. The second (recording) vessel <NUM> may instead be a fixed structure such as a platform, or the cable <NUM> may run to shore and terminate on land. The receivers <NUM> may be located inside a borehole (e.g. as part of a Vertical Seismic Profile recording system), or trenched into the sea floor.

Additionally, although the description of the marine survey system <NUM> is described with one seismic source <NUM> (represented in <FIG> as an air gun array) and one type of receiver <NUM> (represented in <FIG> as a set of hydrophones), it should be noted that the marine survey system <NUM> may include multiple seismic sources <NUM> and one or more receivers <NUM>, and these may be of multiple types. In the same manner, although the above descriptions of the marine survey system <NUM> are described with ocean-bottom cable <NUM>, it should be noted that the marine survey system <NUM> may include multiple cables <NUM> similar to cable <NUM>. In addition, additional vessels <NUM> may include additional seismic source(s) <NUM> to perform the operations of the marine survey system <NUM>, and the additional sources may be of different types. The vessels <NUM> may also tow streamers with additional receivers <NUM> that move with the sources <NUM> (e.g., traditional towed-streamer recording). In some embodiments all the receivers <NUM> may move with the sources <NUM>.

In some embodiments, the OBS system may be utilized to acquire OBS datasets that are useful in reservoir mapping and characterization. These OBS datasets typically have a bandwidth from approximately <NUM> to <NUM> with relatively high signal-to-noise ratio (SNR) results at low frequencies (e.g., at less than or equal to approximately <NUM>, <NUM>, <NUM>, etc.) relative to 3DHR datasets. Therefore, the OBS dataset is complementary with respect to the bandwidth of a 3DHR dataset acquired via the marine survey system <NUM> (e.g., acquired via a 2D high-resolution seismic acquisition, a 3D high-resolution seismic acquisition, or the like).

Although the methods and systems described herein are primarily directed to marine applications, they also may be applicable in land seismic operations, e.g. to the case of a moving vibratory land source. Regardless of how the seismic data are acquired, a computing system (e.g., for use in conjunction with block <NUM> of <FIG> and block <NUM> of <FIG>) may analyze the seismic waveforms acquired by the seismic receivers <NUM>, <NUM>, and/or <NUM> to determine information regarding the geological structure, the location and property of hydrocarbon deposits, the area for storage of fluids, and the like within the subsurface region <NUM>.

<FIG> is a block diagram of a land survey system <NUM> (e.g., for use in conjunction with block <NUM> of <FIG> and block <NUM> of <FIG>) that may be employed to obtain information regarding the subsurface region <NUM> of the Earth in a non-marine environment. The land survey system <NUM> may include a land-based seismic source <NUM> and land-based receiver <NUM>. In some embodiments, the land survey system <NUM> may include multiple land-based seismic sources <NUM> and one or more land-based receivers <NUM> and <NUM>. Indeed, for discussion purposes, the land survey system <NUM> includes a land-based seismic source <NUM> and two land-based receivers <NUM> and <NUM>. The land-based seismic source <NUM> (e.g., seismic vibrator) may be disposed on a surface <NUM> of the Earth above the subsurface region <NUM> of interest. The land-based seismic source <NUM> may produce energy (e.g., sound waves, seismic waveforms) that is directed at the subsurface region <NUM> of the Earth. Upon reaching various geological formations (e.g., salt domes, faults, folds) within the subsurface region <NUM> the energy output by the land-based seismic source <NUM> may be reflected off of the geological formations and acquired or recorded by one or more land-based receivers (e.g., <NUM> and <NUM>).

In some embodiments, the land-based receivers <NUM> and <NUM> may be dispersed across the surface <NUM> of the Earth to form a grid-like pattern. As such, each land-based receiver <NUM> or <NUM> may receive a reflected seismic waveform in response to energy being directed at the subsurface region <NUM> via the seismic source <NUM>. In some cases, one seismic waveform produced by the seismic source <NUM> may be reflected off of different geological formations and received by different receivers. For example, as shown in <FIG>, the seismic source <NUM> may output energy that may be directed at the subsurface region <NUM> as seismic waveform <NUM>. A first receiver <NUM> may receive the reflection of the seismic waveform <NUM> off of one geological formation and a second receiver <NUM> may receive the reflection of the seismic waveform <NUM> off of a different geological formation. As such, the first receiver <NUM> may receive a reflected seismic waveform <NUM> and the second receiver <NUM> may receive a reflected seismic waveform <NUM>.

Regardless of how the seismic data are acquired, according to the embodiments, a computing system (e.g., for use in conjunction with block <NUM> of <FIG> and block <NUM> of <FIG>) analyzes the seismic waveforms acquired by the receivers <NUM>, <NUM>, <NUM> to determine seismic information regarding the geological structure, the location and property of hydrocarbon deposits, and the like within the subsurface region <NUM>. <FIG> is a block diagram of an example of such a computing system <NUM> that may perform various data analysis operations to analyze the seismic data acquired by the receivers <NUM>, <NUM>, <NUM> to determine the structure and/or predict seismic properties of the geological formations within the subsurface region <NUM>.

Referring now to <FIG>, the computing system <NUM> may include a communication component <NUM>, a processor <NUM>, memory <NUM>, storage <NUM>, input/output (I/O) ports <NUM>, and a display <NUM>. In some embodiments, the computing system <NUM> may omit one or more of the display <NUM>, the communication component <NUM>, and/or the input/output (I/O) ports <NUM>. The communication component <NUM> may be a wireless or wired communication component that may facilitate communication between the receivers <NUM>, <NUM>, <NUM>, one or more databases <NUM>, other computing devices, and/or other communication capable devices. In one embodiment, the computing system <NUM> may receive receiver data <NUM> (e.g., seismic data, seismograms, etc.) via a network component, the database <NUM>, or the like. The processor <NUM> of the computing system <NUM> may analyze or process the receiver data <NUM> to ascertain various features regarding geological formations within the subsurface region <NUM> of the Earth.

The processor <NUM> may be any type of computer processor or microprocessor capable of executing computer-executable code. The processor <NUM> may also include multiple processors that may perform the operations described below. The memory <NUM> and the storage <NUM> may be any suitable articles of manufacture that can serve as media to store processor-executable code, data, or the like. These articles of manufacture may represent computer-readable media (e.g., any suitable form of memory or storage) that may store the processor-executable code used by the processor <NUM> to perform the presently disclosed techniques. Generally, the processor <NUM> may execute software applications that include programs that process seismic data acquired via receivers of a seismic survey according to the embodiments described herein.

The memory <NUM> and the storage <NUM> may also be used to store the data, analysis of the data, the software applications, and the like. The memory <NUM> and the storage <NUM> may represent non-transitory computer-readable media (e.g., any suitable form of memory or storage) that may store the processor-executable code used by the processor <NUM> to perform various techniques described herein. It should be noted that non-transitory merely indicates that the media is tangible and not a signal.

The I/O ports <NUM> may be interfaces that may couple to other peripheral components such as input devices (e.g., keyboard, mouse), sensors, input/output (I/O) modules, and the like. I/O ports <NUM> may enable the computing system <NUM> to communicate with the other devices in the marine survey system <NUM>, the land survey system <NUM>, or the like via the I/O ports <NUM>.

The display <NUM> may depict visualizations associated with software or executable code being processed by the processor <NUM>. In one embodiment, the display <NUM> may be a touch display capable of receiving inputs from a user of the computing system <NUM>. The display <NUM> may also be used to view and analyze results of the analysis of the acquired seismic data to determine the geological formations within the subsurface region <NUM>, the location and property of hydrocarbon deposits within the subsurface region <NUM>, predictions of seismic properties associated with one or more wells in the subsurface region <NUM>, and the like. The display <NUM> may be any suitable type of display, such as a liquid crystal display (LCD), plasma display, or an organic light emitting diode (OLED) display, for example. In addition to depicting the visualization described herein via the display <NUM>, it should be noted that the computing system <NUM> may also depict the visualization via other tangible elements, such as paper (e.g., via printing) and the like.

With the foregoing in mind, the present techniques described herein may also be performed using a supercomputer that employs multiple computing systems <NUM>, a cloud-computing system, or the like to distribute processes to be performed across multiple computing systems <NUM>. In this case, each computing system <NUM> operating as part of a super computer may not include each component listed as part of the computing system <NUM>. For example, each computing system <NUM> may not include the display <NUM> since multiple displays <NUM> may not be useful to for a supercomputer designed to continuously process seismic data.

After performing various types of seismic data processing, the computing system <NUM> may store the results of the analysis in one or more databases <NUM>. The databases <NUM> may be communicatively coupled to a network that may transmit and receive data to and from the computing system <NUM> via the communication component <NUM>. In addition, the databases <NUM> may store information regarding the subsurface region <NUM>, such as previous seismograms, geological sample data, seismic images, and the like regarding the subsurface region <NUM>.

Although the components described above have been discussed with regard to the computing system <NUM>, it should be noted that similar components may make up the computing system <NUM>. Moreover, the computing system <NUM> may also be part of the marine survey system <NUM> or the land survey system <NUM>, and thus may monitor and control certain operations of the seismic sources <NUM> or <NUM>, the receivers <NUM>, <NUM>, <NUM>, and the like. Further, it should be noted that the listed components are provided as example components and the embodiments described herein are not to be limited to the components described with reference to <FIG>.

In some embodiments, the computing system <NUM> may generate a two-dimensional representation or a three-dimensional representation of the subsurface region <NUM> based on the seismic data received via the receivers mentioned above. Additionally, seismic data associated with multiple source/receiver combinations may be combined to create a near continuous profile of the subsurface region <NUM> that can extend for some distance. In a two-dimensional (<NUM>-D) seismic survey, the receiver locations may be placed along a single line, whereas in a three-dimensional (<NUM>-D) survey the receiver locations may be distributed across the surface in a grid pattern. As such, a <NUM>-D seismic survey may provide a cross sectional picture (vertical slice) of the Earth layers as they exist directly beneath the recording locations. A <NUM>-D seismic survey, on the other hand, may create a data "cube" or volume that may correspond to a <NUM>-D picture of the subsurface region <NUM>.

In addition, a <NUM>-D (or time-lapse) seismic survey may include seismic data acquired during a <NUM>-D or <NUM>-D survey at multiple times. Using the different seismic images acquired at different times, the computing system <NUM> may compare the two images to identify changes in the subsurface region <NUM>.

In any case, a seismic survey may be composed of a very large number of individual seismic recordings or traces. As such, the computing system <NUM> may be employed to analyze the acquired seismic data to obtain an image representative of the subsurface region <NUM> and to determine locations and properties of hydrocarbon deposits. To that end, a variety of seismic data processing algorithms may be used to remove noise from the acquired seismic data, migrate the pre-processed seismic data, identify shifts between multiple seismic images, align multiple seismic images, and the like.

After the computing system <NUM> analyzes the acquired seismic data, in the embodiments, the results of the seismic data analysis (e.g., seismogram, seismic images, map of geological formations, etc.) are used to perform various operations within the hydrocarbon exploration and production industries. For instance, as described above, the acquired seismic data may be used to perform the method <NUM> of <FIG> or the method <NUM> of <FIG> that details various processes that may be undertaken based on the analysis of the acquired seismic data.

In some embodiments, the results of the seismic data analysis may be generated in conjunction with a seismic processing scheme that includes seismic data collection, editing of the seismic data, initial processing of the seismic data, signal processing, conditioning, and imaging (which may, for example, include production of imaged sections or volumes) prior to any interpretation of the seismic data, any further image enhancement consistent with the exploration objectives desired, generation of attributes from the processed seismic data, reinterpretation of the seismic data as needed, and determination and/or generation of a drilling prospect or other seismic survey applications. As a result, location of hydrocarbons within a subsurface region <NUM> is identified. Likewise, operational decisions <NUM> may be made based on the seismic data.

Marine vibratory marine seismic sources, as seismic source <NUM>, are generally moving while sourcing, so a vibratory source's "shot point" will be spread out along the source's path. Although current land vibratory sources do not typically move while sourcing, future land vibratory sources may do so. A moving vibratory source's motion may introduce a new complication for processing compared to traditional impulsive sources (where the source imparts its energy into the subsurface <NUM> at approximately a single time or at a relatively short duration of time). If the source signature duration is relatively short, or the data are acquired with the sources and receivers moving together and the array of receivers spatially sample the wavefield sufficiently well (e.g. streamer acquisition), the data can be corrected for the motion so that traditional processing techniques will work to process the acquired seismic signal. However, extended-duration or continuous sources, especially shooting into stationary receivers (e.g., receivers <NUM>), may require the modeling of the source as moving in our modeling, migration, and/or inversion algorithms. To perform this efficiently, reworking of two computational techniques, <NUM>) pulse compression (deconvolution) of the source signature, and <NUM>) using reciprocity to swap the roles of sources and receivers, is undertaken. As discussed in greater detail below, the continuous movement of the source can be approximated as moving in jumps instead of continuously, and is recorded by stationary receivers <NUM>. By replacing a moving seismic source <NUM> with a sum of stationary ones, and noting that for each stationary seismic source <NUM> the standard computational techniques of deconvolution and reciprocity apply as usual, the approximation (moving in jumps) can be utilized to form correct generalizations and can be applied to the case of a continuously moving seismic source <NUM>. While an accompanying computational increase occurs, by taking advantage of the linearity of the wave equation, most of the efficiency savings of the computational techniques can be maintained.

Generally, seismic processing algorithms assume stationary sources (e.g., seismic source <NUM>) and receivers (e.g., receivers <NUM>). In typical acquisition, while the hardware of the seismic source <NUM> may be towed (moving), the released bubble(s) of air that operate as the source are stationary. Therefore, knowing the location of the seismic source <NUM> when fired gives the location of the shot, i.e., the shot location. Likewise, even if receivers <NUM> are towed, the location of each receiver <NUM> at a given time is known. This provides the location of the receiver <NUM> as it records a wavefield and, as the receivers <NUM> are typically numerous and closely spaced, the recorded wavefield can be interpolated back onto a non-moving recording grid, exactly as if it had been recorded with stationary receivers <NUM>. Thus, it is typical to take the data as recorded (with motion due to the seismic sources <NUM> and/or receivers <NUM> being towed), perform a shifting interpolation on the data to correct for the receiver motion (i.e., motion correction pre-processing of the received data), then apply processing algorithms as if the data were generated and received by fixed seismic sources <NUM> and receivers <NUM>.

For a non-impulsive seismic source (where the seismic source imparts its energy into the subsurface <NUM> over a relatively long period of time rather than at approximately a single time or at a relatively short duration of time) as the seismic source <NUM>, the frequency often monotonically increases or decreases over time. An example of this is illustrated in the graph <NUM> of <FIG>. As illustrated, in the graph <NUM>, the frequency of the seismic source signal <NUM> increases over time as it moves (e.g., as it is towed). This allows for a determination of the location (position) of the seismic source for a given recorded seismic signal, since the frequency corresponds to the source time. For example, as illustrated, various frequencies of the seismic source signal <NUM> occur at corresponding times and there is a one-to-one relationship between the position of the seismic source <NUM> and the frequency illustrated as average shot times <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, and <NUM>.

Thus, taking the data as recorded (with motion due to the seismic sources <NUM> and/or receivers <NUM> being towed), a similar process to that described above with respect to impulsive seismic sources <NUM> may be undertaken. More particularly, the recorded wavefields can be interpolated onto a new stationary or fixed grid using the frequency to determine the location of the seismic source <NUM> as the sound was generated. In this manner, the data as recorded can have a source motion correction applied thereto, a receiver motion correction applied, which results in data with fixed seismic sources <NUM> and receivers <NUM> to which processing algorithms are applied as if the data were generated and received by fixed seismic sources <NUM> and receivers <NUM>.

However, in more general cases (i.e., where the seismic sources <NUM> are arbitrary), the data may not be sufficiently spatially sampled (e.g., the seismic sources <NUM> may be fired or positioned too infrequently to provide a sufficient sampling of the wave field), which may be a result of long sweep times, the result of adding additional frequencies (e.g., high frequency transmissions on the end of low frequency sweep), harmonics, etc., that are not sufficiently well sampled. Likewise, the source signature could be scrambled (e.g., may include white or pseudo-random noise), such that the source frequencies are scrambled along the source path and there is not a simple relationship between frequency and source time. These issues can be modeled "as is", i.e., with the processing in the computer mirroring the actual acquisition. However, this is computationally inefficient and costly. Alternatively alternate solutions are available, as discussed below.

Present embodiments herein are described in conjunction with situations in which there is a fixed receiver <NUM> (e.g., an OBS system, such as an OBN system) and moving seismic sources <NUM>. However, the techniques described herein also may be used in situations where the receivers <NUM> are moving and the seismic sources <NUM> are fixed, or where both sources <NUM> and receivers <NUM> are moving but the data can be pre-processed to simulate data recorded with either stationary sources <NUM> or stationary receivers <NUM>, for example using the techniques already described. Thus, as described below, the problem being considered is for OBN acquisition with an arbitrary source (e.g., the seismic source <NUM> can me moving, well sampled, poorly sampled, an arbitrary source signature, etc.). The receivers <NUM> are stationary receivers. There are techniques that typically are used to process data in the OBN system, for example, reciprocity. There are typically many more shot points than there are receivers <NUM> and reciprocity allows for the swapping of the roles of sources (e.g., shot points of the seismic source <NUM>) and receivers (so as not to model the wave field from each shot into the fewer number of receivers <NUM>). Reciprocity provides that for a seismic source <NUM> and receiver <NUM>, the trace that is recorded for that shot-receiver pair is identical if the roles of the seismic source <NUM> and receiver <NUM> are interchanged. This allows the receivers <NUM> (fewer in number) to be treated as sources, whereby each receiver <NUM> is a point having the source emanating therefrom and to the shot locations, which provides the same data set but is computationally more efficient to produce.

Often a notional receiver <NUM> is in reality an array of physical receivers, with the recorded output being a weighted sum of the recordings from all the receivers in the array. Similarly a vibratory source <NUM> or <NUM> often contains multiple sourcing elements (of identical or differing sizes) operating in unison. The principle of reciprocity is directly applicable to the case of a single source and a single receiver, with each being either a point or an array. The source and/or receiver may also have an antenna pattern, for example a marine pressure source being recorded by a vertical geophone on the ocean floor, and reciprocity applies in this case as well. Although the following discussion speaks in terms of omnidirectional point sources and receivers, one of ordinary skill in the art can readily apply the methods described herein to the case of source and/or receiver arrays and of different types of sources and/or receivers.

Reverse-time migration and Full-Waveform Inversion both rely on propagating wavefields forward and/or backwards in time, so the question for application to moving seismic sources <NUM> effectively reduces to doing wave propagation with a moving seismic source <NUM>. Modeling a moving seismic source <NUM> (or receiver <NUM>) is possible, but it introduces extra computations regarding source injection and/or receiver sampling. However, if the source signature extends longer than the time it takes for the waves of interest to make their way from the seismic source <NUM> to receiver <NUM>, then the extra propagation time required to insert the lengthy source signature can entail a significant increase in computational cost. For a stationary seismic source <NUM>, there is a simple solution: first deconvolve the source signature to compress it in time, and then inject the deconvolved signature. For example, in land vibroseis acquisition (e.g., similar to that described in conjunction with <FIG>), where there is an extended-time source signature, pulse compression (e.g., deconvolution) is typically utilized to make the signature more impulsive (e.g., to transform a non-impulsive source signature into an impulsive source signature).

Unfortunately, this technique may not be readily applicable to a moving seismic source <NUM>. Furthermore, the technique of using reciprocity to swap the roles of sources and receivers <NUM> to gain a further significant reduction in computational cost (as there are usually have many more shot points than receivers) also may not be readily available for a moving seismic source <NUM>, potentially greatly increasing the computational cost. However, as will be discussed below, while reciprocity and pulse compression techniques are not generally naively applicable when the seismic sources <NUM> (or receivers <NUM>) are moving, embodiments herein will allow for recovery of most of the savings that would be present if reciprocity and pulse compression techniques were generally naively applicable when the seismic sources <NUM> (or receivers <NUM>) are moving. An example will be discussed below of a simplified case of a moving seismic source <NUM> shooting into a fixed receiver <NUM>. The technique may include approximating the seismic source <NUM> as moving in steps. This examples illustrates why the above noted techniques, unmodified, break down, as well as how to modify them so that they do work in the case involving a moving seismic source <NUM>.

<FIG> illustrates a graph <NUM> of a seismic source signal <NUM> that increases in frequency over time as it moves (e.g., as it is towed). After applying pulse compression to the seismic source signal <NUM>, the duration of the compressed seismic source signal <NUM> is shortened greatly (e.g., there is a greatly reduced sourcing time), as illustrated in the graph <NUM> of <FIG>. Thus, <FIG> demonstrate how deconvolution can compress an extended-time source signature (seismic source signal <NUM>) into a much more compact form (compressed seismic source signal <NUM>). This has advantages for the purpose of modeling using the seismic source signal <NUM>.

For example, assuming the last-arriving waves of interest take <NUM> seconds to travel from source to receiver, then for the seismic source signal <NUM> before deconvolution, there would be modeled approximately <NUM> seconds + <NUM> seconds = <NUM> seconds of propagation time, whereas after deconvolution (i.e., using the compressed seismic source signal <NUM>), there would be modeled approximately <NUM> seconds + <NUM> seconds = <NUM> seconds, a <NUM>-fold savings. This can be accomplished because modeling and deconvolution are both linear operations and commute. Mathematically, deconvolving the seismic source signal <NUM> of <FIG> to generate the compressed seismic source signal <NUM> of <FIG> before modeling with it produces the same result as modeling with the uncompressed source signature (seismic source signal <NUM>) and then deconvolving the recorded output. However, if the seismic source <NUM> is moving there is the additional step of moving the seismic source <NUM> along its path as it is sounding, and this step does not commute with deconvolution. After pulse compression, the entire source signature (seismic source signal <NUM>) must "happen all at once" along the full path of the seismic source <NUM>. Accordingly, in the embodiments, described herein are techniques to inject that into the model.

<FIG> illustrates the graph <NUM> of the seismic source signal <NUM> (uncompressed) as broken into partitions, here presented in graphs <NUM>, <NUM>, <NUM>, and <NUM>. Partition <NUM> of graph <NUM> can be summed with partition <NUM> of graph <NUM>, partition <NUM> of graph <NUM>, and partition <NUM> of graph <NUM> to result exactly in the seismic source signal <NUM> of graph <NUM>. In this manner, the moving seismic source <NUM> is represented as a sum of stationary sources, each having a seismic source signal represented by the respective partitions <NUM>, <NUM>, <NUM>, and <NUM> (i.e., the seismic source signal <NUM> is broken up into four intervals, whereby each interval is associated with a fixed position along the track of the moving seismic source <NUM>, thereby approximating the source as moving in discrete jumps). It should be noted that dividing up the source trajectory into four intervals is an example and that greater or fewer than four intervals can be chosen, for example, based on the characteristics of the seismic source signal <NUM>.

As illustrated in <FIG>, in this jumping-source approximation of continuous motion, the first, second, third, and fourth interval sources (representing partitions <NUM>, <NUM>, <NUM>, and <NUM>) are each associated with a respective position (position <NUM>, <NUM>, <NUM>, and <NUM>) along the moving trajectory <NUM> of the seismic source <NUM> in a velocity model <NUM>. A seismic image is constructed using a high resolution seismic velocity model, such as a full waveform inversion (FWI) model, a tomography model, or the like, applied, via a velocity model builder. The velocity model <NUM> may include data indicative of a change in velocity of the seismic waveforms during propagation through the subsurface region <NUM>. A stationary ocean-bottom receiver <NUM> is illustrated as well as wavefronts for position <NUM> and position <NUM>. In this manner, instead of a having a continuous source location, the locations of the seismic source <NUM> can be approximated as fixed sources at the positions <NUM>, <NUM>, <NUM>, and <NUM>. While this is an approximation, as more positions are added, in the limit, the continuous moving source is modeled. And, by approximating the continuously moving seismic source <NUM> as a fixed seismic source <NUM>, pulse compression, reciprocity, etc. are directly applicable to the fixed sources at the positions <NUM>, <NUM>, <NUM>, and <NUM>.

In the illustrated jumping-source approximation of continuous motion in <FIG>, the first, second, third, and fourth interval sources at positions <NUM>, <NUM>, <NUM>, and <NUM>, each operate in turn over the original source's extended time scale (e.g., the time scale of the seismic source signal <NUM>). However, this may not lead to efficient modeling. For example, one issue with continuously moving seismic sources <NUM> is that deconvolution may not commute with source motion. The few seconds of energy illustrated in graph <NUM> was, in reality, inserted into the seafloor <NUM> over the course of approximately <NUM> seconds. Therefore, an issue arises as to how along the moving source path (i.e., the moving trajectory <NUM> of the seismic source <NUM>) should the pulse of energy represented by the compressed seismic source signal <NUM> be inserted.

Accordingly, instead, one model can be performed for each interval. Thus, for each partition <NUM>, <NUM>, <NUM>, and <NUM>, deconvolution can be performed. Thereafter propagation is performed over the time interval and the portion of the model corresponding to that interval's source, and these operations are performed in parallel. The results (appropriately time- and space-aligned) are summed together to model the full time span of the original seismic source <NUM>. This is one embodiment to approximately model a moving seismic source <NUM> and, for some applications, may be selected. In some embodiments, the same deconvolution operator is applied to all partitions, for example, to allow for the results to be summed together to produce an equivalent result to modeling the jumping sources sequentially (but overlapping) in a single model and then applying the deconvolution operator to the result.

By decomposing the problem into a sum of stationary-source models we can also determine how to correctly model with a pulse-compressed (deconvolved) source. Because the "interval sources" are not moving, in each model source signature (seismic source signal partitions <NUM>, <NUM>, <NUM>, and <NUM>) deconvolution may be performed before a wave extrapolation step. Deconvolving the signature of each stationary interval source can be accomplished using the same linear operator designed to deconvolve the original complete moving source signature (seismic source signal <NUM>). The outputs of the four models are then summed, which could also be achieved by simultaneously injecting all four deconvolved interval sources into a single model (i.e., because the same deconvolution operator was utilized for all the interval sources it can be applied before modeling).

However, other embodiments are described below with respect to continuously moving seismic sources <NUM>, as represented on a discrete computational grid. In practice, a seismic source <NUM> may not be located exactly on a grid point <NUM> of a grid <NUM> of locations. Instead, the seismic source <NUM> may be interpolated onto a region <NUM> (e.g., an active interpolation region) of grid points <NUM> surrounding the location of the seismic source <NUM>, as illustrated in <FIG>. As the seismic source <NUM> moves along, grid points <NUM> near its path will enter the region <NUM> (outlined by a dashed line in <FIG>), then leave it as the source moves on past. In some embodiments, the weighting factor applied to the source signature during the time a grid point <NUM> is within the active region <NUM> is determined by the weighting scheme being used to perform the interpolation, for example, sinc interpolation. As illustrated in <FIG>, the varying size of the circles drawn around the active grid points <NUM> diagramatically indicates the magnitude of the corresponding instantaneous interpolation weights at the snapshot time shown in <FIG>. This corresponds to the manner in which the seismic source signal <NUM> was divided into tapered (i.e. weighted) overlapping intervals <NUM>, <NUM>, <NUM>, and <NUM> sourcing at locations <NUM>, <NUM>, <NUM>, and <NUM>, respectively, in <FIG> and <FIG>. The interpolation weights as a function of time determine the weighting function for each grid point <NUM>.

Every grid point <NUM> that is active at any time along the path of the seismic source <NUM> acts as a stationary "interval source" (i.e., a partition source). To deconvolve a continuously moving seismic source <NUM>, seismic source interpolation weights are calculated for each time and grid point <NUM> along the path of the seismic source. Next, the seismic source signature (seismic source signal <NUM>) is multiplied by the calculated seismic source interpolation weights, time step by time step, to allocate the source signature amongst the nearby grid points <NUM>. This is how a moving source is conventionally represented on a discrete grid. This procedure produces a subset source signature for each grid point <NUM> that ever lies within the active interpolation region <NUM> along the path of the seismic source <NUM>. These affected grid points become the stationary interval sources, each with a corresponding subset source signature.

Thereafter, the subset source signature for each affected grid point <NUM> along the path of the seismic source <NUM> is pulse compressed using a global linear deconvolution operator (i.e., the same deconvolution operator is used for every affected grid point <NUM>). Thereafter, the compressed signature for each grid point <NUM> along the path of the seismic source <NUM> may be injected simultaneously during propagation. In this manner, the pulsed-compressed data can be inserted (injected) at the same time along the entire path of the source. The source injection time is determined by the amount of compression of the interval source signatures, which may depend (at least in part) on the speed of the seismic source <NUM> relative to the spacing of the grid <NUM> of locations and on the bandwidth of the source signature. Thus, utilizing the above noted techniques, pulse compression (deconvolution) of the source signature (the seismic source signal <NUM>) can be achieved for a continuously moving (vibratory) seismic source <NUM> in a manner similar to techniques for processing data from stationary land vibratory sources, such as seismic source <NUM>.

Additionally, in some embodiments, it would be advantageous to utilize reciprocity to swap the roles of seismic sources <NUM> and receivers <NUM> for continuously moving (vibratory) seismic sources <NUM>. The principle of seismic reciprocity is a consequence of a mathematical symmetry of the wave equation, and states that if the roles of a seismic source <NUM> and a receiver <NUM> are interchanged in a seismic model, producing a new reciprocal model, the exact same data trace will be recorded in both experiments. This is not equivalent to time reversal - the waves may take very different paths from source to receiver in the two experiments. Likewise, reciprocity does not say anything about what would be recorded at locations other than the particular receiver <NUM> corresponding to the source location in the reciprocal experiment. Reciprocity is particularly useful when modeling ocean-bottom seismic acquisitions because there are typically many more shot points (e.g., sources) than receivers <NUM>. For example, instead of modeling wavefields emanating from millions of shots, we only need to model wavefields emanating from thousands of receivers <NUM> in the reciprocal experiments.

However, referring back to <FIG>, when the seismic source <NUM> is moving, and it is modeled as a "jumping source" as in example of <FIG>, a straightforward attempt to apply the principle of reciprocity to the moving-source case fails. If the problem is run as a unified extended-time model, then the ocean-bottom node turned source would emit the complete source signature (the seismic source signal <NUM>), smoothly transitioning through each of the four interval source's subsets in turn. Meanwhile the jumping source (turned receiver <NUM>) would listen first at the location <NUM> of the first source, then smoothly transition to the second location <NUM>, then the third location <NUM>, and finally the fourth location <NUM> (e.g., source position) in turn.

However, waves emitted, for example, during the initial first part of the source signature would continue to rattle around in the model after the receiver <NUM> had moved on. This can cause an issue, since the output data would then contain waves emitted during the first interval of the source signature but recorded by receivers <NUM> located at the second location <NUM>, third location <NUM>, and fourth location <NUM> (i.e., source positions), which have no reciprocal relationship with the original model. Thus, a naive attempt at applying reciprocity clearly fails in this example, and by extension to moving sources in general.

Instead, in one embodiment, the problem can be solved by breaking the problem down into a sum of the output of models in which the sources <NUM> and receivers <NUM> are stationary. In each of these "interval models" reciprocity applies as usual. Thus, the reciprocal experiments may be independently run, then the results may be summed, and it will produce the correct answer. This technique provides a way to parallelize the extrapolation. However, efficiency may be affected, as the interval models cannot be run in parallel inside the same model (because the interval source signatures differ between the models).

Thus, in another embodiment, all of the source signatures may be set to a common value (i.e., may be made the same), by once again appealing to the linearity of seismic modeling for stationary sources <NUM> and receivers <NUM>. Thus, instead of injecting the source wavelet, an impulse (or band-limited impulse) can be injected, the results recorded, and then the recorded output convolved with the appropriate source wavelet. This technique may also be used more generally as a way of making forward modeling of vibratory signatures more efficient. It is, therefore, not limited to the above described technique or application.

Stated differently, the present embodiment takes advantage of the linearity of seismic modeling for stationary sources <NUM> and stationary receivers <NUM>, since inputting the source signature and modeling it is equivalent to injecting an impulse, modeling it, and then convolving it with the source signature (since all these operations are linear, they can be convolved in any order to produce the same result). This is useful since now the source signature is the same for every partition (an impulse), meaning that the different modeling runs can be accomplished in parallel (simultaneously) in a single numerical model.

Thus, returning to <FIG>, a delta function (e.g., a Dirac delta function) or a band-limited delta function is inserted at the receiver <NUM> (i.e., the reciprocal source location), and measured (recorded or listened for) at the discrete sub-source locations (e.g., locations <NUM>, <NUM>, <NUM>, and <NUM>) along the source path (i.e., the moving trajectory <NUM> of the seismic source <NUM>). Each wavefield that is recorded is then convolved with the corresponding source signature partition, and then the results are summed together. Because the injected source function is the same for all the receivers, the computation may be done in parallel inside a single model. Thus, to perform reciprocal "jumping-source" modeling, the following steps are undertaken: <NUM>) inject an impulse or band-limited impulse at the location of the ocean-bottom receiver <NUM> turned source, <NUM>) record the resulting wavefield at each of the interval-source locations (e.g., locations <NUM>, <NUM>, <NUM>, and <NUM>), <NUM>) for each location <NUM>, <NUM>, <NUM>, and <NUM>), convolve each recorded wavefield with the corresponding interval-source signature, and <NUM>) sum all the results together. Accordingly, to reciprocal model a continuously moving source shooting into a stationary receiver <NUM>, each grid point <NUM> in the grid <NUM> along the path of the seismic source <NUM> is treated as an interval source location with its own unique interval source signature. As before, for further efficiency we can pulse-compress the signatures as this is performed, using the same deconvolution operator across all the intervals.

Finally, in some embodiments, both the seismic sources <NUM> and receivers <NUM> are independently moving. Referring back to <FIG>, now both the seismic source <NUM> and the receiver <NUM> are in a different position in each interval model. This may prevent performing all the interval models together in a single extrapolation. In the most general case all the grid points <NUM> along the path of the seismic source <NUM> could interact with all the grid points <NUM> along the path of the receiver <NUM>, which leads to large complexities. However, if the source signature has the form of a frequency sweep, this can be taken advantage of by breaking the source signature up into overlapping frequency intervals instead of overlapping time intervals. Non-adjacent frequency intervals can be designed to not overlap, and thus can be separated from each other after modeling by frequency filtering. Thus, in the "jumping source" example in <FIG>, intervals <NUM> and <NUM> can be run together in the same model, and in parallel intervals <NUM> and <NUM> can be run together in the same model, then the results can be summed back together. It should be noted that deconvolution does not change the frequency bandwidth (it merely scales the amplitudes within the bandwidth) so it may be applied to compress the source signatures in this case.

Additionally, returning to <FIG>, there is a strategy illustrated for calculating an average source position to use in a time or frequency window. The following equation <NUM> may be calculated: <MAT> where the angle brackets indicate summing over frequency, W(f) is an optional frequency-dependent weighting term specifying the frequency band being considered, W(t) is an optional time-dependent weighting term specifying the time interval being considered, FT indicates Fourier transformation from time t to frequency f, the vertical bars indicate taking the magnitude of the complex expression inside, and Pa(t) is a source signature amplitude as a function of time. The Fourier sum will pick out the stationary point for each frequency, which in the numerator is scaled by time, so dividing produces the time of the stationary point. To instead find the position of the stationary point, time may be replaced with position as the scale factor.

The specific embodiments described above have been shown by way of example, the scope of the invention being defined by the appended claims.

Claim 1:
A method for modeling moving seismic sources (<NUM>, <NUM>), comprising the following steps executed by a computing system (<NUM>):
receiving a set of seismic data comprising a seismic signal (<NUM>) generated by one or more receivers (<NUM>, <NUM>, <NUM>) in response to energy directed at a subsurface region (<NUM>) by one or more seismic sources (<NUM>) over the course of a set period of time as a time scale;
generating a predetermined number of partitioned seismic signals (<NUM>, <NUM>, <NUM>, <NUM>) from the seismic signal, wherein each partitioned seismic signal (<NUM>, <NUM>, <NUM>, <NUM>) is associated with a respective fixed position (<NUM>, <NUM>, <NUM>, <NUM>) associated with a respective time interval as a portion of the time scale, wherein the predetermined number comprises an integer value greater than one;
applying a pulse compression technique to each partitioned seismic signal of the predetermined number of partitioned seismic signals (<NUM>, <NUM>, <NUM>, <NUM>)) to generate a compressed partitioned seismic signal (<NUM>) corresponding to each partitioned seismic signal of the predetermined number of partitioned seismic signals (<NUM>, <NUM>, <NUM>, <NUM>);
inserting the compressed partitioned seismic signal (<NUM>) corresponding to each partitioned seismic signal of the predetermined number of partitioned seismic signals (<NUM>, <NUM>, <NUM>, <NUM>) in parallel into a velocity model builder; and
summing the results of the velocity model builder obtained after inserting the compressed partitioned seismic signal (<NUM>) corresponding to each partitioned seismic signal (<NUM>, <NUM>, <NUM>, <NUM>) to construct a seismic image based on the time scale and representative of the subsurface region (<NUM>) and to determine locations and properties of hydrocarbon deposits in the subsurface region (<NUM>).