This disclosure relates generally to the field of geophysical prospecting and, more particularly, seismic data processing as used in hydrocarbon exploration. Specifically, the disclosure relates to a method for acquiring, at reduced seismic acquisition cost, data using simultaneous sources in the field, and then constructing pseudo source-records that better meet the requirements for using additional simultaneous sourcing for computer simulations or forward modeling as part of iterative inversion methods that update a subsurface model, such as FWI (Full Wavefield Inversion) or LSRTM (Least-Square Reverse Time Migration), with additional reduction in computational costs.
Acquisition and then Separation
Simultaneous sourcing, also called blended sourcing, is an emerging 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. The tradeoff with simultaneous acquisition is the need to mitigate the overlapping energy or crosstalk between the sources at different locations by a combination of source encoding in the field and by filtering and source separation techniques in processing. Conventional processing requires individual records for each source location and these must be extracted or separated from the recorded data records.
Simultaneous sourcing is most commonly used for vibroseis sources with long sweep functions, which can be easily encoded. With the vibroseis method, each individual vibrator can be driven by a sweep that differs in some manner from the sweeps for other vibrators within the array, for example using differences in the sweep phase, pseudorandom function, sweep rate, sweep frequency range, start time, etc. Some methods require multiple sweeps and multiple records per location for separation. In the special case that the number of sweeps is greater than or equal to the number of vibrators, then the individual source records can be almost perfectly extracted from the multiple combined records by applying an inverse filter as described for the HFVS method in Sallas, et al. (U.S. Pat. No. 5,721,710). With this and similar methods, it is critical that the sources and the receivers do not move during the multiple sweeps. This method gives high quality separated records, because the separation is well-posed; there are as many input records or sweeps as there are output records or separated seismograms. But because multiple sweeps are needed, the method is not efficient and costs are much higher than single-sweep methods. The tradeoff with doing a single sweep is that the separation is ill-posed, and there will be some residual crosstalk noise after extracting the source seismograms. The cross-talk problem is acerbated by the fact that the vibrators output or signature is imperfectly related to the desired pilot signal by distortion and the addition of harmonics and the actual signal is unknown. The cross talk noise is typically mitigated with an iterative data inversion and separation method (Neelamani, et al., U.S. Pat. No. 8,248,886) or by filtering (Huo et al., U.S. Patent Publication No. 2012/0290214).
Simultaneous sourcing can also be used for impulsive sources but there are fewer and less powerful methods to encode impulsive sources. There is little cost saving benefit for use of simultaneous sourcing for land acquisition with dynamite, but use of simultaneous sourcing for airguns in marine acquisition can be beneficial, especially for wide-azimuth acquisition. The use of random firing times for marine sources firing nearly simultaneously but located on different vessels was disclosed by Vaage (U.S. Pat. No. 6,906,981). More recently, simultaneous sourcing has been proposed for multiple vessel shooting of wide-azimuth (WAZ) marine surveys (Beasley et al., “A 3D simultaneous source field test processed using alternating projections: a new active separation method,” Geophysical Prospecting 60, 591-601 (2012)). Simultaneous sourcing is the only way that finely spaced (e.g. 25-m) source points, can be acquired in a single pass of the streamers. Without simultaneous sourcing, multiple passes are required and the survey takes much longer and costs are significantly higher.
We illustrate one configuration for a WAZ marine survey, in
The jitter is a form of encoding that allows the interference to be partially removed by filtering in processing. Since the boats are moving, a delay in firing time necessarily means a slight shift in the firing position around the nominal sourcing interval as determined by the speed of the vessel. Instead of requiring vessel-to-vessel time synchronization, it can be operationally simplier to implement random time delays by generating a “preplot” of sourcing positions along each line with random positional variations around the nominal source interval. During acquisition, each vessel shoots independently of the other vessels at the predetermined sourcing positions. With this method, the exact firing position but not the firing time is predetermined, but the result is still randomization in time. In the current invention, the randomization of sourcing time or position is understood to be equivalent. In either case, it is important to determine the actual firing position and firing time and these values along with other sourcing characteristics comprise the encoding function.
The combined data record obtained with simultaneous sourcing must be separated into individual records for each source for conventional processing. A flow-diagram of the standard process is shown in
The same processing method listed in
Simultaneous sourcing followed by source separation can also be used to assist with computationally-expensive seismic data simulation or forward modeling as described in Neelamani et al. (U.S. Pat. No. 8,248,886). Such forward modeling is a component of seismic imaging or seismic inversion with the output being an image of reflectivity or of formation properties such as the seismic velocity of the subsurface. Forward modeling uses a detailed velocity model and computes the complex wavefields theoretically generated by each source. Considerable computer time can be saved by reducing the number of sources to be modeled at one time by using simultaneous sourcing with some sort of encoding scheme, and then separating the data into the individual source seismograms. This method is identical to the field acquisition, but there are more choices of encoding schemes when done in the computer, and the specific encoded-sequence for a source is perfectly known. One common encoding scheme is to use random scaling in which the output of each source is randomly multiplied by either plus or minus one. This scheme cannot be physically implemented in the field for impulse sources such as airguns or explosives.
As described above, simultaneous sourcing can be used to lower costs to acquire seismic data in the field or to simulate seismic data in the computer. This involves recording one or more composite records containing interference from multiple sources. This can be a short record with sources excited close together in time and forming a spatial source array. It also can be continuous long record with individual sources excited at random or fixed intervals. For conventional imaging and inversion, the composite record must be separated into individual source gathers. Typically, this involves pseudo-separation by extracting a window around the firing-time of the sources and then using filtering or inversion operations to remove interference noise or crosstalk. In the special case, that the number of records are the same or greater than the number of individual sources within a spatial array, the separation is quite good, but acquiring multiple records is expensive. With fewer records, there is a problem in that the separation is imperfect with some crosstalk noise remaining or important signal removed by the filtering or inversion.
Inversion without Separation
Simultaneous sourcing is also used to save computational cost associated with imaging and inversion of seismic data. In these methods, individual seismic source gathers that were acquired sequentially, i.e. one source or source array shot at a time, are encoded in the computer and summed to form a simultaneous source record that is then used to form an image of seismic reflectivity or to determine subsurface properties. Use of this method to increase the speed and reduce cost of conventional (non-iterative and does not improve a sub-surface model) migration is disclosed by Ober et al. (U.S. Pat. No. 6,021,094) and use of the method in inversion is disclosed by Krebs, et al. (U.S. Pat. No. 8,121,823). Crosstalk or interference between sources is also a problem for this use of simultaneous sourcing and such crosstalk manifests itself as noise in the imaging and inversion outputs. The crosstalk can be minimized somewhat by optimizing the computer encoding functions, such as using random scaling instead of phase rotation, but the results may not be as good as the more computer-intensive sequential use of individual sources.
Simultaneous sourcing is particularly useful for inversion, such as full waveform inversion (FWI) and least-square reverse-time migration (LSRTM). These methods, unlike traditional imaging, work to iteratively update a trial model to minimize a data misfit function. The model is either subsurface properties such as velocity for FWI, or the reflectivity for LSRTM. Note that the misfit function is computed without source separation. Since both the forward modeling and the model update method are compute intensive, simultaneous sourcing has a large advantage. Typically all the sources in the survey or all the sources in a swath or sail line are encoded and summed to make a very large simultaneous source array. To minimize the crosstalk noise and to improve the results, the sources can be re-encoded and re-summed every iteration and then used for a model update (Krebs, U.S. Pat. No. 8,121,823). Each group of encoded and summed data may be called a realization of the data. The best results and reduced crosstalk are achieved when multiple realizations are used in the iterative process.
A typical process for the use of simultaneous sourcing in inversion is shown in
The use of simultaneous-sourcing for iterative inversion assumes that the receiver spread and record length are fixed, i.e. all receivers are recording for all sources for the same length of time so that the records can be summed together. The computer is used to forward-model all the sources into all of the receivers as if they were initiated at the same time or nearly the same time. If the point source data are not recorded with a fixed spread, for example if different receiver locations are used to record different shots, then the forward-modeling case does not match the field data case. This can create problems in that the misfit function, the difference between the field and forward-modeled data, will be dominated by the missing energy between the forward modeling and measured data and will not be useful for updating the trial model. Field data recorded by marine streamer is particularly problematic, in that the receiver steamer moves with the boat and is not fixed. A fixed spread is more commonly achieved on land or ocean-bottom recording, but even in this case a rolling-spread in which the active receiver lines change with source position may be acquired and not meet the assumptions of a fixed spread.
Other published attempts to deal with the failure of the fixed-receiver assumption include (1). “Hybrid method for full waveform inversion using simultaneous and sequential source method,” by Routh et al., U.S. Pat. No. 8,437,998; (2) “Simultaneous source encoding and source separation as a practical solution for full wavefield inversion,” by Routh et al., U.S. Publication No. 2012/0073825; (3) “Orthogonal source and receiver encoding,” by Krebs, et al., U.S. Publication No. 2013/0238246; (4) Haber et al., “An effective method for parameter estimation with PDE constraints with multiple right hand sides,” Preprint—UBC at internet address http://www.math.ubc.ca/˜haber/pubs/PdeOptStochV5.pdf (2010).
In this section, we have discussed generating the simultaneous source gather in the computer from data that were recorded sequentially in the field. Krebs, et al. (U.S. Pat. No. 8,121,823) taught that field encoded records that are acquired with an encoded areal source array recorded in a short record could be used in inversion as acquired, without the separation step discussed in the “Acquisition and then Separation” section of this document. By not separating the data, errors from the separation processes are not included in the inversion or imaging steps. Such errors could include a loss or deletion of certain reflection components that are important, for example steep dipping diffractions may be eliminated by error and limit the ability to sharply image bed terminations at small faults. There remains a problem, however, that certain powerful encoding methods available on the computer, such as random scaling, cannot be achieved in the field. In addition, if all the sources are acquired simultaneously in the field with one set of encoding functions, the encoding pattern is fixed and cannot be changed each iteration to make multiple realizations of the data. Finally, the requirements for using simultaneous sourcing for inversion are not always achieved when simultaneous sourcing is used in the field. It is a requirement as discussed above that the data be recorded with a fixed, non-moving spread of receivers for a fixed short length of time. The problems of moving spreads as illustrated above for marine sources is even worse when doing simultaneous sourcing in the field. In addition, it is not practical to use computer simulation to exactly simulate the data as acquired continuously by land wireless receivers for weeks, as illustrated in
The present invention uses simultaneous sourcing in the field in such a way as to overcome problems from non-fixed spreads and long recording times to yield a plurality of pseudo super-source records that can be computer encoded and stacked to make multiple realizations of the data that can be changed each iteration of the inversion.
This invention is a method for acquiring, at reduced seismic acquisition cost, data using simultaneous sources in the field, and then constructing pseudo source-records that better meet the requirements for using additional simultaneous sourcing for computer simulations or forward modeling as part of iterative inversion, such as FWI (Full Wavefield Inversion) or LSRTM (Least-Squares Reverse Time Migration), with additional reduction in computational costs. By better meeting the requirements of simultaneous sourcing for FWI or RTM, artifacts and crosstalk are reduced in the output. The method can be used for marine streamer acquisition and other non-fixed spread geometries to acquire both positive and negative offsets and to mitigate the “missing data” problem for simultaneous-source FWI. It can also be used for land data to overcome issues with moving spreads and long continuous records, where a long continuous record means a data record too long to be effectively computer simulated.
A first embodiment of the invention is a method for performing simultaneous inversion (without separation) of multiple sources where the data being inverted are field data records generated by two or more interfering or overlapping sources. Steps of this method may include:
A second embodiment of the invention is an application of the first embodiment to data acquired under survey conditions in which the fixed-receiver assumption necessary for simultaneous-source inversion is not satisfied. Steps of this method may include:
(i) constructing from the shot records a plurality of pseudo super-shot records, constructed such that each has data from a full spread of receivers;
(ii) encoding each pseudo super-shot record and stacking to form a simultaneous-source record of measured data;
(iii) using a computer to simulate the simultaneous-source record of measured data, using the same encoding used in (ii) and also the field encoding, and using an assumed subsurface model of velocity or other physical property; and
(iv) comparing the simulated simultaneous-source record with the simultaneous-source record of measured data, and determining from that an adjustment to the subsurface model of velocity or other physical property.
The above-described first embodiment of the invention may be used without the additional features of the second embodiment, for example when processing data where all sources illuminate a full spread of receivers. The updated or adjusted velocity model resulting from the present inventive method may be used to migrate the seismic data to generate an image of the subsurface, or for other seismic data processing and interpretation purposes relating to exploration for hydrocarbons.
The present invention and its advantages will be better understood by referring to the following detailed description and the attached drawings in which:
Due to patent law restrictions on the use of color,
The invention is first described in its basic form, then specific embodiments for marine and land data are described. This invention uses simultaneous sourcing in the field in such a way as to enhance the ability to further use simultaneous sourcing in iterative inversion by reducing the effects of crosstalk noise and better approximating acquisition by a fixed spread of receivers. The invention constructs, from acquisition records, what may be called pseudo super-source (or super-shot) records, each with the same duration and spatial extent. Each pseudo super-source record contains recorded energy from multiple sources, each source energized with a field encoding scheme (e.g., random time shifts, random source positions, phase rotations, sweep function, or other method) and each record is constructed by the operations of windowing, time shifting, summing and appending the original field records. The survey is acquired in a manner that allows these pseudo super-shot records to be constructed so that the sources can be properly simulated simultaneously in a computer. In particular, seismic energy that would be generated by a synthetic source and recorded within a predetermined distance Dsource within the spread and time duration Tsource is represented within the measured pseudo super-shot record. This requirement may require some groups of source points to be repeated into different receiver spreads with the same encoding as previously used. The multiple super-shot records are then separately encoded in the computer, preferably with random scaling such as multiplying by randomly selected +1 or −1, and then summed and used for inversion or imaging. Preferably, the computer encoding scheme is changed in subsequent iterations of the inversion of the inversion or imaging.
Basic steps in one embodiment of the present inventive method are given in the flow chart of
In Step 702, one or more field records are obtained that are generated with “simultaneous” sourcing so that energy from the different sources partially overlaps in time. In other words, the sources do not have to be activated exactly simultaneously, and the small time shifts between them are one way of performing the field encoding referred to in Step 702. A field record is typically all—or a subset—of the data recorded by the active receivers (moving or stationary) in one period of time, with a start time and a stop time and no gaps. The field records can be discrete records of a fixed time duration or they can be a single, continuous time record. If the recording spread is moved during acquisition, then preferably some of the source points within the distance Dsource of the boundary of the first spread are repeated into the second spread with the same encoding scheme previously used so that all energy within the distance Dsource is recorded on both sets of spread positions so they can be appended together.
Then in Step 703, a plurality of what may be called pseudo super-source records of fixed extent and duration are constructed. Preferably, the record extent would span the survey width, as if the survey had been recorded by a fixed spread of receivers the width of the survey, and the record duration would be at least as long as the time for seismic energy to propagate from the source to the target and to the receivers at the maximum useable distance or offset from the source. The construction process can include operations such as extractions of various time windows and trace regions from the field records. In addition, a pad of zero traces can be attached and a pad of time can be added before or after the windows. An objective of the construction of a pseudo super-source record is that every receiver location within an offset distance Dsource from the location of the source has appropriate data, i.e. data that would have been recorded if there had been a fixed receiver spread when the source shot occurred. Typically, the data from every field record will appear in at least one pseudo super-source record. The various windows can then be appended or summed together to form a pseudo super-shot record. Then in Step 704, each shot that influences or contributes to the region of interest is identified along with its field encoding function, and start time relative to the zero time of the pseudo super-shot record. The contributing or influential shots can be assumed to be those for which the source is excited within the distance Dsource and a time Tsource from the boundary of the region of interest. This information is combined with the computer-encoding function and used for the computer simulation step 706.
Next in Step 705, the different pseudo super-shot records are computer encoded, preferably, but not necessarily (any incoherent encoding scheme will work), by random scaling in which they are randomly multiplied by plus or minus one (±1). Then all the pseudo records are summed together to form one simultaneous source record. The computer is then used to compute the forward modeling simulation in one step for all the sources within the simultaneous record, which were identified in Step 704, as if all the sources had been fired simultaneously or nearly simultaneously (Step 706). (In other words, a wave propagation equation is solved with appropriate boundary and initial conditions and assuming a subsurface velocity model, using numerical methods such as iterative finite difference.) The computer simulation is made using the combined field and computer encoding schemes, i.e. what might be called double encoding. When simulating in Step 706 a simultaneous-source record corresponding to a simultaneous-source measured record from Step 705, the simultaneous-source simulated record is generated using a combination of the computer encoding that was used in step 705 combined with the field encoding from step 704/702. In Step 707, the recorded records from 703 and the simulated records from 706 are compared over a region of interest, and the results are used to update the subsurface model. If more iterations of the imaging or inversion is needed as determined in Step 708, then preferably the computer encoding Step 705 is repeated with a different encoding function.
Marine Embodiment
In this section, a particular embodiment is described that overcomes the moving spread problem for marine streamer, which was illustrated in
All the sources fire within the same source interval but with different random time delays or random positions around the nominal source location, and a single record of fixed length is recorded as illustrated as 901 in
In Step 703, a pseudo super-source record is constructed. Each record that was recorded with identical rear and front sources at the same position are time aligned to match the source timing and appended. Traces may be padded (i.e., zeros added) at the end or beginning. This makes one long record 912 that preferably spans the entire sail line with sources separated by approximately the length of the streamer. This pseudo super-source record now better approximates a fixed spread because both positive and negative offsets are recorded from each source position up to a distance of Dsource. Here Dsource is naturally the streamer length. Now all these sources can be simultaneously simulated in the computer, for example by putting groups of sources at 922, 932, 942 and 952.
In Step 703, additional pseudo super-source records are constructed, each having the same spatial extent and time duration as illustrated in
In Step 704, the source location and encoding information, including time shifts, are determined for each pseudo super-source record relative to the boundaries of the pseudo record. For example, the start time of each source is adjusted by the time shifts used to form the pseudo record and is now relative to zero time of the pseudo record. This information will be used in step 706, combined with the computer-encoding used in Step 705, in simultaneously simulating the encoded pseudo records.
In Step 705, each pseudo super-source record containing many shots is encoded in the computer. Preferably this is done by randomly multiplying by +1 or −1. Alternatively, phase rotations or another form of encoding can be used. Then, the encoded pseudo records are stacked or summed, as shown in the illustration of 1112 in
In Step 706, all the sources in the sail line are computer-simulated at one time using a combination of the field encoding determined in Step 704/702 and the computer encoding used in Step 705. Further savings in computational cost may be achieved by limiting the region of the model used in a single-sail line simulation. This simulation is illustrated with the sunbursts in 1116. This may involve extending or padding the modeling space by an additional region as indicated in 1113, which allows the forward modeling to generate all the bits of energy recorded in the data window 1118. Next, in Step 707, the measured simultaneous source record over the region of interest (1118 in the example) is compared to the simulated simultaneous source record and the result is used to update the subsurface model. Because the simulated energy from all source positions that influence the region of interest are present in both the measured and simulated data—at least up to a distance and time of Dsource and Tsource from each source firing position—the problem that the comparison or misfit function is distorted by artifacts from creating the simultaneous source record is avoided. By constructing the pseudo records, the requirements of a fixed spread and small trace duration are met. With additional iterations of the inversion or imaging step, the computer encoding is preferably changed by repeating Step 705 with a different and encoding and thereby forming multiple realizations of the data that further reduce crosstalk and artifacts.
It is straightforward to modify the example shown here for different acquisition requirements involving more streamer vessels and sets of streamers and more source vessels. The source position and the firing pattern are chosen so that pseudo super-source gathers can be constructed that better approximates recording by a fixed spread for the sail line or for the entire survey. For example, additional boats towing sources can be used in front of the streamer vessel and further behind the end of the streamer and fired simultaneously with the other sources to record longer offset data for the sail line. In addition, vessels can be located on both sides of the streamer vessels so as to better approximate a cross-line fixed spread allowing all the sources in the survey to be simulated simultaneously in one computational forward modeling effort.
Land Embodiment
Data acquisition on land or on the ocean bottom is considered next. Here sensors are not moving as in a marine streamer, but the group of active receivers may change during the survey. This is often called rolling the spread. In
In Step 703, several pseudo super-source records of fixed size and duration are constructed. Preferably the duration is longer than Tlisten but short enough to be efficiently simulated in the computer. Construction for this example may be illustrated in two steps. In
Then in Step 704, the source locations, encoding function and firing time relative to zero time of the super source records 1401 and 1402 are identified. The sources should be within a time of Tsource from above the top of the window or within a distance of Dsource from the boundaries of the record. In Step 705, the super-source records are computer encoded and summed, making a measured simultaneous source record as illustrated in
The foregoing application is directed to particular embodiments of the present invention 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, at least some of the steps in the present inventive method are performed on a computer, i.e. the invention is computer implemented.
This application claims the benefit of U.S. Provisional Patent Application 61/869,292, filed Aug. 23, 2013, entitled SIMULTANEOUS SOURCING DURING BOTH SEISMIC ACQUISITION AND SEISMIC INVERSION, the entirety of which is incorporated by reference herein.
Number | Name | Date | Kind |
---|---|---|---|
3812457 | Weller | May 1974 | A |
3864667 | Bahjat | Feb 1975 | A |
4159463 | Silverman | Jun 1979 | A |
4168485 | Payton et al. | Sep 1979 | A |
4545039 | Savit | Oct 1985 | A |
4562540 | Devaney | Dec 1985 | A |
4575830 | Ingram et al. | Mar 1986 | A |
4594662 | Devaney | Jun 1986 | A |
4636956 | Vannier et al. | Jan 1987 | A |
4675851 | Savit et al. | Jun 1987 | A |
4686654 | Savit | Aug 1987 | A |
4707812 | Martinez | Nov 1987 | A |
4715020 | Landrum, Jr. | Dec 1987 | A |
4766574 | Whitmore et al. | Aug 1988 | A |
4780856 | Becquey | Oct 1988 | A |
4823326 | Ward | Apr 1989 | A |
4924390 | Parsons et al. | May 1990 | A |
4953657 | Edington | Sep 1990 | A |
4969129 | Currie | Nov 1990 | A |
4982374 | Edington et al. | Jan 1991 | A |
5260911 | Mason et al. | Nov 1993 | A |
5469062 | Meyer, Jr. | Nov 1995 | A |
5583825 | Carrazzone et al. | Dec 1996 | A |
5677893 | de Hoop et al. | Oct 1997 | A |
5715213 | Allen | Feb 1998 | A |
5717655 | Beasley | Feb 1998 | A |
5719821 | Sallas et al. | Feb 1998 | A |
5721710 | Sallas et al. | Feb 1998 | A |
5790473 | Allen | Aug 1998 | A |
5798982 | He et al. | Aug 1998 | A |
5822269 | Allen | Oct 1998 | A |
5838634 | Jones et al. | Nov 1998 | A |
5852588 | de Hoop et al. | Dec 1998 | A |
5878372 | Tabarovsky et al. | Mar 1999 | A |
5920828 | Norris et al. | Jul 1999 | A |
5924049 | Beasley et al. | Jul 1999 | A |
5999488 | Smith | Dec 1999 | A |
5999489 | Lazaratos | Dec 1999 | A |
6005916 | Johnson et al. | Dec 1999 | A |
6014342 | Lazaratos | Jan 2000 | A |
6021094 | Ober et al. | Feb 2000 | A |
6028818 | Jeffryes | Feb 2000 | A |
6058073 | VerWest | May 2000 | A |
6125330 | Robertson et al. | Sep 2000 | A |
6219621 | Hornbostel | Apr 2001 | B1 |
6225803 | Chen | May 2001 | B1 |
6311133 | Lailly et al. | Oct 2001 | B1 |
6317695 | Zhou et al. | Nov 2001 | B1 |
6327537 | Ikelle | Dec 2001 | B1 |
6374201 | Grizon et al. | Apr 2002 | B1 |
6381543 | Guerillot et al. | Apr 2002 | B1 |
6388947 | Washbourne et al. | May 2002 | B1 |
6480790 | Calvert et al. | Nov 2002 | B1 |
6522973 | Tonellot et al. | Feb 2003 | B1 |
6545944 | de Kok | Apr 2003 | B2 |
6549854 | Malinverno et al. | Apr 2003 | B1 |
6574564 | Lailly et al. | Jun 2003 | B2 |
6593746 | Stolarczyk | Jul 2003 | B2 |
6662147 | Fournier et al. | Dec 2003 | B1 |
6665615 | Van Riel et al. | Dec 2003 | B2 |
6687619 | Moerig et al. | Feb 2004 | B2 |
6687659 | Shen | Feb 2004 | B1 |
6704245 | Becquey | Mar 2004 | B2 |
6714867 | Meunier | Mar 2004 | B2 |
6735527 | Levin | May 2004 | B1 |
6754590 | Moldoveanu | Jun 2004 | B1 |
6766256 | Jeffryes | Jul 2004 | B2 |
6826486 | Malinverno | Nov 2004 | B1 |
6836448 | Robertsson et al. | Dec 2004 | B2 |
6842701 | Moerig et al. | Jan 2005 | B2 |
6859734 | Bednar | Feb 2005 | B2 |
6865487 | Charron | Mar 2005 | B2 |
6865488 | Moerig et al. | Mar 2005 | B2 |
6876928 | Van Riel et al. | Apr 2005 | B2 |
6882938 | Vaage et al. | Apr 2005 | B2 |
6882958 | Schmidt et al. | Apr 2005 | B2 |
6901333 | Van Riel et al. | May 2005 | B2 |
6903999 | Curtis et al. | Jun 2005 | B2 |
6906981 | Vauge | Jun 2005 | B2 |
6927698 | Stolarczyk | Aug 2005 | B2 |
6944546 | Xiao et al. | Sep 2005 | B2 |
6947843 | Fisher et al. | Sep 2005 | B2 |
6970397 | Castagna et al. | Nov 2005 | B2 |
6977866 | Huffman et al. | Dec 2005 | B2 |
6999880 | Lee | Feb 2006 | B2 |
7046581 | Calvert | May 2006 | B2 |
7050356 | Jeffryes | May 2006 | B2 |
7069149 | Goff et al. | Jun 2006 | B2 |
7072767 | Routh et al. | Jul 2006 | B2 |
7092823 | Lailly et al. | Aug 2006 | B2 |
7110900 | Adler et al. | Sep 2006 | B2 |
7184367 | Yin | Feb 2007 | B2 |
7230879 | Herkenhoff et al. | Jun 2007 | B2 |
7271747 | Baraniuk et al. | Sep 2007 | B2 |
7330799 | Lefebvre et al. | Feb 2008 | B2 |
7337069 | Masson et al. | Feb 2008 | B2 |
7373251 | Hamman et al. | May 2008 | B2 |
7373252 | Sherrill et al. | May 2008 | B2 |
7376046 | Jeffryes | May 2008 | B2 |
7376539 | Lecomte | May 2008 | B2 |
7400978 | Langlais et al. | Jul 2008 | B2 |
7436734 | Krohn | Oct 2008 | B2 |
7480206 | Hill | Jan 2009 | B2 |
7584056 | Koren | Sep 2009 | B2 |
7599798 | Beasley et al. | Oct 2009 | B2 |
7602670 | Jeffryes | Oct 2009 | B2 |
7616523 | Tabti et al. | Nov 2009 | B1 |
7620534 | Pita et al. | Nov 2009 | B2 |
7620536 | Chow | Nov 2009 | B2 |
7646924 | Donoho | Jan 2010 | B2 |
7672194 | Jeffryes | Mar 2010 | B2 |
7672824 | Dutta et al. | Mar 2010 | B2 |
7675815 | Saenger et al. | Mar 2010 | B2 |
7679990 | Herkenhoff et al. | Mar 2010 | B2 |
7684281 | Vaage et al. | Mar 2010 | B2 |
7710821 | Robertsson et al. | May 2010 | B2 |
7715985 | Van Manen et al. | May 2010 | B2 |
7715986 | Nemeth et al. | May 2010 | B2 |
7725266 | Sirgue et al. | May 2010 | B2 |
7791980 | Robertsson et al. | Sep 2010 | B2 |
7835072 | Izumi | Nov 2010 | B2 |
7840625 | Candes et al. | Nov 2010 | B2 |
7940601 | Ghosh | May 2011 | B2 |
8121823 | Krebs et al. | Feb 2012 | B2 |
8248886 | Neelamani et al. | Aug 2012 | B2 |
8428925 | Krebs et al. | Apr 2013 | B2 |
8437998 | Routh et al. | May 2013 | B2 |
8688381 | Routh et al. | Apr 2014 | B2 |
20020099504 | Cross et al. | Jul 2002 | A1 |
20020120429 | Ortoleva | Aug 2002 | A1 |
20020183980 | Guillaume | Dec 2002 | A1 |
20040199330 | Routh et al. | Oct 2004 | A1 |
20040225483 | Okoniewski et al. | Nov 2004 | A1 |
20050128874 | Herkenhoff et al. | Jun 2005 | A1 |
20060235666 | Assa et al. | Oct 2006 | A1 |
20070036030 | Baumel et al. | Feb 2007 | A1 |
20070038691 | Candes et al. | Feb 2007 | A1 |
20070165486 | Moldoveanu et al. | Jul 2007 | A1 |
20070274155 | Ikelle | Nov 2007 | A1 |
20080175101 | Saenger et al. | Jul 2008 | A1 |
20080306692 | Singer et al. | Dec 2008 | A1 |
20090006054 | Song | Jan 2009 | A1 |
20090067041 | Izumi | Mar 2009 | A1 |
20090070042 | Birchwood et al. | Mar 2009 | A1 |
20090083006 | Mackie | Mar 2009 | A1 |
20090164186 | Haase et al. | Jun 2009 | A1 |
20090164756 | Dokken et al. | Jun 2009 | A1 |
20090187391 | Wendt et al. | Jul 2009 | A1 |
20090248308 | Luling | Oct 2009 | A1 |
20090254320 | Lovatini et al. | Oct 2009 | A1 |
20090259406 | Khadhraoui et al. | Oct 2009 | A1 |
20100008184 | Hegna et al. | Jan 2010 | A1 |
20100018718 | Krebs et al. | Jan 2010 | A1 |
20100039894 | Abma et al. | Feb 2010 | A1 |
20100054082 | McGarry et al. | Mar 2010 | A1 |
20100088035 | Etgen et al. | Apr 2010 | A1 |
20100103772 | Eick et al. | Apr 2010 | A1 |
20100118651 | Liu et al. | May 2010 | A1 |
20100142316 | Keers et al. | Jun 2010 | A1 |
20100161233 | Saenger et al. | Jun 2010 | A1 |
20100161234 | Saenger et al. | Jun 2010 | A1 |
20100185422 | Hoversten | Jul 2010 | A1 |
20100208554 | Chiu et al. | Aug 2010 | A1 |
20100212909 | Baumstein et al. | Aug 2010 | A1 |
20100265797 | Robertsson et al. | Oct 2010 | A1 |
20100270026 | Lazaratos et al. | Oct 2010 | A1 |
20100286919 | Lee et al. | Nov 2010 | A1 |
20100286921 | Lee | Nov 2010 | A1 |
20100299070 | Abma | Nov 2010 | A1 |
20110000678 | Krebs et al. | Jan 2011 | A1 |
20110040926 | Frost et al. | Feb 2011 | A1 |
20110051553 | Scott et al. | Mar 2011 | A1 |
20110090760 | Rickett et al. | Apr 2011 | A1 |
20110131020 | Meng | Jun 2011 | A1 |
20110134722 | Virgilio et al. | Jun 2011 | A1 |
20110182141 | Zhamikov et al. | Jul 2011 | A1 |
20110182144 | Gray | Jul 2011 | A1 |
20110191032 | Moore | Aug 2011 | A1 |
20110194379 | Lee et al. | Aug 2011 | A1 |
20110222370 | Downton et al. | Sep 2011 | A1 |
20110227577 | Zhang et al. | Sep 2011 | A1 |
20110235464 | Brittan et al. | Sep 2011 | A1 |
20110238390 | Krebs et al. | Sep 2011 | A1 |
20110246140 | Abubakar et al. | Oct 2011 | A1 |
20110267921 | Mortel et al. | Nov 2011 | A1 |
20110267923 | Shin | Nov 2011 | A1 |
20110276320 | Krebs et al. | Nov 2011 | A1 |
20110288831 | Tan et al. | Nov 2011 | A1 |
20110299361 | Shin | Dec 2011 | A1 |
20110320180 | Al-Saleh | Dec 2011 | A1 |
20120010862 | Costen | Jan 2012 | A1 |
20120014215 | Saenger et al. | Jan 2012 | A1 |
20120014216 | Saenger et al. | Jan 2012 | A1 |
20120033525 | Abma et al. | Feb 2012 | A1 |
20120051176 | Liu | Mar 2012 | A1 |
20120073824 | Routh | Mar 2012 | A1 |
20120073825 | Routh | Mar 2012 | A1 |
20120082344 | Donoho | Apr 2012 | A1 |
20120143506 | Routh et al. | Jun 2012 | A1 |
20120215506 | Rickett et al. | Aug 2012 | A1 |
20120253682 | Andreoletti | Oct 2012 | A1 |
20120275264 | Kostov et al. | Nov 2012 | A1 |
20120275267 | Neelamani et al. | Nov 2012 | A1 |
20120290214 | Huo et al. | Nov 2012 | A1 |
20120314538 | Washbourne et al. | Dec 2012 | A1 |
20120316790 | Washbourne et al. | Dec 2012 | A1 |
20120316844 | Shah et al. | Dec 2012 | A1 |
20130081752 | Kurimura et al. | Apr 2013 | A1 |
20130135966 | Rommel et al. | May 2013 | A1 |
20130238246 | Krebs et al. | Sep 2013 | A1 |
20130311149 | Tang et al. | Nov 2013 | A1 |
20130311151 | Plessix | Nov 2013 | A1 |
Number | Date | Country |
---|---|---|
2 796 631 | Nov 2011 | CA |
1 094 338 | Apr 2001 | EP |
1 746 443 | Jan 2007 | EP |
2 592 439 | May 2013 | EP |
2 594 962 | May 2013 | EP |
2 390 712 | Jan 2004 | GB |
2 391 665 | Feb 2004 | GB |
WO 2006037815 | Apr 2006 | WO |
WO 2007046711 | Apr 2007 | WO |
WO 2008042081 | Apr 2008 | WO |
WO 2008123920 | Oct 2008 | WO |
WO 2009067041 | May 2009 | WO |
WO 2009117174 | Sep 2009 | WO |
WO 2011040926 | Apr 2011 | WO |
WO 2011091216 | Jul 2011 | WO |
WO 2011093945 | Aug 2011 | WO |
WO 2012024025 | Feb 2012 | WO |
WO 2012041834 | Apr 2012 | WO |
WO 2012047384 | Apr 2012 | WO |
WO 2012083234 | Jun 2012 | WO |
WO 2012134621 | Oct 2012 | WO |
WO 2012170201 | Dec 2012 | WO |
WO 2013081752 | Jun 2013 | WO |
Entry |
---|
Mora, P. (1987), “Elastic Wavefield Inversion,” PhD Thesis, Stanford University, pp. 22-25. |
Mora, P. (1989), “Inversion = migration + tomography,” Geophysics 64, pp. 888-901. |
Nazarian, S. et al. (1983), “Use of spectral analysis of surface waves method for determination of moduli and thickness of pavement systems,” Transport Res. Record 930, pp. 38-45. |
Neelamani, R., (2008), “Simultaneous sourcing without compromise,” 70th Annual Int'l. Conf. and Exh., EAGE, 5 pgs. |
Neelamani, R. (2009), “Efficient seismic forward modeling using simultaneous sources and sparsity,” SEG Expanded Abstracts, pp. 2107-2111. |
Nocedal, J. et al. (2006), “Numerical Optimization, Chapt. 7—Large-Scale Unconstrained Optimization,” Springer, New York, 2nd Edition, pp. 165-176. |
Nocedal, J. et al. (2000), “Numerical Optimization-Calculating Derivatives,” Chapter 8, Springer Verlag, pp. 194-199. |
Ostmo, S. et al. (2002), “Finite-difference iterative migration by linearized waveform inversion in the frequency domain,” SEG Int'l. Expo. & 72nd Ann. Meeting, 4 pgs. |
Park, C.B. et al. (1999), “Multichannel analysis of surface waves,” Geophysics 64(3), pp. 800-808. |
Park, C.B. et al. (2007), “Multichannel analysis of surface waves (MASW)—active and passive methods,” The Leading Edge, pp. 60-64. |
Pica, A. et al. (2005), “3D Surface-Related Multiple Modeling, Principles and Results,” 2005 SEG Ann. Meeting, SEG Expanded Abstracts 24, pp. 2080-2083. |
Plessix, R.E. et al. (2004), “Frequency-domain finite-difference amplitude preserving migration,” Geophys. J. Int. 157, pp. 975-987. |
Porter, R.P. (1989), “Generalized holography with application to inverse scattering and inverse source problems,” In E. Wolf, editor, Progress in Optics XXVII, Elsevier, pp. 317-397. |
Pratt, R.G. et al. (1998), “Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion,” Geophys. J. Int. 133, pp. 341-362. |
Pratt, R.G. (1999), “Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model,” Geophysics 64, pp. 888-901. |
Rawlinson, N. et al. (2008), “A dynamic objective function technique for generating multiple solution models in seismic tomography,” Geophys. J. Int. 178, pp. 295-308. |
Rayleigh, J.W.S. (1899), “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky,” Phil. Mag. 47, pp. 375-384. |
Romero, L.A. et al. (2000), Phase encoding of shot records in prestack migration, Geophysics 65, pp. 426-436. |
Ronen S. et al. (2005), “Imaging Downgoing waves from Ocean Bottom Stations,” SEG Expanded Abstracts, pp. 963-967. |
Routh, P. et al. (2011), “Encoded Simultaneous Source Full-Wavefield Inversion for Spectrally-Shaped Marine Streamer Data,” SEG San Antonio 2011 Ann. Meeting, pp. 2433-2438. |
Ryden, N. et al. (2006), “Fast simulated annealing inversion of surface waves on pavement using phase-velocity spectra,” Geophysics 71(4), pp. R49-R58. |
Sambridge, M.S. et al. (1991), “An Alternative Strategy for Non-Linear Inversion of Seismic Waveforms,” Geophysical Prospecting 39, pp. 723-736. |
Schoenberg, M. et al. (1989), “A calculus for finely layered anisotropic media,” Geophysics 54, pp. 581-589. |
Schuster, G.T. et al. (2010), “Theory of Multisource Crosstalk Reduction by Phase-Encoded Statics,” SEG Denver 2010 Ann. Meeting, pp. 3110-3114. |
Sears, T.J. et al. (2008), “Elastic full waveform inversion of multi-component OBC seismic data,” Geophysical Prospecting 56, pp. 843-862. |
Sheen, D-H. et al. (2006), “Time domain Gauss-Newton seismic waveform inversion in elastic media,” Geophysics J. Int. 167, pp. 1373-1384. |
Shen, P. et al. (2003), “Differential semblance velocity analysis by wave-equation migration,” 73rd Ann. Meeting of Society of Exploration Geophysicists, 4 pgs. |
Sheng, J. et al. (2006), “Early arrival waveform tomography on near-surface refraction data,” Geophysics 71, pp. U47-U57. |
Sheriff, R.E.et al. (1982), “Exploration Seismology”, pp. 134-135. |
Shih, R-C. et al. (1996), “Iterative pre-stack depth migration with velocity analysis,” Terrestrial, Atmospheric & Oceanic Sciences 7(2), pp. 149-158. |
Shin, C. et al. (2001), “Waveform inversion using a logarithmic wavefield,” Geophysics 49, pp. 597-606. |
Simard, P.Y. et al. (1990), “Vector Field Restoration by the Method of Convex Projections,” Computer Vision, Graphics and Image Processing 52, pp. 360-385. |
Sirgue, L. (2004), “Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies,” Geophysics 69, pp. 231-248. |
Soubaras, R. et al. (2007), “Velocity model building by semblance maximization of modulated-shot gathers,” Geophysics 72(5), pp. U67-U73. |
Spitz, S. (2008), “Simultaneous source separation: a prediction-subtraction approach,” 78th Annual Int'l. Meeting, SEG Expanded Abstracts, pp. 2811-2815. |
Stefani, J. (2007), “Acquisition using simultaneous sources,” 69th Annual Conf. and Exh., EAGE Extended Abstracts, 5 pgs. |
Symes, W.W. (2007), “Reverse time migration with optimal checkpointing,” Geophysics 72(5), pp. p. SM213-SM221. |
Symes, W.W. (2009), “Interface error analysis for numerical wave propagation,” Compu. Geosci. 13, pp. 363-371. |
Tang, Y. (2008), “Wave-equation Hessian by phase encoding,” SEG Expanded Abstracts 27, pp. 2201-205. |
Tang, Y. (2009), “Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian,” Geophysics 74, pp. WCA95-WCA107. |
Tang, Y. et al. (2010), “Preconditioning full waveform inversion with phase-encoded Hessian,” SEG Expanded Abstracts 29, pp. 1034-1037. |
Tarantola, A. (1986), “A strategy for nonlinear elastic inversion of seismic reflection data,” Geophysics 51(10), pp. 1893-1903. |
Tarantola, A. (1988), “Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation,” Pure and Applied Geophysics 128, pp. 365-399. |
Tarantola, A. (2005), “Inverse Problem Theory and Methods for Model Parameter Estimation,” SIAM, pp. 79. |
Tarantola, A. (1984), “Inversion of seismic reflection data in the acoustic approximation,” Geophysics 49, pp. 1259-1266. |
Trantham, E.C. (1994), “Controlled-phase acquisition and processing,” SEG Expanded Abstracts 13, pp. 890-894. |
Tsvankin, I. (2001), “Seismic Signatures and Analysis of Reflection Data in Anisotropic Media,” Elsevier Science, p. 8. |
Valenciano, A.A. (2008), “Imaging by Wave-Equation Inversion,” A Dissertation, Stanford University, 138 pgs. |
van Groenestijn, G.J.A. et al. (2009), “Estimating primaries by sparse inversion and application to near-offset reconstruction,” Geophyhsics 74(3), pp. A23-A28. |
van Manen, D.J. (2005), “Making wave by time reversal,” SEG International Exposition and 75th Annual Meeting, Expanded Abstracts, pp. 1763-1766. |
Verschuur, D.J. (2009), Target-oriented, least-squares imaging of blended data, 79th Annual Int'l. Meeting, SEG Expanded Abstracts, pp. 2889-2893. |
Verschuur, D.J. et al. (1992), “Adaptive surface-related multiple elimination,” Geophysics 57(9), pp. 1166-1177. |
Verschuur, D.J. (1989), “Wavelet Estimation by Prestack Multiple Elimination,” SEG Expanded Abstracts 8, pp. 1129-1132. |
Versteeg, R. (1994), “The Marmousi experience: Velocity model determination on a synthetic complex data set,” The Leading Edge, pp. 927-936. |
Vigh, D. et al. (2008), “3D prestack plane-wave, full-waveform inversion,” Geophysics 73(5), pp. VE135-VE144. |
Wang, Y. (2007), “Multiple prediction through inversion: Theoretical advancements and real data application,” Geophysics 72(2), pp. V33-V39. |
Wang, K. et al. (2009), “Simultaneous full-waveform inversion for source wavelet and earth model,” SEG Int'l. Expo. & Ann. Meeting, Expanded Abstracts, pp. 2537-2541. |
Weglein, A.B. (2003), “Inverse scattering series and seismic exploration,” Inverse Problems 19, pp. R27-R83. |
Wong, M. et al. (2010), “Joint least-squares inversion of up- and down-going signal for ocean bottom data sets,” SEG Expanded Abstracts 29, pp. 2752-2756. |
Wu R-S. et al. (2006), “Directional illumination analysis using beamlet decomposition and propagation,” Geophysics 71(4), pp. S147-S159. |
Xia, J. et al. (2004), “Utilization of high-frequency Rayleigh waves in near-surface geophysics,” The Leading Edge, pp. 753-759. |
Xie, X. et al. (2002), “Extracting angle domain information from migrated wavefield,” SEG Expanded Abstracts21, pp. 1360-1363. |
Xie, X.-B. et al. (2006), “Wave-equation-based seismic illumination analysis,” Geophysics 71(5), pp. S169-S177. |
Yang, K. et al. (2000), “Quasi-Orthogonal Sequences for Code-Division Multiple-Access Systems,” IEEE Transactions on Information Theory 46(3), pp. 982-993. |
Yoon, K. et al. (2004), “Challenges in reverse-time migration,” SEG Expanded Abstracts 23, pp. 1057-1060. |
Young, J. et al. (2011), “An application of random projection to parameter estimation in partial differential equations,” SIAM, 20 pgs. |
Zhang, Y. (2005), “Delayed-shot 3D depth migration,” Geophysics 70, pp. E21-E28. |
Ziolkowski, A. (1991), “Why don't we measure seismic signatures?,” Geophysics 56(2), pp. 190-201. |
U.S. Appl. No. 14/272,020, filed May 7, 2014, Wang et al. |
U.S. Appl. No. 14/286,107, filed May 23, 2014, Hu et al. |
U.S. Appl. No. 14/311,945, filed Jun. 20, 2014, Bansal et al. |
U.S. Appl. No. 14/329,431, filed Jul. 11, 2014, Krohn et al. |
U.S. Appl. No. 14/330,767, filed Jul. 14, 2014, Tang et al. |
Abt, D.L. et al. (2010), “North American lithospheric discontinuity structured imaged by Ps and Sp receiver functions”, J. Geophys. Res., 24 pgs. |
Akerberg, P., et al. (2008), “Simultaneous source separation by sparse radon transform,” 78th SEG Annual International Meeting, Expanded Abstracts, pp. 2801-2805. |
Aki, K. et al. (1980), “Quantitative Seismology: Theory and Methods Volume I—Chapter 7—Surface Waves in a Vertically Heterogenous Medium,” W.H. Freeman and Co., pp. 259-318. |
Aki, K. et al. (1980), “Quantitative Seismology: Theory and Methods Volume I,” W.H. Freeman and Co., p. 173. |
Aki et al. (1980), “Quantitative Seismology, Theory and Methods,” Chapter 5.20, W.H. Freeman & Co., pp. 133-155. |
Amundsen, L. (2001), “Elimination of free-surface related multiples without need of the source wavelet,” Geophysics 60(1), pp. 327-341. |
Anderson, J.E. et al. (2008), “Sources Near the Free-Surface Boundary: Pitfalls for Elastic Finite-Difference Seismic Simulation and Multi-Grid Waveform Inversion,” 70th EAGE Conf. & Exh., 4 pgs. |
Barr, F.J. et al. (1989), “Attenuation of Water-col. Reverberations Using Pressure and Velocity Detectors in a Water-Bottom Cable,” 59th Annual SEG meeting, Expanded Abstracts, pp. 653-656. |
Baumstein, A. et al. (2009), “Scaling of the Objective Function Gradient for Full Wavefield Inversion,” SEG Houston 2009 Int'l. Expo and Annual Meeting, pp. 224-2247. |
Beasley, C. (2008), “A new look at marine simultaneous sources,” The Leading Edge 27(7), pp. 914-917. |
Beasley, C. (2012), “A 3D simultaneous source field test processed using alternating projections: a new active separation method,” Geophsyical Prospecting 60, pp. 591-601. |
Beaty, K.S. et al. (2003), “Repeatability of multimode Rayleigh-wave dispersion studies,” Geophysics 68(3), pp. 782-790. |
Beaty, K.S. et al. (2002), “Simulated annealing inversion of multimode Rayleigh wave dispersion waves for geological structure,” Geophys. J. Int. 151, pp. 622-631. |
Becquey, M. et al. (2002), “Pseudo-Random Coded Simultaneous Vibroseismics,” SEG Int'l. Exposition and 72th Annl. Mtg., 4 pgs. |
Ben-Hadj-Ali, H. et al. (2009), “Three-dimensional frequency-domain full waveform inversion with phase encoding,” SEG Expanded Abstracts, pp. 2288-2292. |
Ben-Hadj-Ali, H. et al. (2011), “An efficient frequency-domain full waveform inversion method using simultaneous encoded sources,” Geophysics 76(4), pp. R109-R124. |
Benitez, D. et al. (2001), “The use of the Hilbert transform in ECG signal analysis,” Computers in Biology and Medicine 31, pp. 399-406. |
Berenger, J-P. (1994), “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,” J. of Computational Physics 114, pp. 185-200. |
Berkhout, A.J. (1987), “Applied Seismic Wave Theory,” Elsevier Science Publishers, p. 142. |
Berkhout, A.J. (1992), “Areal shot record technology,” Journal of Seismic Exploration 1, pp. 251-264. |
Berkhout, A.J. (2008), “Changing the mindset in seismic data acquisition,” The Leading Edge 27(7), pp. 924-938. |
Beylkin, G. (1985), “Imaging of discontinuities in the inverse scattring problem by inversion of a causal generalized Radon transform,” J Math. Phys. 26, pp. 99-108. |
Biondi, B. (1992), “Velocity estimation by beam stack,” Geophysics 57(8), pp. 1034-1047. |
Bonomi, E. et al. (2006), “Wavefield Migration plus Monte Carlo Imaging of 3D Prestack Seismic Data,” Geophysical Prospecting 54, pp. 505-514. |
Boonyasiriwat, C. et al. (2010), 3D Multisource Full-Waveform using Dynamic Random Phase Encoding, SEG Denver 2010 Annual Meeting, pp. 1044-1049. |
Boonyasiriwat, C. et al. (2010), 3D Multisource Full-Waveform using Dynamic Random Phase Encoding, SEG Denver 2010 Annual Meeting, pp. 3120-3124. |
Bunks, C., et al. (1995), “Multiscale seismic waveform inversion,” Geophysics 60, pp. 1457-1473. |
Burstedde, G. et al. (2009), “Algorithmic strategies for full waveform inversion: 1D experiments,” Geophysics 74(6), pp. WCC17-WCC46. |
Chavent, G. et al. (1999), “An optimal true-amplitude least-squares prestack depth-migration operator,” Geophysics 64(2), pp. 508-515. |
Choi, Y. et al. (2011), “Application of encoded multisource waveform inversion to marine-streamer acquisition based on the global correlation,” 73rd EAGE Conference, Abstract, pp. F026. |
Choi, Y et al. (2012), “Application of multi-source waveform inversion to marine stream data using the global correlation norm,” Geophysical Prospecting 60, pp. 748-758. |
Clapp, R.G. (2009), “Reverse time migration with random boundaries,” SEG International Exposition and Meeting, Expanded Abstracts, pp. 2809-2813. |
Dai, W. et al. (2010), “3D Multi-source Least-squares Reverse Time Migration,” SEG Denver 2010 Annual Meeting, pp. 3120-3124. |
Delprat-Jannuad, F. et al. (2005), “A fundamental limitation for the reconstruction of impedance profiles from seismic data,” Geophysics 70(1), pp. R1-R14. |
Dickens, T.A. et al. (2011), RTM angle gathers using Poynting vectors, SEG Expanded Abstracts 30, pp. 3109-3113. |
Donerici, B. et al. (1005), “Improved FDTD Subgridding Algorithms Via Digital Filtering and Domain Overriding,” IEEE Transactions on Antennas and Propagation 53(9), pp. 2938-2951. |
Downey, N. et al. (2011), “Random-Beam Full-Wavefield Inversion,” 2011 San Antonio Annual Meeting, pp. 2423-2427. |
Dunkin, J W et al. (1973), “Effect of Normal Moveout on a Seismic Pluse,” Geophysics 38(4), pp. 635-642. |
Dziewonski A. et al. (1981), “Preliminary Reference Earth Model”, Phys. Earth Planet. Int. 25(4), pp. 297-356. |
Ernst, F.E. et al. (2000), “Tomography of dispersive media,” J Acoust. Soc. Am 108(1), pp. 105-116. |
Ernst, F.E. et al. (2002), “Removal of scattered guided waves from seismic data,” Geophysics 67(4), pp. 1240-1248. |
Esmersoy, C. (1990), “Inversion of P and SV waves from multicomponent offset vertical seismic profiles”, Geophysics 55(1), pp. 39-50. |
Etgen, J.T. et al. (2007), “Computational methods for large-scale 3D acoustic finite-difference modeling: A tutorial,” Geophysics 72(5), pp. SM223-SM230. |
Fallat, M.R. et al. (1999), “Geoacoustic inversion via local, global, and hybrid algorithms,” Journal of the Acoustical Society of America 105, pp. 3219-3230. |
Fichtner, A. et al. (2006), “The adjoint method in seismology I. Theory,” Physics of the Earth and Planetary Interiors 157, pp. 86-104. |
Forbriger, T. (2003), “Inversion of shallow-seismic wavefields: I. Wavefield transformation,” Geophys. J Int. 153, pp. 719-734. |
Gao, H. et al. (2008), “Implementation of perfectly matched layers in an arbitrary geometrical boundary for leastic wave modeling,” Geophysics J. Int. 174, pp. 1029-1036. |
Gibson, B. et al. (1984), “Predictive deconvolution and the zero-phase source,” Geophysics 49(4), pp. 379-397. |
Godfrey, R. J. et al. (1998), “Imaging the Foiaven Ghost,” SEG Expanded Abstracts, 4 pgs. |
Griewank, A. (1992), “Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation,” 1 Optimization Methods and Software, pp. 35-54. |
Griewank, A. (2000), Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Society for Industrial and Applied Mathematics, 49 pgs. |
Griewank, A. et al. (2000), “Algorithm 799: An implementation of checkpointing for the reverse or adjoint mode of computational differentiation,” 26 ACM Transactions on Mathematical Software, pp. 19-45. |
Griewank, A. et al. (1996), “Algorithm 755: A package for the automatic differentiation of algorithms written in C/C++,” ACM Transactions on Mathematical Software 22(2), pp. 131-167. |
Haber, E. et al. (2010), “An effective method for parameter estimation with PDE constraints with multiple right hand sides,” Preprint—UBC http://www.math.ubc.ca/˜haber/pubs/PdeOptStochV5.pdf. |
Hampson, D.P. et al. (2005), “Simultaneous inversion of pre-stack seismic data,” SEG 75th Annual Int'l. Meeting, Expanded Abstracts, pp. 1633-1637. |
Heinkenschloss, M. (2008), :“Numerical Solution of Implicity Constrained Optimization Problems,” CAAM Technical Report TR08-05, 25 pgs. |
Helbig, K. (1994), “Foundations of Anisotropy for Exploration Seismics,” Chapter 5, pp. 185-194. |
Herrmann, F.J. (2010), “Randomized dimensionality reduction for full-waveform inversion,” EAGE abstract G001, EAGE Barcelona meeting, 5 pgs. |
Holschneider, J. et al. (2005), “Characterization of dispersive surface waves using continuous wavelet transforms,” Geophys. J. Int. 163, pp. 463-478. |
Hu, L.Z. et al. (1987), “Wave-field transformations of vertical seismic profiles,” Geophysics 52, pp. 307-321. |
Huang, Y. et al. (2012), “Multisource least-squares migration of marine streamer and land data with frequency-division encoding,” Geophysical Prospecting 60, pp. 663-680. |
Igel, H. et al. (1996), “Waveform inversion of marine reflection seismograms for P impedance and Poisson's ratio,” Geophys. J. Int. 124, pp. 363-371. |
Ikelle, L.T. (2007), “Coding and decoding: Seismic data modeling, acquisition, and processing,” 77th Annual Int'l. Meeting, SEG Expanded Abstracts, pp. 66-70. |
Jackson, D.R. et al. (1991), “Phase conjugation in underwater acoustics,” J. Acoust. Soc. Am. 89(1), pp. 171-181. |
Jing, X. et al. (2000), “Encoding multiple shot gathers in prestack migration,” SEG International Exposition and 70th Annual Meeting Expanded Abstracts, pp. 786-789. |
Kennett, B.L.N. (1991), “The removal of free surface interactions from three-component seismograms”, Geophys. J. Int. 104, pp. 153-163. |
Kennett, B.L.N. et al. (1988), “Subspace methods for large inverse problems with multiple parameter classes,” Geophysical J. 94, pp. 237-247. |
Krebs, J.R. (2008), “Fast Full-wavefield seismic inversion using encoded sources,” Geophysics 74(6), pp. WCC177-WCC188. |
Krohn, C.E. (1984), “Geophone ground coupling,” Geophysics 49(6), pp. 722-731. |
Kroode, F.T. et al. (2009), “Wave Equation Based Model Building and Imaging in Complex Settings,” OTC 20215, 2009 Offshore Technology Conf., Houston, TX, May 4-7, 2009, 8 pgs. |
Kulesh, M. et al. (2008), “Modeling of Wave Dispersion Using Continuous Wavelet Transforms II: Wavelet-based Frequency-velocity Analysis,” Pure Applied Geophysics 165, pp. 255-270. |
Lancaster, S. et al. (2000), “Fast-track ‘colored’ inversion,” 70th SEG Ann. Meeting, Expanded Abstracts, pp. 1572-1575. |
Lazaratos, S. et al. (2009), “Inversion of Pre-migration Spectral Shaping,” 2009 SEG Houston Int'l. Expo. & Ann. Meeting, Expanded Abstracts, pp. 2383-2387. |
Lazaratos, S. (2006), “Spectral Shaping Inversion for Elastic and Rock Property Estimation,” Research Disclosure, Issue 511, pp. 1453-1459. |
Lazaratos, S. et al. (2011), “Improving the convergence rate of full wavefield inversion using spectral shaping,” SEG Expanded Abstracts 30, pp. 2428-2432. |
Lecomte, I. (2008), “Resolution and illumination analyses in PSDM: A ray-based approach,” The Leading Edge, pp. 650-663. |
Lee, S. et al. (2010), “Subsurface parameter estimation in full wavefield inversion and reverse time migration,” SEG Denver 2010 Annual Meeting, pp. 1065-1069. |
Levanon, N. (1988), “Radar Principles,” Chpt. 1, John Whiley & Sons, New York, pp. 1-18. |
Liao, Q. et al. (1995), “2.5D full-wavefield viscoacoustic inversion,” Geophysical Prospecting 43, pp. 1043-1059. |
Liu, F. et al. (2007), “Reverse-time migration using one-way wavefield imaging condition,” SEG Expanded Abstracts 26, pp. 2170-2174. |
Liu, F. et al. (2011), “An effective imaging condition for reverse-time migration using wavefield decomposition,” Geophysics 76, pp. S29-S39. |
Maharramov, M. et al. (2007) , “Localized image-difference wave-equation tomography,” SEG Annual Meeting, Expanded Abstracts, pp. 3009-3013. |
Malmedy, V. et al. (2009), “Approximating Hessians in unconstrained optimization arising from discretized problems,” Computational Optimization and Applications, pp. 1-16. |
Marcinkovich, C. et al. (2003), “On the implementation of perfectly matched layers in a three-dimensional fourth-order velocity-stress finite difference scheme,” J. of Geophysical Research 108(B5), 2276. |
Martin, G.S. et al. (2006), “Marmousi2: An elastic upgrade for Marmousi,” The Leading Edge, pp. 156-166. |
Meier, M.A. et al. (2009), “Converted wave resolution,” Geophysics, 74(2):doi:10.1190/1.3074303, pp. Q1-Q16. |
Moghaddam, P.P. et al. (2010), “Randomized full-waveform inversion: a dimenstionality-reduction approach,” 80th SEG Ann. Meeting, Expanded Abstracts, pp. 977-982. |
Mora, P. (1987), “Nonlinear two-dimensional elastic inversion of multi-offset seismic data,” Geophysics 52, pp. 1211-1228. |
Number | Date | Country | |
---|---|---|---|
20150057938 A1 | Feb 2015 | US |
Number | Date | Country | |
---|---|---|---|
61869292 | Aug 2013 | US |