Patent Publication Number: US-2019196038-A1

Title: Full Wavefield Inversion of Ocean Bottom Seismic Data

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the priority benefit of U.S. Provisional Patent Application No. 62/609,400 filed Dec. 22, 2017 entitled FULL WAVEFIELD INVERSION OF OCEAN BOTTOM SEISMIC DATA, the entirety of which is incorporated by reference herein. 
    
    
     TECHNOLOGICAL FIELD 
     This disclosure relates generally to the field of geophysical prospecting and, more particularly, to seismic data processing. Specifically, the disclosure relates to a method full wavefield inversion of ocean bottom seismic data. 
     BACKGROUND 
     This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art. 
     Seismic data are conventionally acquired with sources of acoustic energy that send sound waves into the earth. These sound waves reflect from the earth&#39;s rock strata, are measured and recorded at or near the surface, and the data incorporated into algorithms that construct images of the subsurface. In the offshore environment, the measurement is usually by sensors deployed along streamers that are towed behind a seismic vessel. Less commonly, measurement is by sensors deployed along the seafloor in the form of Ocean-bottom Cables (OBC), Ocean-bottom Nodes (OBN), or, generically, Ocean-bottom Sensors (OBS). 
     Simultaneous sourcing, also called blended sourcing, is a seismic acquisition method for reducing acquisition costs and improving spatial sampling. Conventionally, surveys are acquired by locating a single point source or an array of point sources at a single source location, firing the sources at the same time and then recording the response for the time needed for the sources to finish firing followed by a listening time in which all returns from the subsurface target are recorded. Optionally, the firing of the sources can be repeated and multiple records can be recorded at the same location. Then, the source array is moved to another location, and the process is repeated. The cost of acquiring seismic data by this sequential method is related to the time needed to record each individual source location and the number of such locations, and this cost often limits the ability to record data at fine sampling. By firing one or more point sources at different source locations at the same time or at nearly the same time within the same data record, acquisition time and cost can be reduced and sampling increased. This may be referred to as simultaneous acquisition. Originally, when the method was introduced, the interfering sources were excited at exactly the same time or simultaneously. Today, the same term is also used for acquisition in which sources fire within the same time window as another source even though the firing of the sources is not simultaneous in time and differs by some time delay. Generally, the sources that fire at nearly the same time within the same short record form an extended spatial or areal array, with no expectation that the positions of the individual point sources are close together. Also, the overlapping or interfering signals may come from sources on a single vessel, sources on different vessels, or a combination of both. 
     An important goal of seismic prospecting is to accurately image subsurface structures commonly referred to as reflectors. Seismic prospecting is facilitated by obtaining raw seismic data during performance of a seismic survey. During a seismic survey, seismic energy can be generated at ground or sea level by, for example, a controlled explosion (or other form of source, such as vibrators), and delivered to the earth. Seismic waves are reflected from underground structures and are received by a number of sensors/receivers, such as geophones. The seismic data received by the geophones is processed in an effort to create an accurate mapping of the underground environment. The processed data is then examined with a goal of identifying geological formations that may contain hydrocarbons (e.g., oil and/or natural gas). 
     Full Wavefield Inversion (FWI) is a seismic method capable of utilizing the full seismic record, including the seismic events that are treated as “noise” by standard inversion algorithms. The goal of FWI is to build a realistic subsurface model by minimizing the misfit between the recorded seismic data and synthetic (or modeled) data obtained via numerical simulation. 
     One important mathematical algorithm applied to seismic data is Full Wavefield Inversion, variously known as Full Waveform Inversion or FWI (Xu et al., “3-D Prestack Full-Wavefield Inversion,” Geophysics, vol 60, no. 6, pp 1805-1818, 1995, the entirety of which is hereby incorporated by reference; Gauthier et al., “Two-Dimensional Nonlinear Inversion of Seismic Waveforms: Numerical Results,” Geophysics, vol. 51, no. 7, pp. 1387-1403, 1986, the entirety of which is hereby incorporated by reference). FWI creates and solves an inversion problem to find, at a minimum, a model of the velocities (or other physical property, such as impedance) of geologic strata along with their locations. FWI accomplishes this by minimizing the difference between measured seismic data and synthetic data computed from an estimate of the subsurface velocities and knowledge of the source excitations. Data are typically synthesized using techniques such as finite differences or finite elements. The requirement that the measured and synthetic data match is typically expressed in terms of minimizing an objective function. The objective function will at least contain some measure of the difference between acquired and synthetic data and may include one or more additional terms to stabilize the computed earth model (typically velocity but any physical property used in FWI), which is normally called model regularization terms to ensure the smoothness of the model or to preserve boundaries of the model as a part of the objective function, or to ensure consistency with other, non-seismic, data. Requiring that the objective function decrease results in mathematical formulae for the model gradient, which is the mathematical direction in which the model should be updated. 
     Typically, trial step sizes are taken in this direction and their impact on the objective function compared before deciding upon an actual model update consisting of both a gradient direction and a step size. After updating the model, the process may be iterated, further adjusting the model and decreasing the data difference between measured and synthetic data. The iterations are stopped when the difference is sufficiently small or the model sufficiently accurate. Various physical parameters can be included in the earth model, such as density, compressional velocity, shear velocity, anisotropy, and attenuation. 
     FWI is a computationally-intensive application and many techniques have been developed to reduce the time and costs associated with it. In particular, FWI is usually applied to OBS data in the form of common-receiver gathers and by invoking reciprocity (Liu, et al., “3-D Time-Domain Full Waveform Inversion of a Valhall OBC Dataset,” abstracts of the 82nd Annual International Meeting, Society of Exploration Geophysicists, Las Vegas, 2012). A common-receiver gather is seismic data recorded in a particular sensor from all of the source excitations. This is in contrast to a common-shot gather, which is the data from a particular source excitation as recorded in all sensors. In typical OBS applications, there are far fewer Ocean-bottom Sensors (hundreds to a few thousand) than source excitations (tens of thousands to one million or more). As a result, there are far fewer common-receiver gathers than common-shot gathers in an OBS dataset. 
     Reciprocity is a property of the underlying equations governing propagation of acoustic and elastic waves in the earth. Reciprocity implies that OBS data may be treated as if a source had been located on the seafloor and the data recorded by sensors at the location of the physical sources, near the surface. For conventional acquisition, where there is no concern that reflections from different source excitations may overlap in time, the common-receiver data can be assembled as if the seafloor “source” was excited only once to generate signals at all of the surface “sensors”. That is, the data synthesis and back-propagation steps in FWI can usually be carried out on common-receiver OBS data using reciprocity, resulting in considerable savings of computational time and resources. 
     FWI can be directly carried out on simultaneous-source common-shot gathers. Such data can always be partitioned into moderate time intervals, say 5-15 seconds but rarely more than 30 seconds, corresponding to a small number of source excitations, say 2-4 but rarely more than 8. As long as the timing and locations of the different source excitations are understood, the synthesis step for simultaneous-source shot gathers can readily be carried out by standard methods. Likewise, the mathematical analysis for updating the model is unchanged from that for conventional data. 
     Unfortunately, the same is not true when applying FWI to simultaneous-source common-receiver gathers. Common-receiver data will have been acquired over the course of many hours (for streamer data) or many weeks (for OBS data). Time intervals such as these are far too long to efficiently carry out the synthesis and back-propagation steps in FWI to invert the simultaneous-source data as it was acquired. Reciprocity is a statement about a sensor at one location and a source at one location and it cannot be directly applied to the overlapped data acquired during simultaneous-source acquisition. For simultaneous-source data, where the overlap among signals from different sources cannot be ignored, it is not possible to assemble a common-receiver gather as if the seafloor “source” was excited only once to generate signals at all of the surfaces sensors”. Without some additional inventive step, the savings in time and computational resources afforded by reciprocity are lost for simultaneous-source OBS data. 
     The implied solution, typified in Paramo et al., “AVO Analysis of Independent Simultaneous Source OBC Data from Trinidad,” abstracts of the 83rd Annual International Meeting, Society of Exploration Geophysicists, Houston, 2013, pp. 368-372 the entirety of which is hereby incorporated by reference, is to deblend the simultaneous-source OBS data. Deblending is described in Wang, et al., “Advanced Deblending Scheme for Independent Simultaneous Source Data,” Abstracts of the 25th Annual Conference and Exhibition, Australian Society of Exploration Geophysicists, 2016, the entirety of which is hereby incorporated by reference, and references therein. Deblending applies techniques to reconstruct the seismic data that would have been acquired if the excitations had been separated by enough time to avoid any overlap—in other words, to avoid any interference among the excitations. In this vein, simultaneous source data is sometimes referred to as “blended” data. Deblending operates by filtering away the interference in some domain where it appears random and then, optionally, solving an inversion problem that requires the separate, deblended outputs to sum correctly to match the input, blended dataset when the source excitation times are taken into account. When successful, the resulting deblended data can be used in FWI, as common-shot gathers for streamer data or common-receiver gathers for OBS data. However, deblending suffers from inaccuracies and potential data inadequacies inherent in the filtering methods (such as FK, Radon, or curvelet filters), where geologically-important signals might be mis-characterized as noise. Deblending also results in the significant computational expense, complexity, and approximations of solving a large number of inversion-based problems with the twin objectives of ensuring that the output data have the lowest levels of interference and successfully reconstruct the input simultaneous-source data. 
     A related concept is that of “pseudo-deblending”, which assembles recorded seismic traces according to the excitation time of each source. Setting the requirements of reciprocity aside, it is possible to assemble a simultaneous-source, common-receiver gather by selecting any subset of all source excitations, ignoring the effects of interference. The result does no damage to the data and allows the geophysicist to examine both the coherent signals from the selected subset and the (usually) incoherent signals from interfering source excitations. However, unlike a fully deblended gather, it cannot be synthesized directly with reciprocity and therefore cannot be used within FWI unless further inventive steps are taken. 
     In actual applications of simultaneous-source acquisition, practitioners typically introduce some amount of randomization among the source locations and/or their excitation times. The primary purpose is to cause the interference among overlapping signals to become incoherent and thereby more easily mitigated with deblending or other signal processing techniques. A side effect is to reduce the amount of noise or “crosstalk” present in the model gradient and thereby improve the quality of the updated model. This type of randomization will not be confused with the selection of randomized subsets of data while computing the model gradient and forming a model update (Krebs et al, U.S. Pat. No. 8,694,299, the entirety of which is hereby incorporated by reference). The selection of randomized data subsets is an effort to improve the efficiency of FWI by reducing the burden of computing synthetics and a model update during each iteration while ensuring that the final earth model adequately explains all of the data. 
     It is useful to clarify some confusion over the use of the term “simultaneous-source” in the geophysics literature. The seismic acquisition and deblending literature typically use simultaneous-sourcing in the same sense as above: field measurements containing seismic data from two or more sources. The fact that seismic energy may propagate over great distances and long periods of time will cause no confusion to one skilled in the arts of seismic acquisition and processing. Simultaneous-sourcing occurs when useful signals from different source excitations arrive in the receiving apparatus at the same time. This would typically occur when the sources are within 10 km of each other and excited within 6 seconds of each other although useful information has been recovered from sources separated by as much as 50 km and excited within 30 seconds of each other. 
     The FWI literature, on the other hand, usually employs “simultaneous-source” to describe data that have been artificially summed or blended after being recorded by conventional means. In the present context, where the application of reciprocity is particularly useful, this approach corresponds to summing many common-receiver gathers (as many as 50 or more) then synthesizing them at the same time, resulting in considerable time and computational savings (Krebs et al, U.S. Pat. No. 8,121,823, the entirety of which is hereby incorporated by reference). 
     In contrast to the FWI encoding technique, simultaneous sourcing herein refers to field acquisition of overlapping data from more than one source excitation. In addition to small, random time shifts on the order of 0-2 seconds, the source excitations can be separated by several seconds. 
     SUMMARY 
     A method of full wavefield inversion using simultaneous-source, ocean bottom sensor (OBS) data, including: obtaining, with a computer, simultaneous-source OBS data recorded by receivers in a seismic acquisition; generating, with a computer, synthetic OBS seismic data from a model based on reciprocity; blending, with a computer, the synthetic OBS seismic data; differencing, with a computer, the simultaneous-source OBS data recorded by receivers and the synthetic data to form a pseudo-deblended residual; updating the model based on the pseudo-deblended residual; and prospecting for hydrocarbons at a location derived from the updated model. 
     In the method, the blending of the synthetic OBS seismic data can be based on field acquisition parameters. 
     In the method, the generating synthetic OBS seismic data using reciprocity can include synthesizing source excitation locations in the simultaneous-source OBS data recorded by receivers in the seismic acquisition. 
     In the method, the model can be an earth model. 
     The method can further include imaging subsurface structures from the updated model. 
     A method of full wavefield inversion using simultaneous-source, ocean bottom sensor (OBS) data, including: obtaining, with a computer, simultaneous-source OBS data recorded by receivers in a seismic acquisition; obtaining, with a computer at least one of conventional streamer seismic data, conventional OBS seismic data, and simultaneous-source streamer seismic data; generating, with a computer, synthetic OBS seismic data from a model based on reciprocity; blending, with a computer, the synthetic OBS seismic data corresponding to the obtained simultaneous source OBS seismic data; differencing, with a computer, the simultaneous-source OBS data recorded by receivers and the synthetic OBS seismic data to form a pseudo-deblended residual; differencing, with a computer, the conventional OBS seismic data or streamer seismic data and corresponding synthetic seismic data to obtain a conventional OBS residual or a streamer residual; updating, with a computer, the model based on one or more of the pseudo-deblended residual, the conventional OBS residual, or the streamer residual; and prospecting for hydrocarbons at a location derived from the updated model. 
     In the method, the blending of the synthetic OBS seismic data can be based on field acquisition parameters. 
     In the method, the generating synthetic OBS seismic data using reciprocity can include synthesizing source excitation locations in the simultaneous-source OBS data recorded by receivers in the seismic acquisition. 
     In the method, the model can be an earth model. 
     The method can further include imaging subsurface structures from the updated model. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       While the present disclosure is susceptible to various modifications and alternative forms, specific example embodiments thereof have been shown in the drawings and are herein described in detail. It should be understood, however, that the description herein of specific example embodiments is not intended to limit the disclosure to the particular forms disclosed herein, but on the contrary, this disclosure is to cover all modifications and equivalents as defined by the appended claims. It should also be understood that the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating principles of exemplary embodiments of the present invention. Moreover, certain dimensions may be exaggerated to help visually convey such principles. 
         FIG. 1  illustrates an example of full wavefield inversion. 
         FIG. 2  illustrates an example of full wavefield inversion applied to OBS data. 
         FIG. 3  illustrates an example of full wavefield inversion using deblending. 
         FIG. 4  illustrates an example of full wavefield inversion applied to OBS data without deblending. 
         FIG. 5  illustrates an example of full wavefield inversion applied to OBS data without deblending and utilizing field acquisition parameters. 
         FIG. 6  illustrates an example of full wavefield inversion applied to a combined streamer and OBS data set. 
         FIG. 7  illustrates an example of a common-shot gather of conventional OBS data. 
         FIG. 8  illustrates an example of a common-shot gather of simultaneous-source OBS data. 
         FIG. 9  illustrates an example of a common-receiver OBS gather constructed by reciprocity. 
         FIG. 10  illustrates a common-receiver, simultaneous-source OBS gather after pseudo-deblending. 
         FIG. 11  illustrates a common-receiver OBS gather synthesized using reciprocity. 
         FIG. 12  illustrates a common-receiver, simultaneous-source OBS gather blended from synthetic data. 
         FIG. 13  illustrates an example of an OBS data residual. 
     
    
    
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS 
     Exemplary embodiments are described herein. However, to the extent that the following description is specific to a particular embodiment, this is intended to be for exemplary purposes only and simply provides a description of the exemplary embodiments. Accordingly, the invention is not limited to the specific embodiments described below, but rather, it includes all alternatives, modifications, and equivalents falling within the true spirit and scope of the appended claims. 
     The present technological advancement can solve the technical problem of applying FWI to simultaneous-source OBS data by synthesizing conventional OBS data using reciprocity and blending it so that it may be directly compared to acquired simultaneous-source OBS data. Central to this technological improvement is an understanding of how OBS seismic data can be efficiently synthesized by invoking reciprocity and then blended to match simultaneous-source data as it was acquired in the field. 
     The present technological advancement aims to improve the technological fields of geophysical processing and hydrocarbon prospecting (including exploration, development, and production) by providing a method that applies FWI to simultaneous-source OBS data while retaining the computational advantages of reciprocity. The present technological advancement improves how the computer implements FWI by enabling the computer to work with blended data, which improves computer efficiency. 
     FWI is a computer-implemented geophysical method that is used to invert for subsurface properties, such as velocity or acoustic impedance. The crux of any FWI algorithm can be described as follows: using a starting subsurface physical property model, synthetic seismic data are generated, i.e. modeled or simulated, by solving the wave equation using a numerical scheme (e.g., finite-difference, finite-element etc.). The term velocity model or physical property model as used herein refers to an array of numbers, typically a 3-D array, where each number, which may be called a model parameter, is a value of velocity or another physical property in a cell, where a subsurface region has been conceptually divided into discrete cells for computational purposes. The synthetic seismic data are compared with the field seismic data and using the difference between the two, an error or objective function is calculated. Using the objective function, a modified subsurface model is generated which is used to simulate a new set of synthetic seismic data. This new set of synthetic seismic data is compared with the field data to generate a new objective function. A global or local optimization method is used to minimize the objective function and to update the subsurface model. 
     Referring to the description of Full Wavefield Inversion shown in  FIG. 1 , an initial earth model  100 , is used to generate synthetic seismic data  102 , by means of well-known techniques such as finite differences or finite elements. Earth model  100 , may have been developed by a variety of techniques including semblance or focusing analysis of seismic data, well ties, FWI applied to different seismic data, or correlations with models developed from other, non-seismic datasets. Measured seismic data  104 , is sorted to common-shot gathers  106 , and synthetic data  102 , are subtracted from the common-shot gathers to produce data residual  108 . Common-shot gathers are preferred because they are efficiently synthesized. Minimizing an objective function which includes a data mismatch term results in a computed model gradient  110 . Trial step sizes or more general line search techniques determine a preferred direction along the model gradient. Taken together, the gradient and update direction form a model update  112 , which leads to an updated earth model  114 . Generating synthetic data  102 , from the updated earth model  114 , begins the next iteration cycle in FWI process  116 . 
       FIG. 2  illustrates modifications of the FWI process to accommodate conventional OBS seismic data. In this scenario, initial earth model  100 , is used to generate synthetic common-receiver data by application of reciprocity, which permits the interchange of source and receiver locations for purposes of computation. As discussed above, this permits a significant reduction in computational workload because of the numbers of source excitation locations are typically much larger than the number of seafloor OBS receiver locations. While it is entirely possible to synthesize common-shot gathers and then sort data to produce common-receiver, synthetic reciprocity data  204 , direct synthesis of common-receiver gathers is far less costly. OBS seismic data  200 , are sorted to common-receiver gathers  202 , and synthetic data  204 , are subtracted to form data residual  108 . Minimizing an objective function containing the data misfit, results in the computation of a model gradient  110 , and the determination of a model update  112 , and an updated earth model. The process is iterated by FWI iteration loop  206 , to further reduce the misfit and improve the accuracy of the earth model. 
       FIG. 3  describes the use of deblending to accommodate simultaneous-source OBS data in the FWI process. Simultaneous-source data  300 , are deblended to produce deblended data  302 , and then sorted to common-receiver gathers  202 . By invoking reciprocity to switch source and receiver to generate OBS common receiver gathers, initial earth model  100 , can be used to direct synthesize common-receiver gathers as synthetic data  204 , and these can be subtracted from common-receiver gathers  202 , to form data residual  108 . The remaining steps of computing a model gradient  110 , forming a model update  112 , updating the earth model  114 , and iterating FWI loop  206 , proceed in the same way as the conventional OBS flow shown in  FIG. 2 . 
     An example of the present technological advancement, described in  FIG. 4 , avoids the time- and resource-consuming and potentially inaccurate deblending step  302 . Here, simultaneous-source OBS data containing signal from multiple sources  300 , are sorted to common-receiver gathers  202 , without regard to the requirements of reciprocity that applies to only one source and receiver pair. As before, synthetic data  204 , are efficiently generated from initial earth model  100 , by invoking reciprocity. However, synthetic data  204 , are now blended  400 , to properly estimate the interference present in common-receiver gathers  202 . In this form, synthetic data can be subtracted from acquired data to produce pseudo-deblended residual  402 . Those skilled in the art of FWI will understand that there can be additional considerations to take into account for interferences in a common-receiver gathers involved in synthesis step  204 . In particular, sufficient data should be synthesized to match not only the coherent signals in common-receiver gathers  202 , but, after blending, to also match the interference present in gathers  202 . Most often, an obvious subset of source locations which account for the coherent signals in gathers  202 , will also suffice to reproduce the interference after blending step  400 . However, there may be instances where gathers  202 , have been preprocessed (for example, by muting long offsets) so that additional source locations should be synthesized in order to properly reproduce the interference. The remaining steps of computing a model gradient  110 , forming a model update  112 , updating the earth model  114 , and iterating the new FWI loop  404 , proceed in the same way as the conventional OBS flow shown in  FIG. 2 . 
     In a preferred embodiment of the present technological advancement, shown in  FIG. 5 , there is recognition that field acquisition parameters  500 , have a role in supporting the present technological advancement. Field acquisition parameters  500 , can include the times and locations of source excitations along with locations of sensors and the time intervals for which they recorded data. There is a considerable amount of techniques within industry regarding the placement and timing of source excitations and sensors, both to ensure sufficient illumination of the subsurface and to assist with the accurate and efficient deblending of simultaneous-source data. Many of these parameters are planned prior to the seismic survey in the form of shot schedules and pre-plots. Actual values will differ somewhat because of the vagaries of weather, ocean currents, marine mammals, battery life, and ship traffic. While pre-planned values will guide the operation of simultaneous-source data acquisition  300 , actual values will be recorded and incorporated into synthesis step  204  to ensure synthetic data have the same source excitation times and locations as actual recorded values, and are blended on computer in the same way as happened in the field at the blending step  400 . As can be seen from  FIG. 5 , iterating the FWI loop  502  otherwise carries on similarly to iterating the FWI loop  404  as described in  FIG. 4 . 
     Taken together with existing art, the present technological advancement provides a complete method for efficiently applying FWI to datasets including any combination of conventional (i.e., non-simultaneous source) and simultaneous sources together with streamer and OBS sensors. This is illustrated in  FIG. 6 , where conventional streamer data  104 , and simultaneous-source streamer data  600 , are assembled into common-shot gathers  106 , which can be readily synthesized (not shown). Likewise, simultaneous-source OBS data  300 , and conventional OBS data  200 , can be assembled into common-receiver gathers  202 , which can be readily synthesized by the methods described above. In this form, data residuals for streamer  602 , and data residuals for OBS  604 , can be computed separately and a combined model gradient by data residuals of streamer and OBS  606 , determined as part of an FWI iteration loop. In particular, it offers the efficient acquisition and inversion of long-offset, wide-azimuth, and high-resolution seismic data without sacrificing accuracy and enduring time delays associated with deblending. 
     To further illustrate the concepts herein,  FIG. 7  shows a common-shot gather  106 , of conventional OBS data. Coherent signals  700 , are apparent as functions of time (vertical axis) and sensor location (horizontal axis). It is apparent that signals from the source were recorded by the closest sensor at location  702  and by more distant sensors at the left and right extremities. 
     As shown in  FIG. 8 , a common-shot gather of simultaneous-source OBS data  300 , is somewhat more complex. Coherent signals  800 , are again apparent as functions of time and sensor location. Having selected sensor locations along the horizontal axis to fully represent a source excitation near a sensor at  802 , we are forced to observe signals from an interfering source located near a sensor at  804 . 
       FIG. 9  shows a conventional, common-receiver OBS gather  202 , constructed by invoking reciprocity. At first glance, these data are not significantly distinct from the common-shot gather shown in  FIG. 7 . However, coherent signals  900 , are now associated with different source locations along the horizontal axis. At approximate location  902 , there existed a source that was physically closest to this sensor. A careful look will furthermore show that the gather in  FIG. 9  includes more data than the gather in  FIG. 7 , reflecting the fact that this survey involved fewer sensors than source locations. 
     The simultaneous-source, common-receiver OBS gather  202 , shown in  FIG. 10  is noticeably different. Coherent signals  1000 , are apparent as functions of time and source location and location  1002  corresponds to a source location closest to this sensor. Having chosen source locations to fully represent these coherent data from the same source, the interference  1004 , associated with an additional, simultaneous source is now apparent. This interference is not coherent because it comes from a source that was excited at random times relative to the source that generated coherent signal  1000 . Despite the random appearance of interference  1004 , it is not noise but is valid signal from a secondary source. Simultaneous-source gather  202 , is said to be pseudo-deblended because it is intended to make a particular set of signals from the same source coherent with the side effect of randomizing other source signals and without any effort to fully deblend or separate signals from the two sources. 
     Reciprocity offers an efficient way to synthesize common-receiver gathers such as that shown in  FIG. 11 . Here, common-receiver OBS gather  204 , contains coherent signal  1100 . Of all the source excitation locations displayed along the horizontal axis, the location at about  1102  is nearest the sensor. This gather was synthesized from a very simple earth model therefore matches only a small part of gather  202  shown in  FIG. 9 . If the FWI loop were iterated, the earth model would become more complex and better match the real earth in the region of this survey, while gather  204  would better match gather  202 . 
     In addition to the computational efficiency already afforded by reciprocity, the practitioner is free to select additional source locations to be synthesized with little or no extra computational effort. As a result, it is straightforward, based on the field acquisition parameters, to synthesize enough data to construct the simultaneous-source receiver gather  400 , shown in  FIG. 12 . Coherent signal  1200  is apparent along with approximate location  1202 , of a source nearest to the sensor. Interference  1204 , from an additional source is random relative to the first source, based on actual excitation times measured in the field. Since the horizontal axis has been calibrated to display the location of the first source, the second source appears to be closest to the sensor at location  1206 , where the first source is some distance away. 
     It will be appreciated by those skilled in the art that the ability to apply FWI directly to simultaneous source data, forming blended synthetics and residuals from multiple sources in a single computational step rather than computing them in multiple steps, represents a valuable efficiency gain. Synthesizing simultaneous-source gathers, such as  400 , which contain data from two or more sources translate directly to decreased FWI run times by factors of two or more. 
     To complete the illustration of the method, synthetic gather  400  has been subtracted from pseudo-deblended gather  202  shown in  FIG. 10  to generate the pseudo-deblended residual  402 , shown in  FIG. 13 . Careful study of coherent signal  1300 , interference  1304 , and closest source location  1302 , will reveal that the amplitudes in  FIG. 13  are decreased relative to those in  FIG. 10 , indicating that the earth model has some features that are generally correct and which can be further improved by computing a gradient and forming a model update. We can reasonably expect that this residual will further decrease as the FWI loop is iterated and the data are fit by the synthetics. 
     Furthermore, the present technological advancement can be used to manage hydrocarbons. As used herein, hydrocarbon management includes hydrocarbon extraction, hydrocarbon production, hydrocarbon exploration, identifying potential hydrocarbon resources, identifying well locations, determining well injection and/or extraction rates, identifying reservoir connectivity, acquiring, disposing of and/or abandoning hydrocarbon resources, reviewing prior hydrocarbon management decisions, and any other hydrocarbon-related acts or activities. 
     In all practical applications, the present technological advancement must be used in conjunction with a computer, programmed in accordance with the disclosures herein. Preferably, in order to efficiently perform FWI, the computer is a high performance computer (HPC), known as to those skilled in the art, Such high performance computers typically involve clusters of nodes, each node having multiple CPU&#39;s and computer memory that allow parallel computation. The models may be visualized and edited using any interactive visualization programs and associated hardware, such as monitors and projectors. The architecture of system may vary and may be composed of any number of suitable hardware structures capable of executing logical operations and displaying the output according to the present technological advancement. Those of ordinary skill in the art are aware of suitable supercomputers available from Cray or IBM. 
     The foregoing application is directed to particular embodiments of the present technological advancement for the purpose of illustrating it. It will be apparent, however, to one skilled in the art, that many modifications and variations to the embodiments described herein are possible. All such modifications and variations are intended to be within the scope of the present invention, as defined in the appended claims. Persons skilled in the art will readily recognize that in preferred embodiments of the invention, some or all of the steps in the present inventive method are performed using a computer, i.e. the invention is computer implemented. In such cases, the resulting gradient or updated physical properties model may be downloaded or saved to computer storage.