Marine surveys commonly employ water guns as energy sources, which are designed to rapidly eject compressed air just below the ocean surface. No matter what the mechanism, the energy source creates sound energy that propagates down through the subsurface and is partially reflected back towards the surface by boundaries between geologic formations of different physical properties.

Pressure sensors record several seconds of data immediately following activation of the energy source and provide measurements or "times" of the reflected events from the subsurface geologic horizons. This is the basic physical principle behind all seismic reflection technology.

In practice, during a seismic survey many seismic traces are simultaneously recorded at different distances or "offsets" from each energy source placement. The receivers are distributed in a desired geometry that varies from survey to survey. An example of a commonly used pattern known as Common Shot Point ("CSP") is shown

in Fig. 1A. The associated seismic traces which represent the reflected sound energy from the subsurface formations are shown in Fig. 1B. In Fig. lA, a single source 30 generates sound energy which travels along various paths 32 and reflects off formations 34, 36 to be detected by receivers 38 at the earth's surface 40. The traces 42, numbered 1,...,N in Fig. lB, record events 44, 45, and 46 which are signals corresponding to the energy reflection events in time. Each event 44 is recorded on each of the traces 42 from energy traveling along the different paths 32 from source 30 to the corresponding receiver 38. Each recording of event 44 on the traces 42 is related because the energy that is detected is reflected off the same formation (e.g., 34), but at different horizontal points 35(1) to 35(N) as shown in Fig. 1A. Events 45 and 46 may be similarly described.

For example, each event 45 which is recorded on the traces 42 is related because energy is reflected off horizontal points 37(1) to 37(N) along formation 36 and detected by corresponding receivers 38(1) to 38(N).

There are many different stages in the processing of seismic data that make corrections, combine information, and extract parameters from the seismic traces. Different processes require the traces to be grouped in different manners according to some common value of acquisition geometry of the seismic survey.

Each method for grouping the seismic traces typically has a different name. A particular group or set of traces is called a "seismic gather" or "gather". All the seismic traces in Fig. 1B form what is called a Common Shot Point or CSP gather.

One of the most important groupings of seismic data for imaging the subsurface is the Common Mid Point ("CMP") gather. The geometry of the sources and receivers is illustrated in Fig. 2A, and the

corresponding CMP gather is shown in Fig. 2B. In this case, traces 52, numbered 1 ,N in Fig. 2B, that are recorded and grouped together come from a number of different sources 50 (similar to source 30) during the acquisition of the seismic survey. Each trace in the CMP gather 52 differs from the other traces in the gather 52 in that it represents, as for the CSP gather 42, seismic energy that has taken a different path to the CMP. Fig.

2A shows the different energy travel paths 62 taken between pairs of sources 50 and receivers 48 (numbered 1,...,N and similar to receivers 38) and reflected at common points 58 and 60 in the subsurface horizons 34 and 36, respectively. The shared characteristic of each of the traces in a CMP gather is that the center (or mid- point) 51 between each associated source 50 and receiver 48 pair is at the same location at the surface 40. The traces 52 of Fig. 2B have events 54, 55, and 56 recorded in time which are related by like numerals across the traces 52 for the different travel paths 62 between sources 50 and each receiver 48. The distance 61 from any of the sources 50 to the corresponding receiver 48 is known as the "receiver offset" or "offset" of the trace.

One of the fundamental assumptions used in much of the processing of seismic data is that the earth is composed of geologic layers which lay flat. Under this assumption, all of the energy reflected from the subsurface geologic boundaries represents the same physical locations as events on all traces in a CMP gather (although the arrival times on each trace will be different) The sound energy generated by a seismic source propagates through the subsurface at the sound velocity of the different rock formations. These are known as seismic velocities. A very critical, time consuming stage in terms of both computer resources and calendar

time in processing seismic data is the extraction of estimates of the seismic velocities of different subsurface regions from CMP gathers. The receiver offset 61 is different for each trace in the group of traces 52 in the CMP gather and the traces are nearly always ordered from near to far offset. The energy reflected from a particular subsurface horizon (e.g., 34 or 36) will take longer to travel to the receivers 48 with larger offset. Therefore, there will be a time difference on each trace in the CMP gather 52 corresponding to the difference in the arrival of the reflected energy. These time differences are known as the "time moveout", "reflection moveout", or "moveout".

Referring to Fig. 3, the seismic velocities are used to time shift (also referred to as "moveout correct", "Normal Moveout Correct", or "NMO correct") the amplitude values on all the traces in the CMP gather 52.

The time shift aligns or "flattens" the arrival times of the events on each trace from common subsurface reflection points (e.g., 58 or 60) which results in an NMO corrected CMP gather 66. Following this flattening process, the amplitude values on every trace in the CMP gather 52 are summed at each time sample and averaged to form a single stacked seismic trace 68. The trace 68 has recorded events 54', 55' and 56' corresponding to recorded events 54, 55, and 56. The process is used to diminish the noise within the data and to enhance the reflected events (54, 55, 56) from the subsurface (34 or 36). The accuracy and detail of an image of the subsurface from a seismic survey is highly dependent on the quality of the velocity analysis stage of the processing.

Two assumptions about the structure of the earth's subsurface are critical for extracting velocity information from seismic data. The first is that the

earth is composed of flat layers of rock of different physical properties and the second is that the density and seismic velocity are constant within each layer (i.e., having no variation vertically or horizontally).

Under these assumptions, the arrival times of the energy reflected from a particular boundary between two layers of rock are a function of the receiver offset and the velocity: T2 (X) = T2(0) + (X/V) 2, where x is the receiver offset, T(x) is the arrival time of the event at receiver offset x, T(0) is the arrival time at a hypothetical zero offset receiver, and V is the root mean square velocity of the rock from the surface down to the particular rock layer boundary. As shown for the seismic CMP gather 52 in Fig. 4, using this equation it is apparent that the moveout or arrival time difference between traces on the CMP gather 52 follows a hyperbolic curve 70 (or 72) where the curvature is determined by the velocity. Time windows 74 and 76 for this velocity analysis are also shown in Fig. 4. The time differences between adjacent traces on the CMP gather 52 for events that fall perfectly on the hyperbola (70, 72) are known as Normal Moveout or NMO times.

While much of the process for determining velocities has been computer automated, some portions still require human interpretation. Most of the computer methods for determining seismic velocities from a CMP gather are based on performing a large number of computations on the similarity of the data taken from each of the traces within the gather. The results of these computations are either used in another computer analysis that attempts to determine the velocities or, more commonly, displayed to trained interpreters to pick

the best velocities from the results. In general, the differences between the various known methods are in the particular computation used to measure the similarity of the data and in the methods used to pick velocities from the results. The general procedure is as follows: 1. Pick a starting time on the trace within the CMP gather that has the smallest receiver offset (the near offset trace) 2. Compute the beginning times on each trace in the CMP gather for a particular velocity assuming the hyperbolic moveout equation.

3. Run the computation to compare the similarity of the data taken from all the traces in the gather.

4. Choose a new velocity for the next computation and repeat steps 2 and 3 until the entire range of velocities has been tested.

5. Choose a new starting time on the near offset trace and repeat steps 2 through 4 until the entire range of times on the CMP gather has been tested.

The above process typically is run on a number of CMP gathers spaced throughout a seismic survey and the results are used in the final step to pick the velocities.

The overall process is computer and manpower- intensive. The results depend not only on the parameters used in the computational stage but also on the experience of the person interpreting the computational results. It is not uncommon to have to repeat either the computation or the interpretation phases in order to improve the results or to provide a denser velocity analysis by analyzing more CMP gathers at a closer

spacing.

While the general method for determining velocities used in the normal moveout correction and summing of CMP gathers to form stacked seismic traces is widely used throughout the industry, there are some recognized limitations that affect the quality of the results. These limitations include the following: 1. The assumption that the earth is composed of flat layers is unrealistic. Real layers may have dips, dip gradients, or offsets caused by faulting of the subsurface.

2. Real earth layers do not have constant physical properties. They may be anisotropic and inhomogeneous which leads to both vertical and horizontal variations in seismic velocity and layer density.

3. Both 1 and 2 lead to deviations from hyperbolicity in the arrival times across a CMP gather for a particular event. Therefore, events will not align exactly in the moveout correction process and a corresponding inaccuracy in the stacking of the traces within the CMP gather will result.

4. There are generally many more layers to the real earth geology than there are velocities picked on a given CMP gather. This means that only a few events within a CMP are targeted for accurate stacking and the velocities used for the events in between are based on an interpolation.

5. Due to the amount of resources required by the velocity analysis, the process is not run on every CMP gather within a survey. Instead, the analysis is run at a much coarser interval.

Therefore, if the velocities within the subsurface

change laterally at a rate much faster than the spacing of the velocity analysis, it will greatly degrade the quality of the stacked data.

6. In the process of moveout-correcting the arrival times on all traces in a particular CMP gather, the farther offset traces are affected by what is known as "moveout stretch" which affects the frequency and also degrades the events on the stacked trace.

SUMMARY In general, in one aspect, the invention features a method of aligning arrival times of related events in a group of seismic traces. The method may include determining representations for each trace and substituting a reference representation for a portion of the representations. The method may also include combining another portion of the representations with the reference representation for each trace and forming a new group of seismic traces with aligned arrival times based on the combination.

In general, in another aspect, the invention features another method of aligning arrival times of recorded events in a group of seismic traces. The method may include determining amplitude and phase represen- tations for a plurality of traces within the group and determining a reference phase representation from the plurality of traces. The method may also include: (1) substituting the reference phase representation for the phase representation of each of the plurality of traces; (2) combining the amplitude representation and the substituted reference phase representation for each of the plurality of traces; and (3) using the combined amplitude representation and substituted reference phase representation to align arrival times of recorded events

in the plurality of traces.

In general, in anther aspect, the invention features a method of substituting phase spectra in seismic data signals to align related seismic arrivals.

The method may include: (1) forming amplitude and phase signals corresponding to the seismic data signals; (2) substituting different phase signals derived from the seismic data signals for the phase signals; and (3) forming new seismic data signals by combining the amplitude and substituted phase signals.

In general, in another aspect, the invention features another method of aligning arrival times of related events in a group of seismic traces. The method may include: (1) extracting a phase spectrum from a first trace in a plurality of traces within the group of traces as a reference phase spectrum; (2) substituting the reference phase spectrum for the phase spectrum of a second trace in the plurality of traces; (3) creating a new trace by averaging the first trace and the second trace with the substituted phase spectrum; (4) extracting a phase spectrum from the new trace as a new reference phase spectrum; (5) This new reference phase spectrum is now substituted 550 for the phase spectra of all the traces in the original gather used in the process thus far plus the next higher numbered trace in the gather which results in aligning the arrival times of related events on all these traces to those on the first trace; (6) creating a next new trace by averaging all traces with flattened arrival times; and (7) aligning all arrival times of all final traces having common phase spectra and unchanged amplitude spectra to the times of the related events on the first trace in the plurality of traces.

In general, in another aspect, the invention features another method of aligning arrival times of

related events in a group of seismic traces. The method may include: (1) taking a subgroup of traces from an original seismic gather; (2) determining a reference phase spectrum for the subgroup; (3) substituting the reference phase spectrum for a phase spectrum of a trace of the subgroup with the trace with the substituted phase spectrum becoming a trace within a new seismic gather; (4) increasing trace number for each trace in the subgroup to form a new subgroup; (5) shifting the arrival times of related seismic events in the new seismic gather closer to times on a first trace in the original gather with the amplitude spectra of all traces in the new seismic gather being the same as they were in the original gather and the new seismic gather becoming a seismic gather for a next iteration; (6) increasing number of traces in the new subgroup to a next higher number; (7) applying a phase optimization technique to the new (last) seismic gather; and (8) substantially aligning the arrival times.

In general, in another aspect, the invention features a computer system that may include a storage medium that stores instructions used for aligning related events in a group of seismic traces. The computer system may also include a processor coupled to the storage medium and instructions for instructing the processor to: (1) form amplitude and phase signals corresponding to the group of seismic traces; (2) substitute different phase signals for the phase signals; and (3) form a new group of seismic traces based on the amplitude and substituted phase signals.

Advantages of the invention may include one or more of the following: (1) complete or substantially complete alignment along all events in the gather; (2) a significant improvement in stacked data image quality based on (1); (3) no NMO stretch; and (4) greatly reduced

processing time due to eliminating the need for velocity analysis for stacking.

Other features and advantages will become apparent from the following description, from the drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1A illustrates a typical arrangement for a CSP group of seismic sources and receivers.

Fig. 1B shows example traces obtained using the CSP method.

Fig. 2A illustrates a typical arrangement for a CMP group of seismic sources and receivers.

Fig. 2B shows example traces obtained using the CMP method.

Fig. 3 is a diagram of a prior art CMP prestack gather of seismic traces before and after NMO correction and after stacking.

Fig. 4 is a diagram of a prior art gather of seismic traces showing the time and velocity dependent hyperbolic curvature of related seismic events across a CMP gather of traces and example time windows for velocity analysis.

Fig. 5 is a block diagram of a computer system in accordance with an embodiment of the invention.

Fig. 6A illustrates a CMP gather of original seismic traces recorded for a single reflection event to which a method in accordance with the invention will be

applied.

Fig. 6B illustrates amplitude spectra for the gather of Fig. 6A.

Fig. 6C illustrates phase spectra for the gather of Fig. 6A.

Fig. 6D illustrates amplitude spectra after application of the method to the gather of Fig. 6A.

Fig. 6E illustrates phase spectra after application of the method to the gather of Fig. 6A.

Fig. 6F illustrates an aligned CMP gather after application of the method to the gather of Fig. 6A.

Fig. 7 is a flow diagram of a method in accordance with an embodiment of the invention.

Fig. 8A shows a CMP gather before application of a method in accordance with an embodiment of the invention.

Fig. 8B shows an aligned CMP gather after application of the method in accordance with the invention to the CMP gather of Fig. 8A.

Fig. 9 is a flow diagram of a general method in accordance with an embodiment of the invention.

Fig. 10 is a flow diagram of a method of stacking an aligned group of selected seismic traces in accordance with the invention.

Fig. 11 is a flow diagram of a method of aligning

an NMO corrected group of selected seismic traces resulting in stacked seismic data providing a higher resolution image of the subsurface in accordance with the invention.

Fig. 12 is a flow diagram of a method of flattening arrival times of related reflection events to run analyses over time windows on each trace starting with a series of stacked seismic traces in accordance with an embodiment of the invention.

Figs. 13A and 13B are a flow diagram of a method in accordance with an embodiment of the invention.

Fig. 14A and 14B are a flow diagram of a method in accordance with an embodiment of the invention.

DETAILED DESCRIPTION The invention allows the arrival times of all related reflection events on a group of selected seismic traces (a seismic gather) to be "aligned" (also referred to as "moved out" or "flattened") without any need for velocity analysis. The invention involves applying a common phase to each of the traces within the seismic gather. This common phase is referred to as the "reference phase spectrum" (or "RPS") for the seismic gather, and the process as a whole is referred to as "Phase Moveout" (or "PMO") . When the traces are recomputed with the RPS, all related seismic events may be aligned along time lines and the amplitude spectrum of each trace remains unchanged. Advantageously, PMO may be implemented completely under computer automation (i.e., with no human intervention) through all of the gathers in a large 2-D or 3-D seismic survey.

An example of a computer system for automatic

implementation in accordance with an embodiment of the invention is shown in Fig. 5. Fig. 5 shows a computer system 100 that includes a CPU 102 (e.g., a microprocessor or microcontroller) coupled to a memory device 104 (e.g., a hard disk, ROM, CD-ROM, DRAM or other RAM, flash memory, registers or other volatile and/or nonvolatile memory), a display (e.g., a monitor) 106, a keyboard 108, and input/ output devices 110 (e.g., a mouse or trackball, modem, telephone lines or other communication links, etc.). In general, instructions (PMO code) 112 are stored in the memory device 104 which instruct the CPU 102 to carry out the PMO method of the invention. When PMO is initiated under control of the CPU 102, a user may input data through keyboard 108, or data may be input or output through I/O (input/output) devices 110. Data may be displayed on display 106. The data may be stored in memory device 104 and the stored data may be accessed to perform tasks under control of the CPU 102. Alternatively, data may be input to the computer 100 through I/O devices 110 (communication links) from other computers or instrumentation at remote locations (not shown). The communication links are not shown but will be understood to be incorporated in I/O devices 110.

Implementations of the invention are based on recognizing that the time location of a single wavelet is encoded in the phase spectrum of the trace. With traces recorded from a single reflection event, the arrival times may be flattened by replacing the phase spectra in all the traces. For example, the phase spectrum of the first trace (in a CMP gather this may be the trace with the smallest receiver-offset distance) may be used as such a replacement. Referring to Figs. 6A-F for traces and spectra, an example of this procedure, shown in Fig.

7, in accordance with an embodiment of the invention is

described below.

With traces 10A-E (Fig. 6A) recorded 202 (Fig. 7) from a reflection event (or reflection events) information about the arrival times of all the events is encoded 204 into the phase spectrum 12A-E (Fig. 6C) of each recorded signal of the associated seismic gather 20 (Fig. 6A). With PMO, a single RPS 14 (Fig. 6E) is determined 206 (e.g., from trace number "1" (10A) of Fig.

6A) for all the traces in the seismic gather 20 and substituted 208 for the phase spectrum 12A-E of each trace in the group 20. A seismic gather 20' (Fig. 6F) that results is composed 210 of traces 10'A-E having exactly the same amplitude spectra 16A-E (Figs. 6B and 6D) as the original traces 10A-E. All traces 10'A-E also have a common phase spectrum 14 (e.g., phase spectrum 12A of Fig. 6C), and the arrival times of related reflection events are all aligned 212. The arrival of related reflection events that were at different times on each trace of the traces 10A-E in the original CMP gather 20 may be aligned at the same time as on the first trace 10A in Fig. 6A (and 10'A in Fig. 6F) following application of PMO. An example of a CMP gather before PMO is shown in Fig. 8A and an example of a CMP gather after PMO is shown in Fig. 8B with trace "1" 80 indicated in both figures.

This computer instruction-implemented process (e.g.

instructions 112 stored in memory 104) is described mathematically below.

Given a group of seismic traces designated Si(t) for i=l,...,N, where t=time and N=number of traces in the group, the complex Fourier Transform of the jth (lsjsN) trace designated Sj(f) can be written as: Sj(f) = F [Sj (t) ] = Aj (f)eij'f'.

"F[ ]" represents the process of taking the Fourier

Transform, "f" is the temporal frequency, and "Aj(f)" is the amplitude spectrum and " j(f)" is the phase spectrum of the Fourier Transform of the jth trace. If "+R(f)" is a reference phase spectrum determined in an implementation of the invention, a new group of seismic traces S'i(t) for i=l, . . . ,N may be formed. This is done by substituting fR( f) for each fi(f) while retaining each Ai(f) in the frequency domain and then taking the inverse Fourier Transform back to the time domain as follows: S'i(f) = Ai(f)ei Rf) for i=1,...,N S'i(t) = F-l[S'i(f)] for i=l,...,N, where "F-1[ ]" represents the process of taking the inverse Fourier Transform. Each trace in the new group of seismic traces, S'i(t), has exactly the same amplitude spectrum, Ai(f), as in the original group and all traces in the new group have a common phase spectrum, fR ( f)- As shown in Fig. 9, a method in accordance with the invention may use the following procedure: (1) compute 410 the complex Fourier transform of each trace within the selected group (e.g., group 20 in Fig. 6A) of seismic traces; (2) separate 420 the complex Fourier transform of each seismic trace into an amplitude spectrum (e.g., amplitude spectra 16A-E in Fig. 6B) and a phase spectrum (e.g., phase spectra 12A-E in Fig. 6C); (3) determine 430 an RPS (e.g., RPS 14 in Fig. 6E) for the entire group of seismic traces (specific implementations of PMO differ in how the RPS is determined, as will be described below); (4) substitute 440 the RPS for the phase spectrum of each of the seismic traces within the selected group; (5) combine 450 the amplitude and the new phase spectra (now the RPS) for each seismic trace within the selected group into a new complex Fourier Transform for each trace; and (6) compute

460 the inverse Fourier transform of the new complex Fourier Transform for each seismic trace within the selected group to form 470 a new group (e.g., group 20' in Fig. 6F) of seismic traces where the arrival times of related seismic events have been aligned in time.

Although adjacent traces in a seismic gather may be described as differing in the arrival times of related reflection events, these differences may also be described as differences in phase of one trace relative to the other. If all the traces 10' in the gather 20' have a common phase, the related reflection events may have the same arrival times. Implementations of the invention may differ in how the common phase or RPS 14 for the seismic gather 20 (or 20') is determined and in the data used in making such determination. Various exemplary embodiments of the invention will now be discussed.

FLATTENING REFLECTION EVENTS ON CMP GATHERS If one compares two adjacent traces within a CMP gather (e.g., trace numbers "4" and "5" of Fig. 6A), it is commonly accepted that the two traces differ principally in the arrival times of the reflection events (e.g., 10D and 10E of Fig. 6A) due to the greater travel times of the events recorded on the trace with the larger receiver-offset (e.g., trace number "5"). The traces will be very similar in general waveform character because they result from propagation of waves through essentially the same body of subsurface rock. Rather than simply ascribing a time difference between a smaller receiver-offset trace and a larger receiver-offset trace, the difference between the traces may be viewed instead as a difference in phase. If both traces had the same phase, then peaks would be aligned with peaks, troughs would be aligned with troughs, zero crossings with zero

crossings, etc. Generalizing this concept, if all the traces in the CMP gather had the same phase then there could be perfect alignment of all the recorded events.

1. Application To Stackinq CMP Data Referring to Fig. 10, once the reflection events have been aligned (continuing from step 470 in Fig. 9) and the traces (e.g., traces 10A-E in Fig. 6A) may be completely (or substantially) moveout-corrected, if the CMP data are to be stacked, the traces may be summed 480 and averaged 490. This procedure may result 500 in a completely (or substantially) aligned stack with no velocity analysis necessary. In this manner, the process may be used to align and stack all related reflection events on all CMP gathers from a survey with no velocity analysis or need for human interpretation. A data set stacked after application of PMO may, therefore, be significantly enhanced over conventional NMO stacking and may be performed in a fraction of the time. Moreover, because PMO does not rely on conventional velocity analysis, PMO may avoid any of its inherent errors.

2. Application To Computinq Prestack Attributes Any parameter that describes how an analysis that is run on a related seismic event on every trace in a CMP gather changes as a function of the receiver-offset (i.e., that varies across the CMP gather) is termed, in general, a "prestack attribute". The analysis may require knowing all the arrival times on each trace within the CMP gather for every seismic event that the analysis is to be run on. This generally may only be known for a few events within a particular CMP gather, and then only under the assumptions inherent in velocity analysis. In addition, the velocity analysis may be run only on widely spaced CMP gathers and the results may

have to be interpolated to imply the arrival times on intermediate ones. Using PMO in accordance with an embodiment of the invention to align all events on every gather (e.g., continuing from block 470 of Fig. 9), analyses on the CMP gathers may be run for every gather in the survey at all time positions within each gather.

This results in entire traces of the value of prestack attributes at every position within the survey and a large increase in the amount of information that can be extracted from the prestack data. For example, there are a variety of ways to calculate what is known as the AVO (amplitude vs. offset) of an event on a CMP gather. In general, the procedure involves knowing the arrival times of a particular portion of a related event on every trace in the CMP gather, extracting an estimate of the amplitude on every trace from all the data in a time window (all the data on a trace between a specified beginning and ending time) about these arrival times, and then computing a value that is a measure of how these amplitudes change as a function of the receiver offset associated with the traces. By first applying PMO to a CMP gather, there is no need to know the arrival times of any events on any of the traces. Instead, a time window is placed at the beginning of every trace in the gather, the amplitude extraction and computing the AVO measure are performed. The time window can be shifted one sample down the trace and procedure repeated until the end of the time range of the PMO corrected CMP gather is reached. The result is a calculated trace of the AVO attribute for the entire time range of the CMP gather.

This procedure can now be done on every CMP gather in the survey resulting in a AVO attribute for the entire survey.

FLATTENING OF REFLECTION EVENTS ON NMO CORRECTED CMP GATHERS Many times significant misalignment of related seismic reflection events can occur on NMO corrected CMP gathers. This misalignment may occur for several reasons including, for example: (1) the sparse number of time positions for which velocities are determined within a CMP gather; (2) the velocity analysis is only performed on widely spaced CMP gathers within a survey; (3) related seismic reflection events may be coming from non-flat lying interfaces and not fit the NMO assumption of hyperbolic moveout; or (4) the subsurface may contain rapid horizontal changes in the seismic velocities.

Referred to as residual moveout, this misalignment can have many adverse effects on the image of the subsurface produced by stacking these data (events).

Referring to Fig. 11, in accordance with a method of the invention, starting with CMP gathers that have been previously NMO corrected 800, PMO may also be applied 810 as detailed in blocks 410-470 of Fig. 9.

This may remove 820 the residual moveout from the CMP gathers and the resulting stacked seismic data may provide 830 a higher resolution image of the subsurface.

FLATTENING EVENTS ON STACKED DATA -- APPLICATION TO COMPUTING STACKED ATTRIBUTES While seismic events on adjacent traces in a stacked seismic section represent energy reflected from the same subsurface horizons, they will differ in arrival times. This is due to differences in depth of the horizons (e.g., 34 or 36 of Fig. 2A) along a horizontal direction of the earth's surface. For example, the horizons may dip or slant, and there may be variations in the subsurface velocities. "Stacked attributes" are parameters calculated on every trace in a stacked seismic

section on or about individual horizons. The difficulties in implementing analyses on stacked sections are similar to those on prestack (e.g., CMP gathered) seismic data in that the arrival times to the reflection event may have to be known on each trace and for every horizon for which the attribute is to be calculated.

Referring to Fig. 12, in accordance with an embodiment of the invention, starting 850 with a series of stacked seismic traces, PMO may be used to flatten 860 the arrival times of related reflection events on the series of stacked seismic traces. Analyses associated with the attributes may then be run 870 on the data between the same beginning and ending times on each trace.

ORDER OF TRACES WITHIN SEISMIC GATHERS Whether during processing, interpretation, or analysis, seismic traces are grouped or gathered according to one or more unique values of the parameters associated with the acquisition geometry. For example, in a CMP gather, seismic traces are grouped together because they share the same physical location of the mid- point (e.g., 51 in Fig. 2A) between the associated sources and receivers. This is stored as a unique CMP number. As another example, a common offset gather includes every seismic trace that has the same distance between the source and receiver (receiver-offset).

Within each type of seismic gather there is also a standard ordering of the seismic traces based on a second parameter. For example, the traces within each CMP gather may be ordered from smallest to largest receiver- offset, and within a common-offset gather they may be ordered from smallest to largest CMP number.

Because there is always a prescribed order to the traces within a seismic gather, there is no loss of generality in referring to each seismic trace by its

number within the gather. For example, in referring to the 20th trace within a CMP gather, it is known that this is the trace with the 20th smallest value of receiver- offset. In the descriptions below, when traces are referred to as the first, second, third, etc. trace (or trace 1, trace 2, trace 3, etc.), it is to be understood that the trace being referred to is well-defined and that this is applicable to all types of seismic gathers.

DETERMINING THE RPS Implementation 1 In one embodiment, instructions (e.g., programmed instructions 112) are executed by the CPU (e.g., CPU 102) to carry out PMO. A procedure for choosing the RPS in accordance with the invention is the following: (1) the phase spectrum of any one of the traces within a seismic gather may be used as the RPS (e.g., RPS 14 of Fig. 6E) for this group of selected seismic traces; and (2) the arrival times of all the related seismic reflection events are aligned with the arrival times of these same events on this one trace. In the case of a CMP gather, the logical trace to use would be the first trace in the gather (i.e., the one with the smallest receiver-offset, e.g., trace "1" (10A) of Fig. 6A). Alignment of all arrival times in the CMP gather (resulting, for example, in traces 20' in Fig. 6F) would be to the near receiver- offset time of the first trace. The phase spectrum of the first trace (or any other trace within the group in other embodiment in accordance with the invention) would, therefore, be used at block 430 of Fig. 9.

The above procedure uses only one trace for determining the RPS. There are other embodiments in accordance with the invention which use all the available traces to determine the RPS. These other embodiments may

reduce the effects from, for example, extraneous information such as ground roll, strong multiple reflections, and other non-linear effects. Moreover, these embodiments may reduce the effects of any individual trace within a gather that contains high levels of noise or even no signal at all due to receiver difficulties during acquisition. By using all the available traces (e.g., traces 10A-E of Fig. 6A) within the gather to determine the RPS (e.g., RPS 14), these embodiments flatten all the arrival times. A process that attempts to generate the best possible RPS from all the available traces in a gather will be referred to herein as "phase optimization". Two such methods of phase optimization in accordance with the invention are described below, both of which may be implemented with programmed instructions stored in the memory device for execution by the CPU.

Implementation 2 An iterative method in accordance with the invention uses successively more traces from the original seismic gather at each stage to determine an RPS until all the traces have been incorporated into the process. This process is shown in Figs. 13A-B beginning at start block 505. The phase spectrum of the first trace is extracted 510 as the RPS and substituted 520 for the phase spectrum of the second trace to align the arrival times of the related seismic events of the two traces relative to the arrival times on the first. A new trace is created by averaging 530 these two traces with flattened arrival times and the phase spectrum of this new trace is extracted 540 and used as the new RPS. The new RPS is now substituted 550 for the phase spectra of all the traces in the original gather used in the process thus far plus the next higher numbered trace in the gather

which results in aligning the arrival times of related events on all these traces to those on the first trace.

A next new trace is then created 560 by averaging all the traces with flattened arrival times. The process continues by returning to block 540 through block 570 and extracting the new RPS until all the traces in the gather have been included.

When all iterations of this procedure are completed as indicated in block 570, all traces in the new seismic gather have a common phase spectrum and all arrival times are aligned 580 to the times of the related seismic events on the first trace. The amplitude spectrum of each trace in the new seismic gather is unchanged from what it was in the original and the process terminates at end block 585.

Implementation 3 Another iterative phase optimization method in accordance with an embodiment of the invention operates to align the arrival times of all the related seismic events in the gather to those times on the first trace while limiting undue influence of the phase spectrum of the first trace. This is important because the distribution of energy between events in the first trace may significantly affect how it is distributed between events on other traces. Moreover, events in the first trace may be propagated through the entire seismic gather during the process of aligning arrival times. Referring to Figs. 14A-B, the method begins at start block 605. A subgroup of traces, always odd in number, initially consisting of 3 traces (e.g., traces 10A-C in Fig. 6A) and beginning with the first trace (e.g., trace 10A), is taken 610 from the seismic gather (e.g., group 20). The procedure detailed in blocks 505-585 of Implementation 2 (Figs. 13A-B) is used to determine 620 the RPS for this

subgroup. This RPS is then substituted 630 back only for the phase spectrum of the middle trace in the subgroup which then becomes 640 a trace within a new seismic gather. The trace number for each trace in the subgroup is then increased 650 by one to form a new subgroup. The process then returns to block 620 for determining the RPS, and the procedure is repeated until the end of the seismic gather is reached 660. At this point there is now a new seismic gather in which the arrival times of all related seismic events have not been aligned to the times on the original first trace, but the events have been shifted 670 closer to them and the amplitude spectra of all the traces in the new seismic gather are the same as they were in the original gather.

This new seismic gather now becomes 680 the seismic gather for the next iteration. The number of traces in the subgroup is now increased 690 to the next higher odd number and the above procedure is repeated 700 to form another new seismic gather. Successive iterations in which the number of traces in the subgroup is increased (three, five, seven,...) gradually: (1) incorporate information from more and more traces for determining the RPS; (2) shift the arrival times of related seismic events closer to those on the first trace, while greatly diminishing the effect of the phase spectrum of the first trace on the process; and (3) leave the amplitude spectrum of each trace in the new seismic gather for each iteration unchanged from what it was in the original.

This process could be repeated indefinitely. In practice, however, after a few iterations (decision block 700) the principle gains of the method have been achieved and the process is stopped. The phase optimization technique detailed in blocks 505-585 of Implementation 2 (Figs. 13A-B) is applied 710 to the new (last) seismic gather for a substantially complete alignment 720 of the

arrival times, and end block 725 is reached. Typically, the user determines that the principal gains of, for example, less influence of the minimum offset trace (e.g., trace "1" (10A) of Fig. 6A) and more careful preservation of amplitude information, have been achieved.

Although specific embodiments have been disclosed, other embodiments and implementations of the invention are contemplated within the scope of the following claims.