Introduction to Seismic Reflection Imaging References: J.M. Reynolds, An Introduction to Applied and Environmental Geophysics, John Wiley & Sons, pp (NB missing from Killam Lib) O. Yilmaz, Seismic Data Processing, Soc. Exploration Geophys., Tulsa, OK. Basic data processing flowchart (after Yilmaz, 1987)

FIELD GEOMETRY FOR MULTICHANNEL SEISMIC (MCS) PROFILES

Layouts for (A)a comon-shot gather; (B)a cmmon mid-point gather; and (C)a common receiver gather.

Sequence of survey layouts to acquire a 6-fold coverage; S indicates the source and G a geophone (or hydrophone).

Descriptions of a pre-stack seismic data set in: (A)shot-receiver coordinate systems (a surface diagram); (B)Midpoint-offset coordinate systems (a sub-surface diagram or stacking diagram)

A.Composite shallow reflection record made up of five separate 12-channel records, each of which was recorded with a different time delay between the shot instant and the start of recording. B.Corresponding time-distance graph identifying the major seismic events on the record. The optimum window is that range of source-receiver separations that allows the target reflection to be observed without interference from other events.

Example of a common mid- point gather

Types of filters: (A) bandpass; (B) low-cut (high-pass); (C) high-cut (low-pass); (D) notch.

The application of a time-varying gain function to a waveform exhibiting spherical divergence, in order to recover signal amplitudes at later travel times. Gain functions are applied in discrete windows(labelled 1 to 5 as shown).

Filtering out a reverberant signal: At each relevant time sample (ie T = 1, 2, …) the signal amplitude S is multiplied by the corresponding segment of the filter F (S * F). Taking this a stage at a time, we have: Stage A: At T=0, the first element of the filter (1) is multiplied by the corresponding sample of the signal (1), hence the output = 1 Stage B: At T=1, the first element of the filter (1) is multiplied by the corresponding sample of the signal (-1) giving a value of -1. This is added to the product of the second element of the filter (1) and its corresponding sample of the signal (1) to give a value of 1. The overall output is then, = 0. Stage C: As for Stage B but shifted by one time sample (T=2) Stage D: As for Stage C but shifted by one time sample (T=3)

The principle of convolution (deonvolution is similar but in opposite direction): Step 1: Convolve source wavelet and reflectivity series by multiplying the first sample of the source wavelet (1) by the first component of the reflectivity series (1) to give the first constituent of the output response (= 1) Step 2: Move the source wavelet array over one sample and multiply the samples for each component; hence (1x0.5) + (1 x -0.5) = 0 Step 3: Move the source wavelet array over one sample and repeat as for Step 2; hence (0.5x1)+(0.5x-0.5)+(1x0.5) = 0.5+(-0.25)+0.5 = 0.75 Step 4: (0.5x(-0.5)+(0.5x0.5) = 0 Step 5: (0.5x0.5) = 0.25 deconvolution convolution

VELOCITY ANALYSIS Depth section of individual seismic velocity layers (Vn) and thicknesses (Zn). For this example, the total number of layers n = 6, so (n-1) = 5.

Definition of velocity analysis terms and acoustic impedance and reflection amplitude for a flat layered Earth structure with n layers. Acoustic Impedance At each interface, a reflection occurs at normal incidence with amplitude (A r ) that depends on the change of acoustic impedance (Z) at the interface between layers I and i+1,where Z i = v i *  i ; Z i+1 = v i+1 *  i+1 and Ar = Z i+1 –Z i / Z i+1 +Z i

Selected raypaths and corresponding seismic traces illustrating the effect of normal moveout (NMO). For distances x << 2h,  T = x 2 /(2v 2 t o ) where t 0 = 2h/v. Thus in order to make this correction, we need to know v. Given the source – receiver layout and correspnding raypaths for a common midpoint gather, the resulting seismic traces are illustrated uncorrected on the right and corrected in the middle, after NMO aligns the reflection events. The final stacked trace is shown on the far left.

A constant velocity gather for seismic data at one shotpoint. The same seismic dta are shown in each panel, the only difference being the RMS velocity applied to the data (labelled at the top of each panel). Three events have been circled (A, B,and C). The two-way travel time (in seconds) and RMS velocity (in ft/s) for the three events are: Event A, 0.8s and 6400 ft/s; Event B, 1.7 s and 9600 ft/s; Event C, 2.3 s and ft/s.

Left panel: CMP gather with 4 prominent reflectors identified by number. Centre panel: Amplitude spectrum calculated by summing the NMO corrected gather for a spectrum of assumed velocities and travel times. Right panel: The t 2 – x 2 velocity analysis applied to the CMP gather for the major reflectors 1-4. The resulting velocity values, derived from the slopes of the lines, are plotted as triangles on the velocity spectrum (centre panel).

Constant velocity profile along a seismic line. Velocity analyses have been carried out at the shot points indicated and the velocities are labelled in units of ft/s.

POST-STACK MIGRATION A stacked seismic section before migration (left) and the same section after time migration (right). Note the narrowing of the salt dome and the clarification of the collapse structures on its top.

The principle of migration. (A)Dipping reflector C-D on a stacked section is migrated to its correct geometry C’-D’ (B)The migration process moves an event (E) by a lateral distance d x and vertically by d t. The gradient of the event increases from  t to. Calculation of vertical and horizontal displacements through migration depend on knowing the velocity of the layer.

The principle of the diffraction stack or Kirchhoff migration (A)A diffractor lies at a depth h vertically below a receiver (B)This gives rise to a diffraction event (hyperbola) on a seismic reflection record because the event is wrongly assumed to come from a reflector vertically beneath the receiver. (C)A diffraction stack hyperbola for a known velocity is matched against the observed diffraction. (D)Given a correct match along the hyperbola, all the events are summed and the observed diffraction is shrunk back to a point.

Diffraction hyperbolae calculated using increasing velocities with depth. A slow velocity results in a “tight” hyperbola (uppermost curve) while that associated with the fastest velocity has both the broadest “window” and the flattest of the curves.

(A) Migration panel showing a ‘smile’ caused by a low velocity estimate in layer 1 (arrows) (B) Migration panel showing a ‘frown’ created by a high velocity estimate in layer 1, (C) Migration panel showing a flat event in the case of a correct velocity. The depth of the reflected event is not dependent upon offset.

(A)Stack of a seismic reflection record in the Gulf of Mexico. Three events are indicated by numbers 1-3. (B)The same section after migration. The difference in position of event 3 (see arrows) between the two sections is very marked, with the event being restored to the salt overhang on the migrated section.