# Velocity analysis

Series | Investigations in Geophysics |
---|---|

Author | Öz Yilmaz |

DOI | http://dx.doi.org/10.1190/1.9781560801580 |

ISBN | ISBN 978-1-56080-094-1 |

Store | SEG Online Store |

## Contents

## Basic data processing sequence

In addition to providing an improved signal-to-noise ratio, multifold coverage with nonzero-offset recording yields velocity information about the subsurface and provides critical data to correct gathers or normal moveout and stack traces. Velocity analysis is performed on selected CMP gathers or groups of gathers. The output from one type of velocity analysis is a table of numbers as a function of velocity versus two-way zero-offset time (velocity spectrum). These numbers represent a measure of signal coherency and semblance along the hyperbolic trajectories governed by velocity, offset, and traveltime.

Figure 1.5-11 shows the velocity spectra derived from the CMP gathers as in Figure 1.5-9. The horizontal axis in each spectrum represents the scanned normal-moveout velocity with a range of 1000 to 5000 m/s, and the vertical axis represents the two-way zero-offset time from 0 to 8 s. Red indicates the maximum coherency measure. The curve in each spectrum represents the velocity function based on the picked maximum coherency values associated with primary reflections. The pairs of numbers along each curve denote the time-velocity values for each pick. Velocity-time pairs are picked from these spectra based on maximum coherency peaks to form velocity/normal moveout functions at analysis locations.

The velocity functions picked at analysis locations then are spatially interpolated between the analysis locations to create a velocity field as shown in Figure 1.5-12. Red in the shallow portion and blue in the deep portion of the section correspond to low and high velocities, respectively. This velocity field is used to supply a velocity function for each CMP gather along the profile.

In areas with complex structure, velocity spectra often fail to provide sufficient accuracy in velocity picks. When this is the case, the data are stacked with a range of constant velocities, and the constant-velocity stacks themselves are used in picking velocities.

## Velocity analysis and statics corrections

Normal moveout is the basis for determining velocities from seismic data. Computed velocities can in turn be used to correct for NMO so that reflections are aligned in the traces of a CMP gather before stacking. From equation (**15**), we can develop a practical way to determine stacking velocity from a CMP gather. Equation (**14**) describes a line on the *t*^{2} − *x*^{2} plane. The slope of the line is [math](1/v_{NMO}^{2})[/math] and the intercept value at *x* = 0 is *t*_{0}. The synthetic gather in Figure 3.2-1 was derived from the velocity model in Figure 3.1-8. The far right frame of Figure 3.2-1 shows the picked traveltimes of four events at a number of offsets plotted on the *t*^{2} − *x*^{2} plane. To find the stacking velocity for a given event, the points corresponding to that event have been connected by a straight line. The inverse of the slope of the line is the stacking velocity. (In practice, least-squares fitting can be used to define the line slopes.) A comparison between the computed stacking velocities and the actual rms velocities is made in Table 3-4.

[math]t^2(x)=t^2(0)+\frac{x^2}{v^2_{NMO}}.[/math] **(**)

[math]t^2_{stk}(x)=t^2_{stk}(0)+\frac{x^2}{v^2_{stk}},[/math] **(**)

The *t*^{2} − *x*^{2} velocity analysis is a reliable way to estimate stacking velocities. The accuracy of the method depends on the signal-to-noise ratio, which affects the quality of picking. In Figure 3.2-1, results are compared with the velocity spectrum (center frame) approach, which is discussed later in the section.

A real data example is shown in Figure 3.2-2. Velocities estimated from the *t*^{2} − *x*^{2} analysis are shown by triangles on the velocity spectrum. Note that agreement between the *t*^{2} − *x*^{2} approach and the picks from the velocity spectrum are satisfactory.

t_{0}, s |
Computed Stacking Velocities, m/s | Actual rms Velocities, m/s |

0.4 | 2000 | 2000 |

0.8 | 2264 | 2264 |

1.2 | 2519 | 2533 |

1.6 | 2828 | 2806 |

Claerbout^{[1]} proposed a way to determine interval velocities manually from CMP gathers. The basic idea is illustrated in Figure 3.2-3. First, measure the slope along a slanted path that is tangential to both the top and bottom reflections of the interval of interest (slope 1). Then, connect the two tangential points and measure the slope of this line (slope 2). The interval velocity then is equal to the square root of the product of the two slope values. The accuracy of this method primarily depends on the signal-to-noise ratio.

The method of constant velocity scans of a CMP gather is an alternative technique for velocity analysis. Figure 3.2-4b shows a CMP gather which has been NMO corrected repeatedly using a range of constant velocities between 1500 and 4500 m/s. Scan the constant-velocity moveout-corrected gathers displayed to the right of the original gather (b) starting from the low-velocity end and identify flat events. A velocity function can be composed by noting the velocity-time pairs that correspond to the flat events (Table 3-5). By using this velocity function, the CMP gather (Figure 3.2-4b) is moveout corrected for stacking (Figure 3.2-4a).

Accuracy in velocity picking depends on cable length, the two-way zero-offset time associated with the reflection event, and the velocity itself. The higher the velocity, the deeper the reflector and the shorter the cable length, the poorer the velocity resolution. The resolution in velocity picking also depends on the signal bandwidth; the more compact the wavelet is along the reflection traveltime trajectory in the CMP gather, the more accurate is the velocity pick. Prestack deconvolution (field data examples) prior to velocity analysis aimed at wavelet compression helps to improve velocity resolution.

While Figure 3.2-4 exhibits primary reflection events before 3 s, Figure 3.2-5 exhibits primary reflections below 3 s. Follow the NMO for event *A*. Note that this event is overcorrected at low velocities and undercorrected at high velocities. The event is flat on the NMO-corrected gather that corresponds to the 2500 m/s velocity; thus, this is the optimum stacking velocity for event *A*. Event *B* is flat on the NMO-corrected gather that corresponds to the 2800 m/s velocity. Nevertheless, there is a range of velocities around 2800 m/s which exhibits nearly flat character for event *B*. This results in an uncertainty in making an accurate velocity pick.

The most important reason to obtain a reliable velocity function is to get the best quality stack of signal. Therefore, stacking velocities often are estimated from data stacked with a range of constant velocities on the basis of stacked event amplitude and continuity. Figure 3.2-6 illustrates this approach. Here, a portion of a line containing 100 CMP gathers has been NMO-corrected and stacked with a range of constant velocities. The resulting constant-velocity CMP stacks then were displayed as a panel. Stacking velocities are picked directly from the constant-velocity stack (CVS) panel by choosing the velocity that yields the best stack response at a selected event time.

The panel of constant-velocity stacks in Figure 3.2-7 demonstrates how velocity resolution decreases with increasing depth. The deep event at 3.6 s seems to stack at a wide range of velocity values.

A variation of CVS analysis is a panel of CMP stacks using a family of velocity functions that are a fixed percentage higher and lower than a base velocity function (Figure 3.2-8). This type of velocity analysis panel usually is used in combination with a velocity spectrum computed at the central CMP location to pick an optimum stacking velocity function.

**Figure 3.2-1**The*t*^{2}−*x*^{2}**velocity analysis**applied to the synthetic gather derived from the velocity function depicted in Figure 3.1-8. The center panel is the velocity spectrum based on equation (**19b**).**Figure 3.2-2**The*t*^{2}−*x*^{2}**velocity analysis**applied to a CMP gather. The triangles on the velocity spectrum (center panel based on equation**19b**) represent velocity values derived from the slopes of the lines shown on the graph at the right.**Figure 3.2-3**The interval velocity between two reflectors is equal to the square-root of the products of the slope values measured as shown above. This is the same gather as in Figure 3.1-7a. Trace spacing is 50 m, slope 1 = 3150/0.43, slope 2 = 550/0.44, and thus, the interval velocity between 0.8 and 1.2 s is 3026 m/s.**Figure 3.2-4**Part 2: Constant-velocity moveout corrections applied to a CMP gather (b) using a velocity range of 1500-4500 m/s with an increment of 100 m/s. Based on flatness of events in the moveout-corrected gathers, a velocity function is picked and used in moveout correction (a) for optimum stack.**Figure 3.2-6**Part I: Constant-velocity stacks of 100 CMP gathers using a velocity range of 1500-4500 m/s with an increment of 100 m/s. Scan these panels and observe maximum stack power for each primary reflection and compose a velocity function in the form of a table of pairs of two-way zero-offset time and velocity. The CMP stack using a picked velocity function for moveout correction is displayed to the left of the 1500-m/s panel.**Figure 3.2-6**Part 2: Constant-velocity stacks of 100 CMP gathers using a velocity range of 1500-4500 m/s with an increment of 100 m/s. Scan these panels and observe maximum stack power for each primary reflection and compose a velocity function in the form of a table of pairs of two-way zero-offset time and velocity. The CMP stack using a picked velocity function for moveout correction is displayed to the left of the 1500-m/s panel.**Figure 3.2-6**Part 3: Constant-velocity stacks of 100 CMP gathers using a velocity range of 1500-4500 m/s with an increment of 100 m/s. Scan these panels and observe maximum stack power for each primary reflection and compose a velocity function in the form of a table of pairs of two-way zero-offset time and velocity. The CMP stack using a picked velocity function for moveout correction is displayed to the left of the 1500-m/s panel.

The constant velocities used in the CVS method described above should be chosen carefully. There are two issues to consider besides the expected range of actual velocities in the subsurface: (a) the range of velocities needed to stack the data and (b) the spacing between trial stacking velocities. In choosing a range, consideration should be given to the fact that dipping events and useful out-of-plane reflections may have anomalously high stacking velocities. In choosing the spacing of constant velocities, keep in mind that it is moveout, not velocity, that is the basis for velocity estimation. Thus, it is better to scan in increments of equal Δ*t _{NMO}* than equal

*v*. This prevents oversampling of the high-velocity events and undersampling of the low-velocity events. A good way to choose Δ(Δ

_{NMO}*t*) is to pick it so that the moveout difference between adjacent trial velocities at the maximum offset to be stacked is approximately 1/3 of the dominant period of the data (S. Doherty, 1986, personal communication). Shallow data have short maximum offsets because of muting, while deep data have large dominant periods. Thus, the number of trial stacking velocities needed to adequately sample the data can be reduced considerably.

_{NMO}Two-way Zero-Offset time, ms | RMS Velocity Picked, m/s |

0 | 1500 |

100 | 1500 |

760 | 1900 |

1400 | 2700 |

1800 | 3000 |

2150 | 3600 |

5000 | 4000 |

The CVS method is especially useful in areas with complex structure (Exercise 3-5). In such areas, this method allows the interpreter to directly choose the stack with the best possible event continuity. (Often the stacking velocities themselves are of minimal importance.) Constant-velocity stacks often contain many CMP traces and sometimes consist of an entire line.

The velocity spectrum method, unlike the CVS method, is based on the crosscorrelation of the traces in a CMP gather and not on lateral continuity of the stacked events. Because of this, when compared to the CVS method, it is more suitable for data heavily contaminated with multiple reflections and somewhat less suitable for data associated with complex structures.

## Processing of 3-D seismic data

Once the data are sorted into common-cell gathers, velocity analysis is performed. In this respect, there is no difference between 2-D and 3-D data processing. For 2-D data processing, a number of neighboring CMP gathers are included in the velocity analysis to increase the signal-to-noise ratio. Similarly, a number of common-cell gathers are included in the 3-D velocity analysis. This number can be, say, 5 in the inline and 5 in the crossline direction, for a total of 25 common-cell gathers. For the 3-D example, velocity analyses are performed at certain intervals (e.g., 0.5 km) along selected inlines that may be as much as 0.5 km apart. The results of velocity analyses at selected control points are used to derive the 3-D velocity field for all common-cell gathers over the entire survey. This is achieved by performing a 3-D interpolation of the velocity functions between the control points.

## See also

- Preprocessing
- Deconvolution
- CMP sorting
- Normal-moveout correction
- Multiple attenuation
- Dip-moveout correction
- CMP stacking
- Poststack processing
- Migration
- Residual statics corrections
- Quality control in processing
- Parsimony in processing
- The velocity spectrum
- Measure of coherency
- Factors affecting velocity estimates
- Interactive velocity analysis
- Horizon velocity analysis
- Coherency attribute stacks
- 3-D refraction statics corrections
- Azimuth dependence of moveout velocities
- 3-D dip-moveout correction
- Inversion to zero offset
- Aspects of 3-D DMO correction — a summary
- 3-D residual statics corrections
- 3-D migration
- Trace interpolation

## References

- ↑ Claerbout (1978), Claerbout, J. F., 1978, How to derive interval velocities using a pencil and straight edge: Stanford Expl. Proj., Rep. No. 14.