Patent Description:
The wavefield can be reconstructed in overlapping blocks of data. For receiver-side processing, the individual blocks may be defined by a number of recording channels in a streamer cable, a number of streamer cables, and a fixed time duration. Overlapping windows may be processed for one shot gather, and the reconstructed data for that shot gather may be output, before moving to the next shot gather. That is, each shot gather can be processed individually.

<CIT> describes a method for processing synchronous array seismic data comprising acquiring seismic data from a plurality of sensors positioned in a borehole to obtain synchronized array measurements, applying a reverse-time data propagation process to the synchronized array measurements to obtain dynamic particle parameters associated with subsurface locations, applying at least one imaging condition, using a processing unit, to the dynamic particle parameters to obtain imaging values associated with subsurface locations and locating a subsurface position of an energy source from the imaging values associated with subsurface locations. <CIT> describes a method for seismic imaging implementing a seismic modeling algorithm utilizing Forward Wave Inversion technique for revising Reverse Time Migration models used for sub-surface modeling. The technique requires large communication bandwidth and low latency to convert a parallel problem into one solved using massive domain partitioning. The partitioning of a velocity model into processing blocks allows each sub-problem to fit in a local cache, increasing locality and bandwidth and reducing latency. The RTM seismic data processing utilizes data that includes combined shot data, i.e., shot data selected from amongst a plurality of shots that are combined at like spatial points of the volume. An iterative approach is applied such that the correction term RTM generates at each iteration in the iterative approach is used for refining the model, and the updated model is used for generating a further refined RTM model. Similarly, <CIT> describes a method using RTM and FWI techniques. Since in RTM and FWI, the forward wave propagation is iteratively calculated on time step increments, there are very high statistical correlation between the intermediate wavefields at the adjacent time steps. This correlation is exploited in compression of the intermediate wavefields so as to achieve much higher compression ratio and avoid the disk IO bottleneck and reduce the overall computing time substantially. Further, during simulation of a reverse wavefield, reverse predictive encoding technique is performed such that snapshots are not recovered in the reverse propagation path due to a prediction chain.

The present invention resides in a method for reconstructing source side and receiver side seismic wavefields as defined in claim <NUM>, a computer system as defined in claim <NUM> and a non-transitory computer-readable medium as defined in claim <NUM>.

It will be appreciated that this summary is intended merely to introduce some aspects of the present methods, systems, and media, which are more fully described and/or claimed below. Accordingly, this summary is not intended to be limiting.

The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the description of the invention and the appended claims, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term "and/or" as used herein refers to and encompasses any possible combinations of one or more of the associated listed items. It will be further understood that the terms "includes," "including," "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Further, as used herein, the term "if" may be construed to mean "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context.

<FIG> illustrate simplified, schematic views of oilfield <NUM> having subterranean formation <NUM> containing reservoir <NUM> therein in accordance with implementations of various technologies and techniques described herein. <FIG> illustrates a survey operation being performed by a survey tool, such as seismic truck <NUM>, to measure properties of the subterranean formation. The survey operation is a seismic survey operation for producing sound vibrations. In <FIG>, one such sound vibration, e.g., sound vibration <NUM> generated by source <NUM>, reflects off horizons <NUM> in earth formation <NUM>. A set of sound vibrations is received by sensors, such as geophone-receivers <NUM>, situated on the earth's surface. The data received <NUM> is provided as input data to a computer <NUM> of a seismic truck <NUM>, and responsive to the input data, computer <NUM> generates seismic data output <NUM>. This seismic data output may be stored, transmitted or further processed as desired, for example, by data reduction.

<FIG> illustrates a drilling operation being performed by drilling tools <NUM> suspended by rig <NUM> and advanced into subterranean formations <NUM> to form wellbore <NUM>. Mud pit <NUM> is used to draw drilling mud into the drilling tools via flow line <NUM> for circulating drilling mud down through the drilling tools, then up wellbore <NUM> and back to the surface. The drilling mud is typically filtered and returned to the mud pit. A circulating system may be used for storing, controlling, or filtering the flowing drilling mud. The drilling tools are advanced into subterranean formations <NUM> to reach reservoir <NUM>. Each well may target one or more reservoirs. The drilling tools are adapted for measuring downhole properties using logging while drilling tools. The logging while drilling tools may also be adapted for taking core sample <NUM> as shown.

Typically, the wellbore is drilled according to a drilling plan that is established prior to drilling. The drilling plan typically sets forth equipment, pressures, trajectories and/or other parameters that define the drilling process for the wellsite. The drilling operation may then be performed according to the drilling plan. However, as information is gathered, the drilling operation may need to deviate from the drilling plan. Additionally, as drilling or other operations are performed, the subsurface conditions may change. The earth model may also need adjustment as new information is collected.

Surface unit <NUM> may include transceiver <NUM> to allow communications between surface unit <NUM> and various portions of the oilfield <NUM> or other locations. Surface unit <NUM> may also be provided with or functionally connected to one or more controllers (not shown) for actuating mechanisms at oilfield <NUM>. Surface unit <NUM> may then send command signals to oilfield <NUM> in response to data received. Surface unit <NUM> may receive commands via transceiver <NUM> or may itself execute commands to the controller. A processor may be provided to analyze the data (locally or remotely), make the decisions and/or actuate the controller. In this manner, oilfield <NUM> may be selectively adjusted based on the data collected. This technique may be used to optimize (or improve) portions of the field operation, such as controlling drilling, weight on bit, pump rates, or other parameters. These adjustments may be made automatically based on computer protocol, and/or manually by an operator. In some cases, well plans may be adjusted to select optimum (or improved) operating conditions, or to avoid problems.

As shown, the sensor (S) may be positioned in production tool <NUM> or associated equipment, such as Christmas tree <NUM>, gathering network <NUM>, surface facility <NUM>, and/or the production facility, to measure fluid parameters, such as fluid composition, flow rates, pressures, temperatures, and/or other parameters of the production operation.

Data plots <NUM>-<NUM> are examples of static data plots that may be generated by data acquisition tools <NUM>-<NUM>, respectively; however, it should be understood that data plots <NUM>-<NUM> may also be data plots that are updated in real time. These measurements may be analyzed to better define the properties of the formation(s) and/or determine the accuracy of the measurements and/or for checking for errors. The plots of each of the respective measurements may be aligned and scaled for comparison and verification of the properties.

Static data plot <NUM> is a seismic two-way response over a period of time. Static plot <NUM> is core sample data measured from a core sample of the formation <NUM>. The core sample may be used to provide data, such as a graph of the density, porosity, permeability, or some other physical property of the core sample over the length of the core. Tests for density and viscosity may be performed on the fluids in the core at varying pressures and temperatures. Static data plot <NUM> is a logging trace that typically provides a resistivity or other measurement of the formation at various depths.

A production decline curve or graph <NUM> is a dynamic data plot of the fluid flow rate over time. The production decline curve typically provides the production rate as a function of time. As the fluid flows through the wellbore, measurements are taken of fluid properties, such as flow rates, pressures, composition, etc..

While a specific subterranean formation with specific geological structures is depicted, it will be appreciated that oilfield <NUM> may contain a variety of geological structures and/or formations, sometimes having extreme complexity. In some locations, typically below the water line, fluid may occupy pore spaces of the formations. Each of the measurement devices may be used to measure properties of the formations and/or its geological features. While each acquisition tool is shown as being in specific locations in oilfield <NUM>, it will be appreciated that one or more types of measurement may be taken at one or more locations across one or more fields or other locations for comparison and/or analysis.

The data collected from various sources, such as the data acquisition tools of <FIG>, may then be processed and/or evaluated. Typically, seismic data displayed in static data plot <NUM> from data acquisition tool <NUM> is used by a geophysicist to determine characteristics of the subterranean formations and features. The core data shown in static plot <NUM> and/or log data from well log <NUM> are typically used by a geologist to determine various characteristics of the subterranean formation. The production data from graph <NUM> is typically used by the reservoir engineer to determine fluid flow reservoir characteristics. The data analyzed by the geologist, geophysicist and the reservoir engineer may be analyzed using modeling techniques.

<FIG> illustrates an oilfield <NUM> for performing production operations in accordance with implementations of various technologies and techniques described herein. As shown, the oilfield has a plurality of wellsites <NUM> operatively connected to central processing facility <NUM>. The oilfield configuration of <FIG> is not intended to limit the scope of the oilfield application system. Part, or all, of the oilfield may be on land and/or sea. Also, while a single oilfield with a single processing facility and a plurality of wellsites is depicted, any combination of one or more oilfields, one or more processing facilities and one or more wellsites may be present.

Attention is now directed to <FIG>, which illustrates a side view of a marine-based survey <NUM> of a subterranean subsurface <NUM> in accordance with one or more implementations of various techniques described herein. Subsurface <NUM> includes seafloor surface <NUM>. Seismic sources <NUM> may include marine sources such as vibroseis or airguns, which may propagate seismic waves <NUM> (e.g., energy signals) into the Earth over an extended period of time or at a nearly instantaneous energy provided by impulsive sources. The seismic waves may be propagated by marine sources as a frequency sweep signal. For example, marine sources of the vibroseis type may initially emit a seismic wave at a low frequency (e.g., <NUM>) and increase the seismic wave to a high frequency (e.g., <NUM>-<NUM>) over time.

The component(s) of the seismic waves <NUM> may be reflected and converted by seafloor surface <NUM> (i.e., reflector), and seismic wave reflections <NUM> may be received by a plurality of seismic receivers <NUM>. Seismic receivers <NUM> may be disposed on a plurality of streamers (i.e., streamer array <NUM>). The seismic receivers <NUM> may generate electrical signals representative of the received seismic wave reflections <NUM>. The electrical signals may be embedded with information regarding the subsurface <NUM> and captured as a record of seismic data.

In one implementation, seismic wave reflections <NUM> may travel upward and reach the water/air interface at the water surface <NUM>, a portion of reflections <NUM> may then reflect downward again (i.e., sea-surface ghost waves <NUM>) and be received by the plurality of seismic receivers <NUM>. The sea-surface ghost waves <NUM> may be referred to as surface multiples. The point on the water surface <NUM> at which the wave is reflected downward is generally referred to as the downward reflection point.

The electrical signals may be transmitted to a vessel <NUM> via transmission cables, wireless communication or the like. The vessel <NUM> may then transmit the electrical signals to a data processing center. Alternatively, the vessel <NUM> may include an onboard computer capable of processing the electrical signals (i.e., seismic data). Those skilled in the art having the benefit of this disclosure will appreciate that this illustration is highly idealized. For instance, surveys may be of formations deep beneath the surface. The formations may typically include multiple reflectors, some of which may include dipping events, and may generate multiple reflections (including wave conversion) for receipt by the seismic receivers <NUM>. In one implementation, the seismic data may be processed to generate a seismic image of the subsurface <NUM>.

Marine seismic acquisition systems tow each streamer in streamer array <NUM> at the same depth (e.g., <NUM>-<NUM>). However, marine based survey <NUM> may tow each streamer in streamer array <NUM> at different depths such that seismic data may be acquired and processed in a manner that avoids the effects of destructive interference due to sea-surface ghost waves. For instance, marine-based survey <NUM> of <FIG> illustrates eight streamers towed by vessel <NUM> at eight different depths. The depth of each streamer may be controlled and maintained using the birds disposed on each streamer.

In the present disclosure, a method for wavefield reconstruction (e.g., seismic imaging) using multi-measurement streamers is provided. In an embodiment of the present method, rather than reconstructing data for each shot individually, the data for multiple shots is reconstructed simultaneously. This "multi-shot" processing strategy takes advantage of the fact that (for at least some in-line source sampling intervals, e.g., between <NUM> and <NUM>) the seismic wavefield varies slowly and smoothly.

Further, the present disclosure provides an embodiment of a processing strategy that solves a source and receiver side problem simultaneously, and can be extended to include additional source-side effects, such as source-side deghosting, source-side reconstruction, simultaneous source separation, and so on.

The systems and methods described herein use information recorded across multiple activations of the seismic sources, rather than the use of information recorded from a single seismic source. For example, data from multiple sources may be input, and the reconstructed data corresponding to those multiple sources is output. This multiple-shot approach allows for robust results in the presence of strong noise, as noise may be incoherent from shot-to-shot. This can provide a better quality of processed output.

Additionally, the use of a higher-dimensional representation allows for more accurate reconstruction of wavefields generated by complex geological structures. If data quality is already sufficient, then survey parameters that control data quality can be relaxed. The uplift in quality offered by the new approach accounts for this relaxation of survey parameters. For example, increasing the spacing between seismic streamers can reduce data quality, but can have an impact on survey efficiency. The systems and methods described herein thus allow this efficiency improvement without impacting the data quality.

Further, by solving multiple processing steps simultaneously, processing turnaround time can be decreased, and quality can be improved, as errors may not propagate from step-to-step. The systems and methods disclosed herein may provide these benefits and others (when compared to conventional systems and methods) at least in part by defining one or more basis functions that describe a window (partition) of the multi-shot data set that includes a source dimension, decomposing the multi-shot data using the basis functions to create a model that describes the multi-shot data, defining one or more basis functions describing a desired output source and receiver dataset, and/or combing those output basis functions with the decomposed model, to provide an output dataset with desired characteristics.

In one embodiment, the method includes the acquisition of seismic data using a multi-measurement streamer system. A multi-measurement streamer records the acoustic pressure in the water, together with the vertical and horizontal pressure gradients. Pressure gradients can be measured in the water using, for example, particle velocity sensors, or accelerometers. The sensors along the streamer (or channels) are densely spaced, for example, at <NUM>. Such a streamer system may be deployed behind a seismic survey vessel. The streamers may be at least several kilometers long, and are spaced at approximately regular intervals in the cross-line direction (i.e., transverse to the direction of sailing). This spacing may be from <NUM> to <NUM>, depending on the water depth, assumed complexity of the geological formation being surveyed, and survey objectives. At least one seismic source array may be deployed as part of the survey. This source array can be towed behind the survey vessel, or in some situations can be towed behind a dedicated source vessel. The source array can include airgun sources or marine vibrators. As the survey proceeds, the source is fired at (close to) regular intervals that may range from <NUM> to <NUM>.

In single-source reconstruction of multi-measurement wavefields, the data is split into overlapping windows. These windows are defined as functions of both time and position. The spatial window is defined as a fixed window in space incorporating a number of streamers, and a number of channels in each streamer. The time window is defined as a number of time samples. In some instances, the data is transformed into the Fourier domain in one or more of the windowed dimensions. For example, a Fast Fourier Transform to the time domain provides the same window of data in the frequency-space domain. Defining frequency f, the in-line channel co-ordinate xrec, and the corresponding cross-line cable co-ordinate yrec, allows the window of data to be defined as di(f, xrec, yrec). The subscript i corresponds to the type of measurement made, for example, the pressure, the vertical pressure gradient, and/or the horizontal pressure gradient.

One particular type of reconstruction method involves estimating the frequency-slowness spectrum of the data. For a single shot, this spectrum can be defined as D(f, px, py), wherepx, and py correspond to the x- and y-component of slowness. Given a model of the wavefield in this transform domain, m(f, px, py), the data can be described by the combination of that model, and a set of basis functions, bi(f, xrec, yrec, px, py), where the subscript i again refers to the type of measurement that has been made.

The basis functions are chosen to represent each of the measurements, and can be used to describe the seismic wavefield in a particular transform domain. The basis functions describe the physics of each measurement, for example, if di(f, xrec, yrec) corresponds to the cross-line pressure gradient, then bi(f, xrec, yrec, px, py) describes the cross-line pressure gradient. Other effects, such as the receiver side ghost can also be described. The transform domain is chosen as one where the wavefield can be expressed by a few components, as this facilitates the reconstruction of the wavefield in directions where it has been sparsely sampled.

In matching pursuit reconstruction, the data in the transform domain can be estimated as, <MAT>.

This estimated transform, together with mathematical expressions for the physics of each measurement, is used to identify optimum slowness and amplitude values that contribute to an estimate of the model m(f, px, py). This is done iteratively, with the input data di(f, xrec, yrec) being updated after each iteration. After a number of iterations, the estimated model is combined with a set of basis functions that define the desired output data at locations defined by [x_out, y_out], <MAT>.

Where, for example, the output data could correspond to the up-going pressure wavefield, down-going pressure wavefield, and/or total pressure wavefield that would have been observed at locations between the physical streamer positions.

Referring now to <FIG>, there is shown a flowchart of a method <NUM> for reconstructing a wavefield (seismic imaging), according to an embodiment. The method <NUM> includes receiving multi-shot seismic data, as at <NUM>. The data may be acquired using marine streamers, for example, as discussed above. The wavefields are generated by one or several sources.

In an embodiment, the above-described single-source reconstruction methodology is extended to allow the wavefield to be reconstructed across multiple shots. Following on from the description of the single-source method given above, at <NUM>, the data is partitioned into overlapping windows. The data is windowed in an extra dimension, as compared to the single-source method, however. This additional dimension is the source dimension. For ease of description, sources are described herein as being acquired along a line, and the source coordinate along that line will be defined as xsrc, but this is merely an example, and the sources may be acquired along any geometry and defined appropriately.

The spatial window is again defined as a fixed window in space, and the data in this window is now defined as di(f, xrec, yrec, xsrc). For multiple sources, the frequency-slowness spectrum is now be defined as D(f, px, py, psrc), where psrc, is the component of slowness along the source coordinate.

As at <NUM>, a first set of basis functions bi(f, xrec, yrec, px, py), as explained above for the single-source method, is defined.

As at <NUM>, a second set of basis functions, <MAT> is defined that represents the data across the multi-sources within the window, where the subscript j allows different types of sources to be accounted for in the same way that the subscript i allows the different measurements to be account for above.

For each of the sources, the data is decomposed into a first spectrum based in part on the first basis functions for the respective sources for the respective windows, as at <NUM>. For example, the first spectrum may be an estimated receiver slowness spectrum, according to the following: <MAT> where now the receiver coordinates xrec, yrec depend on the source, as the streamers can change shape slightly from shot-to-shot. In another embodiment, the first spectrum may instead be an intercept-time slowness spectrum, or any other suitable spectrum, with the slowness spectrum discussed herein being merely an illustrative example.

In the multi-source case, rather than using the estimated spectra (<NUM>) to reconstruct the wavefield, the method <NUM> includes, at <NUM>, estimating a second spectrum D(f, px, py, psrc) based on both the receiver wavefield and the source wavefield, e.g., using the second set of basis functions and the first spectrum, as follows: <MAT>.

The second spectrum ties together the source and receiver wavefields, and permits the reconstruction of the wavefield across the multiple receiver locations and the multiple source locations. This spectrum, together with mathematical expressions for the physics of the measurements (and potentially different types of source), is used, as at <NUM>, to identify slowness and amplitude values that contribute to an estimate of the model m(f, px, py, psrc), which may be estimated at <NUM>. As above, this may be done iteratively, with the input data di(f, xrec, yrec, xsrc) being updated after individual iterations. After a number of iterations, as at <NUM>, the estimated model may be combined with a set of basis functions that define the desired output data at locations defined by x_s_out, <MAT> where, for example, the output data on the receiver-side may correspond to the up-going pressure wavefield, the down-going pressure wavefield, and/or the total pressure wavefield. It may further correspond to data at locations where a physical receiver/streamer was not placed during data acquisition (i.e., an interpolated data point). The output data on the source-side may correspond to the input source locations, source locations between the input source locations, and/or source wavefields with source signature, radiation pattern, and free surface effects removed.

Thus, the present method allows source and receiver side problems to be solved together. Accordingly, this method may include a solution for the reconstructed wavefield that accounts for noise, since noise is incoherent from shot-to-shot, as well as a solution that takes advantage of the representation of wavefields becoming sparser in higher dimensions.

In some embodiments, blocks <NUM> and <NUM> may be combined to achieve a similar result. In some embodiments, blocks <NUM> and <NUM> may also or instead by combined.

A simple example is now shown for a dataset with a single-receiver dimension, and a single source dimension. There are five receivers spaced at <NUM> in the y-direction, and <NUM> sources space at <NUM> in the x-direction. <FIG> shows a graph <NUM> of the estimated slowness transform, D(f,py), for a given frequency, computed as part of the single-source matching pursuit solution. In this case there are two measurements on the receiver side: the pressure wavefield (i = <NUM>) and the pressure gradient in the y-direction (i = <NUM>).

At the first iteration, the correct slowness value should be picked at receiver slowness number <NUM>; however, from the transform in <FIG>, the matching pursuit solution picks the value at receiver slowness number <NUM>. This leads to a poor quality reconstruction result. This result is shown in the time domain in <FIG>, where the desired output data is the total pressure wavefield recorded at a sampling of <NUM> (versus <NUM> for the input data). Since this is a synthetic example, the desired output data can be modelled precisely, and this is shown in <FIG>, demonstrating that there are errors in this particular reconstruction result.

<FIG> shows the equivalent estimated slowness transform, but for the multi-source case, D(f , py, psrc). A monopole type source is used here (j = <NUM>). The spectrum is now plotted as a two-dimensional image, rather than the line plot as in <FIG>. This two-dimensional spectrum is computed for the five input receiver locations, and the five sources. At the first iteration, the correct slowness should be picked as receiver slowness number <NUM> and source slowness number <NUM>, and this is indeed the case. By performing the transform over both source and receiver coordinates the data becomes sparser (as seen by the spread of energy in the source slowness direction in <FIG>), and the matching pursuit process correctly identifies the component. The effect of this is seen in <FIG>, where the reconstructed data in the time-offset domain corresponding to that in <FIG> is shown. The uplift in the reconstruction result is clear when comparing <FIG> to the expected result in <FIG>.

Equation (<NUM>) may not be computed using some of the possible receiver slowness values. For example, from the results of equation (<NUM>), it may be possible to identify the largest receiver slownesses, which will be the receiver slownesses likely to contribute values to the result of equation <NUM>. This may be a case of stacking the absolute values of the different receiver slowness spectra for the different sources, <MAT>.

From this average amplitude spectra, the larger components can be selected (for example, the largest <NUM> to <NUM>% of values may be used), and those components are used in computing the combined receiver-source spectrum in equation (<NUM>). Provided the percentage value is chosen appropriately, this may reduce the number of computations to find the result in equation (<NUM>).

In the above description, different source components j are mentioned. For the marine vibrator, these components j can correspond to source with different directionality patterns that enable, amongst other applications, beyond Nyquist source reconstruction.

The above-described method employs an iterative matching pursuit process, in which a spectrum is computed at the individual iterations. In some embodiments of matching pursuit, the at least some iterations may be performed without explicitly re-computing the full spectrum. Rather, the spectrum itself can be updated at each iteration.

The multi-source solution can be extended to include separation of simultaneous sources. In this case, the basis functions for the sources correspond to two or more source wavefields, with the encoding of the sources also described within the basis functions. The desired output on the source-side in this case may correspond to the data from the simultaneous sources as if they had been fired separately.

When choosing the fixed window for multi-source solution, there may be two options. One is to fix the window with respect to the streamers themselves, and the other is to fix the window with respect to the Earth. In the first option, the window for each shot corresponds to the same part of the streamer. In the second option, the window for each shot will correspond to a different part of the streamer. While the above solution describes a process of using a matching pursuit solution to estimate the reconstructed wavefield, those skilled in the art will appreciate that other inversion-based methods may be configured to solve the same problem. For example, compressive sensing methods, or other methods involving the minimization of an L1-norm.

<FIG> illustrates a conceptual view of combining information from multiple sources, according to an embodiment. The top row shows the slowness transforms corresponding to equation <NUM>. These slowness transforms may individually contain the information at one frequency from one of five sources (e.g., source <NUM> to source <NUM>) observed on the same 2D receiver array. The grey region represents a particular event in the seismic data.

These are computed independently for each source. The sources are closely spaced (e.g., from <NUM> to <NUM> separation), and the information from source to source may, in this example, not vary quickly. Thus, the <NUM> plots appear similar, but are not the same. The similarity can be exploited by using a set of basis functions that is dependent on the source position (xsrc). Equation (<NUM>) combines the top <NUM> plots using the basis functions dependent on source position. The five 2D slowness transforms then become a single 3D slowness transform that is sketched at the bottom of <FIG>.

<FIG> illustrates a flowchart of a method <NUM> for seismic imaging, according to an embodiment. The method <NUM> includes receiving a multi-shot seismic data set, as at <NUM>. The data set is collected using one or more streamers having recorders configured to detect seismic waves that propagate through a subterranean domain. The method <NUM> includes partitioning the multi-shot seismic data set into windows including a source dimension, as at <NUM>. The windows represent spatially-overlapping areas. The method <NUM> also includes defining one or more first basis functions that describe the windows of the multi-shot seismic data set, as at <NUM>. In at least one embodiment, two or more first basis functions may be used and combined. The method <NUM> also include generating a model that describes a decomposition of the multi-shot seismic data set using the one or more first basis functions, as at <NUM>. The model may describe the data when combined with the basis functions. The method <NUM> also includes defining one or more second basis functions that describe a selected output data, as at <NUM>. The second set of basis functions may be used because the output dataset may have a different configuration than the input dataset. The method <NUM> may also include combining the one or more second basis functions with the model to produce a result for a source side wavefield and a receiver side wavefield, as at <NUM>. The result for the receiver-side wavefield may include an up-going pressure wavefield, a down-going pressure wavefield, a total pressure wavefield, or a combination thereof. The result for the source-side wavefield may include input source locations, source locations between the input source locations, and/or source wavefields with source signature, radiation pattern, and free surface effects removed.

<FIG> illustrates a flowchart of yet another method <NUM> for seismic imaging, according to an embodiment. The method <NUM> may include acquiring seismic data, as at <NUM>. The seismic data is collected using a multi-measurement streamer. The seismic data is acquired in response to two or more closely spaced shots from a seismic source. The seismic source may be an airgun. In another embodiment, the seismic source may be a marine vibrator that emits wavefields with different directivity patterns.

The multi-measurement streamer may contain at least one pressure sensor, and at least one of an accelerometer, geophone, and strain sensor. The method <NUM> also includes processing the acquired streamer data from the two or more closely spaced shots using multi-channel reconstruction, as at <NUM>. Processing includes defining a first set of basis functions that describe the multiple measurements for an individual streamer. Processing also includes defining a second set of basis functions that describe a wavefield emitted by multiple sources. Processing also includes identifying a subset of basis functions and corresponding amplitude factors that fit the multiple measurements and multiple sources. Processing also includes reconstructing a seismic wavefield using equivalent basis functions describing the output wavefield. The subset of basis functions and corresponding amplitude factors may be computed using a matching pursuit method. The reconstruction method may be a sparse inversion process. The processed wavefield represents the downgoing wavefield from the seismic source locations, and the upgoing wavefield at the receiver locations.

The method <NUM> also includes outputting processed source and receiver data at output locations, as at <NUM>. At least one of the output locations is a location where a source or receiver was not present during the survey.

In at least one embodiment, two or more sets of closely-activated shots are activated simultaneously, and the processed wavefield at the output source and receiver locations represents the wavefield as if the two or more sets of shots had been active independently.

In one or more embodiments, the functions described can be implemented in hardware, software, firmware, or any combination thereof. For a software implementation, the techniques described herein can be implemented with modules (e.g., procedures, functions, subprograms, programs, routines, subroutines, modules, software packages, classes, and so on) that perform the functions described herein. A module can be coupled to another module or a hardware circuit by passing and/or receiving information, data, arguments, parameters, or memory contents. Information, arguments, parameters, data, or the like can be passed, forwarded, or transmitted using any suitable means including memory sharing, message passing, token passing, network transmission, and the like. The software codes can be stored in memory units and executed by processors. The memory unit can be implemented within the processor or external to the processor, in which case it can be communicatively coupled to the processor via various means as is known in the art.

In some embodiments, any of the methods of the present disclosure is executed by a computing system. <FIG> illustrates an example of such a computing system <NUM>, in accordance with some embodiments. The computing system <NUM> includes a computer or computer system 1101A, which may be an individual computer system 1101A or an arrangement of distributed computer systems. The computer system 1101A includes one or more analysis module(s) <NUM> configured to perform various tasks according to some embodiments, such as one or more methods disclosed herein. To perform these various tasks, the analysis module <NUM> executes independently, or in coordination with, one or more processors <NUM>, which is (or are) connected to one or more storage media <NUM>. The processor(s) <NUM> is (or are) also connected to a network interface <NUM> to allow the computer system 1101A to communicate over a data network <NUM> with one or more additional computer systems and/or computing systems, such as 1101B, 1101C, and/or 1101D (note that computer systems 1101B, 1101C and/or 1101D may or may not share the same architecture as computer system 1101A, and may be located in different physical locations, e.g., computer systems 1101A and 1101B may be located in a processing facility, while in communication with one or more computer systems such as 1101C and/or 1101D that are located in one or more data centers, and/or located in varying countries on different continents).

The storage media <NUM> is implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment of <FIG> storage media <NUM> is depicted as within computer system 1101A, in some embodiments, storage media <NUM> may be distributed within and/or across multiple internal and/or external enclosures of computing system 1101A and/or additional computing systems. Storage media <NUM> may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories, magnetic disks such as fixed, floppy and removable disks, other magnetic media including tape, optical media such as compact disks (CDs) or digital video disks (DVDs), BLURAY® disks, or other types of optical storage, or other types of storage devices. Note that the instructions discussed above can be provided on one computer-readable or machine-readable storage medium, or alternatively, can be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media is (are) considered to be part of an article (or article of manufacture). The storage medium or media can be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions can be downloaded over a network for execution.

In some embodiments, computing system <NUM> contains one or more wavefield reconstruction module(s) <NUM>. In the example of computing system <NUM>, computer system 1101A includes the wavefield reconstruction module <NUM>. In some embodiments, a single wavefield reconstruction module may be used to perform some or all aspects of one or more embodiments of the methods. In alternate embodiments, a plurality of wavefield reconstruction modules may be used to perform some or all aspects of methods.

It should be appreciated that computing system <NUM> is only one example of a computing system, and that computing system <NUM> may have more or fewer components than shown, may combine additional components not depicted in the example embodiment of <FIG>, and/or computing system <NUM> may have a different configuration or arrangement of the components depicted in <FIG>. The various components shown in <FIG> may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits.

Geologic interpretations, models and/or other interpretation aids may be refined in an iterative fashion; this concept is applicable to embodiments of the present methods discussed herein. This can include use of feedback loops executed on an algorithmic basis, such as at a computing device (e.g., computing system <NUM>, <FIG>), and/or through manual control by a user who may make determinations regarding whether a given step, action, template, model, or set of curves has become sufficiently accurate for the evaluation of the subsurface three-dimensional geologic formation under consideration.

Claim 1:
A method (<NUM>) for reconstructing source side and receiver side seismic wavefields, comprising
acquiring (<NUM>) seismic data that was collected using a multi-measurement streamer (<NUM>), wherein the seismic data is acquired in response to two or more closely-spaced shots;
processing (<NUM>), by a computing system, the acquired streamer data from the two or more closely-spaced shots using multi-channel reconstruction, the processing comprising:
partitioning the seismic data into overlapping windows including a source dimension;
defining (<NUM>) a first set of basis functions that describe multiple measurements for an individual streamer within the respective window;
defining (<NUM>) a second set of basis functions that describe a wavefield emitted by multiple sources within the respective window;
the method being characterized in that the processing further comprises
identifying a subset of basis functions and corresponding amplitude factors that fit the multiple measurements and multiple sources;
defining (<NUM>) a set of output basis functions describing a desired output wavefield, wherein the output basis functions are selected to correspond to the subset of basis functions; and
reconstructing a seismic wavefield using the output basis functions, together with the identified amplitude factors; and
in response (<NUM>) to processing the acquired streamer data, outputting processed source and receiver data at output locations.