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Problems in Exploration Seismology and their Solutions
Problems-in-Exploration-Seismology-and-their-Solutions.jpg
Series Geophysical References Series
Title Problems in Exploration Seismology and their Solutions
Author Lloyd P. Geldart and Robert E. Sheriff
DOI http://dx.doi.org/10.1190/1.9781560801733
ISBN ISBN 9781560801153
Store SEG Online Store


Chapter 10 Geologic interpretation of reflection data

10.1 Improvement due to amplitude preservation

Figures 10.1a and 10.1b show the same data except that Figure 10.1a is a “relative amplitude preserved” section plotted at reduced gain, and with a well log inserted. What conclusions can be drawn from Figure 10.1a that are less evident in Figure 10.1b?

Background

In a sand-shale section, deflections to the left on an SP log (see Telford et al., 1990, chapter 11 for a description of well logs) often indicate sand; a gamma-ray log often appears much the same. Sonic logs usually display slowness (or specific transit time, the reciprocal of velocity), with slowness increasing to the left (velocity increasing to the right).

Ideally we would like to have trace amplitudes depend solely upon the reflection coefficients at the various interfaces. Amplitude preservation attempts to achieve this goal by correcting for extraneous effects including spreading, absorption, nonlinear effects of the recording system, and so on. While we cannot fully compensate for all of the factors that affect amplitude because there are always too many unknowns, we try to maintain the same gain along the seismic line so that lateral changes in reflectivity will be visible. This is particularly important in areas where hydrocarbon accumulations produce significant amplitude changes (often increases or “bright spots” (see problem 10.17). In this area of the U.S. Gulf Coast a common display technique was to decrease the system gain so that only high-amplitude reflections stood out clearly.

Solution

Decreasing the gain emphasizes the highest amplitudes and hydrocarbon accumulations where bright-spot conditions exist. On the other hand, the reduced gain makes it much more difficult to see less prominent reflections and this makes structural interpretation (such as evidences of faulting) more difficult. Relative amplitude-preserved (RAP) sections are generally used as a supplement to, rather than replacement for, regular displays.

Figure 10.1a.  Preserved-amplitude display at lowered gain with well logs inserted.

10.2 Deducing fault geometry from well data

10.2a Well B is 500 m due east of well A and well C is 600 m due north of A. A fault cuts A, B, and C at depths of 800, 1200, and 600 m, respectively. Assuming that these wells are vertical and the fault is planar and extends to the surface, find the surface trace and strike of the fault.

Background

It is shown in Sheriff and Geldart, 1995, problem 15.9a that the direction cosines of a straight line satisfy the equation


(10.2a)

and Sheriff and Geldart, 1995, problem 15.9b gives the equation of a plane whose perpendicular from the origin has length h and direction cosines as


(10.2b)
Figure 10.1b.  Conventional display of seismic line shown in Figure 10.1a.

Solution

We take the origin at well A, the x- and y-axes being positive towards the east and north, respectively, and the z-axis positive vertically downward. The coordinates of the points of intersection of the fault plane with wells A, B, and C are, respectively (0,0,800), (500, 0, 1200), and (0, 600, 600) and these three points all lie on the fault plane. Hence, equation (10.2b) shows that

In addition to these equations we have equation (10.2a) so that we can solve for the four unknowns. Thus , , , Solving these equations we get , , . Using equation (10.2a) we have

We now get , , , and the equation of the fault plane is


(10.2c)

The surface trace is obtained by setting in equation (10.2c), giving

The trace intersects the -axis at , that is, west of A, and cuts the -axis at north of A. The strike is .

10.2b At what depth would you look for this fault in well D located 500 m . of well C?

Solution

The coordinates of the wellhead at D are

Substituting these values in equation (10.2c) gives

10.2c Another fault known to strike N20W cuts wells A and C at depths of 1300 and 1000 m, respectively. Where should it cut well B?

Solution

Let the equation of the fault plane be . With four unknows (, , and ) we need four equations. The fault intersection in well A gives the equation and the intersection in well C gives . The strike is N20W, so the slope of the strike line relative to the -axis is [see equation (4.2)], so . We use these three equations to find , and in terms of , and then the sum to get .

Solving the first three equations gives ,

Then , ,

The equation of the fault plane is thus

Substituting the coordinates of well B, we get

10.3 Structural style

What is the structural style (see Table 10.3a) of Figure 10.3a? While this section is unmigrated, assume that it is nearly perpendicular to strike. Do the velocity data from problem 5.18, which are in the same area, help?

Background

Structural style refers to deformation characteristics that result from stresses in the earth. Lowell (1985) classified these with respect to basic plate-tectonic situations, and Table 10.3a is based on his work. Knowing the general plate-tectonic setting of an area gives an interpreter an appreciation of what structures to expect and helps in selecting the most probable interpretation where several interpretations are possible. It helps, for example, in selecting the most probable types of faults and the orientations of structural features. The structural style depends upon the nature of the prevailing stresses and the manner in which they changed during the history of the area.

Figure 10.3a.  Structural styles and their characteristics (after Lowell, 1985).
Figure 10.3a.  A seismic section (courtesy of Grant Geophysical).

Faults are discussed in problem 10.5 and migration in problem 9.27.

Solution

The data in Figure 10.3a have not been migrated, as we can tell by the conflicting dips in the syncline, so we must mentally migrate them. Assuming that this line is roughly in the dip direction and that the horizontal and vertical distance scales are of the same order, the conflicting dips separate.

There appears to be a fault cutting the shallowest continuous reflections at about 0.6 s at SP 50. The fault surface seems to dip to the left and possibly soles out in the bedding around 2.5 s, with the fairly continuous reflections to the left of the fault rolling over to truncate at the fault.

Figure 10.3b.  Seismic section and interpreted fault.

Correlation of events across the syncline is not obvious. An interpreter sometimes folds a paper section and overlays it on the section to be correlated to see where it matches, or at a work station copies a small vertical rectangle and moves it, e.g., moves the left rectangle in Figure 10.3b to the right rectangle location, to aid in correlating, mentally allowing for changes in interval thicknesses. Based on the indicated correlation, the fault shown is a normal fault and the left side is downthrown. This section seems to match fairly well the basement-detached growth-fault style. Knowledge of the regional geology should help resolve ambiguity.

The velocity data from problem 5.18 suggest consolidated sandstones and/or shales or limey shales such as chalk. The values are too low for well-cemented limestones except below 1.5 s.

10.4 Faulting

How do you reconcile the contradictory dips between the 5- and 6-km marks at the top of the migrated section in Figure 10.4a? What structural style is represented? How would you draw faults?

Background

Structural style is discussed in problem 10.3.

When a burst of energy occurs on only a few traces, it migrates into a wavefront shape, called a smile; the pattern on Figure 10.4a below 3 s is mainly one of intersecting smiles.

Figure 10.4a.  Ardmore Basin (Oklahoma) section.
Figure 10.4b.  Interpretation of Figure 10.4a.

Solution

This section has been migrated, as is evident from the many “smiles” in the lower portion of the section. Migration generally assumes that (1) the line is in the dip direction so that there are no data from off to the side of the line, (2) the velocities used are correct, and (3) all of the data arise from primary reflections or diffractions. If some of these assumptions are not true, the result is conflicting dips, which are abundant on this section. There is no obvious correlation of events at opposite sides of the section.

This structure can be interpreted as a flower structure (solid lines in Figure 10.4b), a structure resulting from a compressional component (or extensional component for a negative flower structure) of strike-slip faulting. If this is the case, the structural style would be classed as basement-involved wrench faulting. The structure may also be interpreted as thrust faulting (dashed line in Figure 10.4b), in which case it would be classed as basement-detached thrusting.

Knowledge of the structural style from other data would help in properly interpreting this line.

10.5 Mapping faults using a grid of lines

Four migrated lines forming a grid are shown in Figures 10.5a,b. Map the three horizons encountered at 1.35, 1.83, and 2.66 s at the intersection of lines B and C. A velocity analysis at this location gives the time-velocity (stacking velocity) pairs in Table 10.5a.

Table 10.5a. Time-velocity pairs from velocity analysis.
0.100 0.600 0.800 1.200 1.400 1.600 2.000 2.700 3.000
1520 1830 1900 2050 2100 2140 2280 2440 2370

Background

Faults are breaks produced by stresses that exceeded the rock strength. The most important basic types are: (1) normal faults caused by extension, where one side slides down the fault surface relative to the other, (2) reverse or thrust faults due to compression, where one block moves up the fault surface relative to the other, (3) strike-slip or transcurrent faults produced by shearing stress, the relative motion being predominantly along strike. Other names are also used in some situations and combinations of these types are also observed.

The most common evidences of faulting are: (a) abrupt termination of events on migrated sections, (b) displacement of events or a distinct displacement pattern, (c) diffractions produced by the terminations of beds, especially evident on unmigrated sections, (d) abrupt changes in dip, especially immediately below a fault, (e) a shadow zone of very poor data or distorted data because of raypath bending in passing through the fault plane, (f) a fault-plane reflection, especially where the fault dip is small.

Whereas unmigrated seismic lines should show the same arrival times at line intersections because the data are acquired at the same locations, dipping data on migrated lines generally will not time-tie because migration moves events according to the apparent dip, which is apt to be different on the two lines. Time-tying migrated sections requires identifying individual reflection events, perhaps because of some distinctive feature, or relating reflections to the corresponding reflections on unmigrated lines, where they should time-tie.

Figure 10.5a.  North-south lines A and C showing the location of one fault (courtesy of Conoco).

Solution

The velocity data in Figure 10.5c indicate a slow section without any significant high-velocity portions, suggesting a clastic section composed of sands and shales. Although there are many coherent events, most are somewhat discontinuous and hardly any have distinctive character or amplitude. Many of the events probably result from interference where local lithologic or thickness changes are responsible for the alignments. Nevertheless, their attitudes probably indicate structure correctly.

Because the lines have been migrated, data should be correctly located except for out-of-the-plane effects. Events are relatively flat so that migration has not shifted them very far and sections tie nicely at line intersections. The principal benefit of migration is that it has sharpened the evidences of faults. Faults as well as seismic events should tie at the intersections of the seismic lines.

Figure 10.5b.  East-west lines B and D showing one fault (courtesy of Conoco).

Interpreted faults are shown on the lines in Figure 10.5b. These faults appear to be normal faults, one shaped like a part of a bowl, curved in both plan and vertical cross-section views. It appears to cut the east-west lines twice. Normal curvilinear faults, often with local increases of dip on the downthrown side adjacent to the fault, suggest that the faulting occurred soon after or contemporaneously with deposition. Such faults often die out along strike. The fault labeled on Figures 10.5e,f with a throw of about 15 ms (one-half cycle) on these lines is probably of this type.

Figure 10.5c.  Velocity data.
Figure 10.5d.  Interpreted horizons and faults (lines A and C).
Figure 10.5e.  Interpreted horizons and faults (lines B and D).

Among the evidences for faulting on seismic sections are relatively systematic discontinuities, local dip into the faults on the downthrown side, somewhat erratic changes of dip on the upthrown side under the faults. The somewhat erratic dips may be caused by raypath bending in penetrating the fault and the fact that the components of the CMP gathers, that were stacked to make each trace, penetrated the fault at different depths with different local changes in velocity, because they cut the fault at different locations.

Figure 10.5f.  Time contour map on the middle picked horizon (b).

An attempt has been made to follow the three horizons along enlargements of these sections; the picks are shown on Figures 10.5d,e. The data tie nicely at the line intersections. Additional lines to tie the data beyond the four line intersections would add considerable confidence to the interpretation.

Reflection has better continuity than the others and hence is the most reliable; it has been mapped in time as Figure 10.5f. Timing involves appreciable uncertainty because so few timing lines are shown, but overall dip directions can be seen and the central structure is probably reliable. The velocity data indicate an interval velocity of 2800 m/s between 1.6 and 2.0 s, so two-way time contours 5 ms apart represent about 7 m. The structure shown in Figure 10.5f appears to be a domal high downthrown to the fault . This type of structure, called a roll-over anticline, is often associated with growth faults. This anticline produces hydrocarbons below the horizon mapped here.

10.6 Fault and stratigraphic interpretation

10.6a In Figure 10.6a, the reflection at about 0.6 s appears to be faulted at SP 5; draw in the fault and describe its probable type and characteristics.

Background

See problem 10.5 for a discussion of types and evidences of faulting. For definitions of geological terms, see Sheriff (2002) or Jackson (1997).

Aggradation (up-building) is associated with rising relative sea level (or subsiding land level) and progradation with a sea-level stillstand. A sequence begins with a fall of sea level and ends with the next sea-level fall.

Figure 10.6b shows terms used to describe the angularities where reflections terminate. Onlap of reflections during rising relative sea level following a fall may indicate a sequence boundary. Toplap often marks no significant change (a stillstand) of relative sea level, and erosional truncation a fall. Downlap and apparent truncation generally result from starvation, that is, not enough sediment being available to permit resolution.

Solution

The fault surfaces in Figure 10.6c are curved and concave upward (listric) and down-thrown to the right and then soling out into bedding planes. Faulting was probably occurring at the time the sediments were being deposited, often a characteristic of growth faults. The dashed fault is not as reliable because the overlying fault may cause fault-shadow effects which cause distortions of deeper data.

10.6b How can changes in the intervals between different reflections in Figure 10.6c be explained?

Solution

The most prominent reflections have been lettered in Figure 10.6c Most of these reflections are at unconformities and may be minor sequence boundaries. In seismic stratigraphy, an unconformity is a break in the time sequence of sediments (a hiatus), and may represent erosion or simply nondeposition. While many unconformities are sequence boundaries, not all are. We have somewhat overinterpreted this section; we believe that, early in an interpretation, one should consider all possibilities, later discarding ideas that appear to be unlikely based on other evidences.

The interval between the seafloor and reflection thins to the right, probably because the source of sediments is far away, that is, relative sea level is high during this time so that the coastline is a long way landward. Downlap onto and toplap below it support this concept.

The interval from to thickens as it approaches the fault, probably because the fault was active during deposition. There is also downlap and perhaps onlap onto . The sediments above and are probably transgressive associated with rises in relative sea level.

Figure 10.6a.  Marine seismic section (from Hatton et al., 1986).
Figure 10.6b.  Terminology for reflection terminations.
Figure 10.6c.  Interpretation of Figure 10.6a.

There is onlap onto . The intervals from to all show thickening to the right and there is onlap onto all of these reflections, Events ., , and suggest shelf edges or offlap breaks.

There is a prominent bulge above reflection ; it appears that there are two shelf edges with some associated slumping. Following the deposition of , sealevel must have fallen below the shelf edge on , as is evident from the onlap onto below the shelf edge. Following this, sealevel must have risen and onlapped onto the shelf of , then formed the shelf edge and fallen again. Note onlap onto the lower part of the bulge and downlap onto thc top of thc bulge.

Note also the probable fault-plane reflection that lies just below the fault that forms the lower boundary of , onto which several reflections onlap. There may be another bulge on the fault between 1.15 and 1.20 s that may be a slope fan.

Data quality is very poor from to . The poor reflection quality may indicate little acoustic impedance contrast. The conflict of dips here may indicate both primary reflections that are probably dipping appreciably to the right and also multiples that are nearly flat. There are probably other faults soling out in this region also. Although is of poor quality, it is probably a major sequence boumdary onto which reflections downlap.

10.7 Interpretation of salt uplift

10.7a Figure 10.7a shows a salt uplift at a shelf edge. How could one tell that this feature is not caused by reef growth, an igneous intrusion, or shale flowage instead of salt uplift?

Background

Under sufficiently high pressure and over long periods of time, salt and shale and some other rocks become plastic and flow; salt, which at depth is lighter than surrounding rocks, is the most common diapiric material. Salt flow may producc pillows, domes, anticlines, salt walls, and other types of features, and the flowing often results in arching of the overlying beds as the salt tries to rise because of its buoyancy, or rises to maintain its depth as the entire section subsides (sinks). In some cases the salt pierces the overlying beds and may even reach the surface. The pierced beds are usually “dragged” upwards, resulting in steep dips adjacent to the sides of the salt structure; this may also be caused by the sediments subsiding while the salt remains at roughly the same depth. Reflections from within the salt are rarely observed. As the salt moves out, the surrounding region from which the salt comes often becomes a rim syncline as sediments subside.

Shale diapirs generally result from overpressuring (see problem 5.9) because interstitial water, laid down as the shale is deposited, cannot escape; as a result, the shale loses shear strength and becomes somewhat fluid (diapiric). Shale diapirs “freeze” into place once the water escapes. Shale diapirs often have a somewhat similar appearance to salt structures.

Figure 10.7a.  Migrated section across a salt dome (courtesy of Grant Geophysical).

Reefs are discussed in problem 10.11, unconformities in problem 10.13. An igneous intrusion would probably have a magnetic signature that could be detected by magnetic measurements.

Solution

If there should be a clear reflection from underneath the feature, its stacking velocity might provide important evidence as to a characteristic velocity. Salt should have an interval velocity around 4.5 km/s whereas the velocity of shale would be much lower and igneous rocks probably higher; a limestone reef should have velocities of about 4.5 km/s or higher. If the regional history were known from other sources, it might indicate the most likely solution. If gravity and/or magnetic data were available, they would help in resolving the difficulty (see problem 10.8).

Since all we have to go on is the single seismic section, we pick the top of the diapir feature in Figure 10.7a at about 3.1 s. Primary reflections appear to extend to at least 4.5 or 5.0 s, and they are bent upward adjacent to the poor reflection zone where the uplift lies. They also suggest a rim syncline, especially prominent to the right of the feature; rim synclines commonly lie above the region of salt withdrawal as salt moved into the uplift, thus reinforcing the interpretation that this is a salt dome. Shale diapirs also occasionally show withdrawal synclines. We note that the vertical extent exceeds the height of most reefs. The pull-up of reflections on both sides of the feature may represent sediments uplifted with the salt. Such pull-up is not usually associated with reefs (although they may show minor pull-up and onlap because of differential compaction), and there is usually little reflection pull-up surrounding igneous intrusions. Shale diapirs ordinarily are not associated with as much pull-up of flank reflections as we see here. Thus we conclude that the feature is probably a salt uplift.

10.7b Does the relief above the unconformity U indicate post-unconformity salt movement, down-drop along faulting at the shelf edge, or differential compaction because of the weight of the postunconformity section?

Solution

There is some minor thinning of the sections below and above , especially just to the left of the salt dome, suggesting some residual upward movement of the salt both before and after . The strong reflection above (at about 1.5 s at the left edge) appears to be undisturbed to the left of the uplift, suggesting that there was no further salt uplift after the time of its deposition, but this and other reflections drop down to the right of the uplift, suggesting that the salt continued to move from the right after . There are indications of a pair of faults cutting suggesting a graben above the salt that does not extend much higher than ; this is consistent with the extension that the downdropping would have produced.

Some parts of the section below show thickness variations which indicate that salt withdrawal underneath them was occurring at the time of their deposition. Several parts of the section below to the left of the uplift suggest progradation.

Regional dip is presumably to the right but reflections below 2.5 s at the right end of the line show counter-regional dip, possibly indicating a growth fault and a rollover anticline just beyond the end of the line.

10.8 Determining the nature of flow structures

If the nature of a flow structure, such as shown in Figures 10.8a or 10.7a, should not be clear, how might gravity, magnetic, or refraction measurements be used to distinguish between salt, shale, and igneous flows? Between these and a reef?

Solution

Salt generally is less dense than sediments (except near the surface) and thus usually has a negative gravity effect. Because it is diamagnetic it has a very small negative magnetic effect, but this effect is often unobservable in the presence of other magnetic effects. Because the high velocity of salt ( 4500 m/s) often distinguishes it, refraction measurements might help.

The density of a shale that is no longer flowing is apt to be similar to that of surrounding sediments so that usually it does not produce a significant gravity effect, even though it was less dense, hence buoyant, when it was flowing. Shale has no distinctive magnetic effect and its velocity is apt to be about the same as surrounding sands and other shales, but its velocity is considerably lower than salt and carbonates which should suffice to distinguish it from them.

Figure 10.8a.  Seismic section at a shelf edge (from Wanslow, 1983).

Igneous rocks usually are fairly dense, often highly magnetic with relatively high velocities; they are thus often associated with positive gravity and magnetic anomalies. Igneous velocities may not be distinctively different from those of carbonates or salt but appreciably larger than shale.

Limestone reefs often have higher velocities than clastic rocks, but limestone density depends strongly on its porosity and its gravity effect may not be distinctive. Limestone generally has no magnetic effect. Because limestone is stronger and less compactible than clastics, differential compaction of surrounding sediments compared to a reef often looks different from the truncation at the edges of diapirs.

While we usually think of a salt diapir as a three-dimensional feature, diapiric salt sometimes forms salt walls that act as a dam. Sediments fill one side of a dam before overflowing to fill the other side, making correlation across the dome very difficult and effectively making a shelf edge. Several indications of shelf edges can be seen under SP 15–16.

It is often difficult to determine the outline of a salt dome, especially to locate its steep and often overhanging flanks. With a migrated section and good quality data, the termination of reflections sometimes indicates the sides of a dome, but often uncertainties in the migration of the steep dips adjacent to the dome and three-dimensional effects do not permit this. In the present case, poor data quality further complicates interpretation.

Note that the sloping seafloor creates velocity distortions (see also problem 10.10), giving an erroneous picture of dips. This will be especially true on the right 40% of this section.

10.9 Mapping irregularly spaced data

10.9a Figure 10.9a is the result of map-migrating Figure 10.9b, which shows the lines of seismic control marked by diagonal dashes. The map shows a high on a north plunging, anticlinal nose. What additional program would you recommend to check weaknesses in the interpretation before recommending a well to test for hydrocarbon accumulation?

Background

In map migration, observed traveltimes to a reflector are mapped along seismic lines and contoured. The contoured surface is then gridded into bins, each bin is migrated, and the result is contoured to yield the migrated map. Migration is discussed further in problem 9.27 (see also Sheriff and Geldart, 1995, section 9.12 for more details).

Solution

Figure 10.9b shows that there is relatively little control on the structure except on the east flank, so appreciable additional seismic work is required before a well location can be selected.

Most of the seismic lines in Figure 10.9a, except for those on the east flank apparently show little structural dip, so the structural picture must be inferred from jump correlations between seismic lines. Jump correlation is highly suspect as faults or dip can also explain the situation even if the correlations are reliable.

In particular, there is little evidence of south dip except that inferred from correlation between disconnected seismic lines. Consequently, a N25E line connecting the two mapped high closures is called for and it should extend far enough north to confirm north dip as well as south dip. There is little control directly over the central high, and the absence of mapped faults in this region may be a consequence of this poor control. At least one east-west line across the high is required. Based on the results of these two lines, additional lines will probably be required.

10.10 Evidences of thickening and thinning

10.10a Figure 10.10a shows a schematic 1:1 geologic section with three parallel beds of equal thicknesses dipping . Assume that the sediment velocity is given by , where is the depth below the sea floor in kilometers, density changes providing the impedance contrasts. The water bottom slopes between 6 and 12 km so that the increase of velocity does not begin until the sea floor. Show how this section would appear on an unmigrated CMP seismic section. Assume coincident source and geophone.

Figure 10.9a.  Migrated map.
Figure 10.9b.  Map of unmigrated seismic data showing lines of control by diagonal dashes (courtesy of Prakla-Seismos).
Figure 10.10a.  Assumed geologic section.

Solution

Because source and geophone are coincident, reflection raypaths are incident on the beds at right angles; such raypaths are shown by short dashes on Figure 10.10a. We let , location, location of reflecting point, slant depth at CMP = raypath length, depth of reflecting point, depth of seafloor above reflecting point, velocity at reflecting point, is the average velocity, -way reflection time , apparent thickness in time.

In Table 10.10a we have calculated (neglecting raypath curvature) the arrival times for the four interfaces at locations 0, 6, and 10 km. Figure 10.10b shows the time section. Note that the beds, which are of equal thickness, apparently thin with depth and also downdip. Also note that an overlying water layer distorts structure and changes the apparent dips and thicknesses.

10.10b Figure 10.10c shows a geologic section with constant velocity layers. Assume constant density and no out-of-the-plane effects; draw the unmigrated zero-offset seismic section. Scale ratio is 1:1.

Table 10.10a. Calculation of apparent thicknesses.
Refln.
A 4.00 0.0 1.24 3.60 3.79 3.30 2.40 3.158
B 5.00 0.0 1.55 4.55 4.78 3.78 2.64 3.621 0.463
C 6.00 0.0 1.80 5.50 5.78 4.25 2.88 4.014 0.393
D 7.00 0.0 2.17 6.45 6.78 4.72 3.11 4.360 0.346
A 2.05 6.0 6.64 1.85 1.95 0.16 2.42 1.96 1.990
B 3.05 6.0 6.95 2.76 2.90 0.24 2.88 2.19 2.648 0.658
C 4.05 6.0 7.31 3.66 3.85 0.33 3.33 2.42 3.182 0.534
D 5.05 6.0 7.62 4.57 4.80 0.40 3.78 2.64 3.636 0.454
* 10.0 1.00* 0.97* 1.50 1.294
** 10.0 1.14 1.50 1.520
B 1.75 10.0 10.54 1.66 1.84 1.13 1.81 1.66 0.976† 2.496
C 2.75 10.0 10.85 2.62 2.89 1.21 2.27 1.89 1.973† 3.493 0.997
D 3.75 10.0 11.16 3.57 3.94 1.28 2.74 2.12 2.745† 4.265 0.772
*Seafloor reflection
**Portion of reflection travel paths in water
†For travel paths in sediments
Figure 10.10b.  Seismic time section.
Figure 10.10c.  Assumed geologic section.
Figure 10.10d.  Unmigrated time section of Figure 10.10c.

Solution

Figure 10.10d shows reflections with solid lines, diffractions with dashed lines, and multiple reflections with short-dashed lines. Note that

  1. reflections are tangent to the diffractions and this would make determining the ends of the reflections difficult;
  2. the horizontal terminations of reflections are at the same horizontal locations as the terminations of the reflectors;
  3. there is no unconformity reflection where there is no change in properties even though the lithology may be different;
  4. the angle of the high-velocity wedge is changed and features below it are distorted;
  5. the top of the basement layer has a kink in it at C, and there would be a small bow-tie effect [see (7) below], because of the overlying high-velocity wedge;
  6. there is no fault-plane reflection on this part of the display, the fault can be located by connecting the crests of the diffractions;
  7. the syncline reflection becomes a buried-focus bow-tie “anticline.”

Ordinary migration would not remedy the effects of velocity changes in the horizontal direction, i.e., it would continue the erroneous appearance of the high-velocity wedge, and it would not remove the kink in the basement surface. However, with the correct migration velocity, diffractions would collapse, reflections would terminate correctly, and the syncline would appear correctly. The fault could then be located by the reflection terminations.

10.11 Recognition of a reef

What kind of feature shows in Figure 10.11a about 75% of the way across from the left end of the section at about 2.5 s? What characteristics help to identify it?

Background

Reefs grow under proper conditions of water temperature, depth, and water clarity. They consist of corals or other marine animals with calcareous parts. Reef growth stops when conditions are no longer suitable, especially when not enough sunlight reaches them. Generally reefs grow sufficiently rapidly that they can keep up with subsidence, but sediment suspended in the water or temperatures that are too low kill them.

Figure 10.11a.  Portion of zero-phase seismic section (courtesy of Grant Geophysical).
Figure 10.11b.  Criteria for reef identification.

Figure 10.11b illustrates some of the criteria useful in recognizing reefs on a seismic section. The top of a reef may have a strong velocity contrast with the overlying sediments and hence produce a strong reflection (a). The reef itself is usually devoid of reflections (b,d). There may be diffractions where surrounding beds are truncated at the reef (c). Back-reef and fore-reef deposition are often distinctly different (e). Differential compaction frequently produces drape over a reef (f). Differences between velocity in the reef and surrounding sediments often produces velocity anomalies below the reef, usually a pull-up (g), but occasionally a push-down (h). The venue of a reef is often a structural high (j), a shelf-edge, a previous reef, or a hinge-line (i).

Figure 10.11c.  Location of the reef.

Solution

This section appears to be nearly zero-phase as many reflections are indicated by single strong peaks that are probably caused by impedance contrasts.

This feature has a number of the characteristics that we associate with reefs. It is located over a hinge line, as can be seen by the change of slope of the underlying reflections; a straight edge can be laid on the reflections to emphasize the change of dip. There is drape over the shaded feature and onlap onto the drape. The reflection pattern also changes on opposite sides of the feature. While there is no obvious velocity anomaly here and the feature in Figure 10.11c is poorly outlined, identifying it as a possible reef seems reasonable. The leftward extension of the moderately strong reflection that reaches the right side of the section just above 2.8 s may mark the base of the reef.

10.12 Seismic sequence boundaries

10.12a Interpret the section shown in Figure 10.12a. Assume that out-of-the-plane data are not important. Pick events that involve angularities between primary reflections in order to identify unconformities and/or seismic sequence boundaries. Note the thinning/thickening of different units.

Figure 10.12a.  Seismic section (from Emery and Myers, 1996).

Background

Seismic sequence analysis is based on the concept that changes in sea level produce more-or-less systematic patterns in marine sediments. Sequence stratigraphy assumes that reflections parallel time surfaces (surfaces that at some past time were the tops of the solid earth) and that stratigraphic patterns result from a combination of (1) absolute sea level (eustasy). (2) uplift or subsidence, (3) supply of sediments, and (4) climatic conditions. Sediments deposited when sea level is lower than it was before and afterward yield lowstand tracts; those deposited when sea level is rising beyond its previous highest value produce transgressive tracts; and those produced when sea level is higher than it was before and afterward yield highstand tracts.

A fall of sea level generally produces an unconformity (see problem 10.13) somewhere, where aerial and sometimes marine exposures are subject to erosion. A sequence consists of the sediments deposited beginning with a sea-level fall and extending to the next sea-level fall. Sequence boundaries are usually evident on seismic lines that are long enough and where the data quality is good and the resolution is sufficient. Changes of sea level are apt to occur at the same time over a large area.

Interpretation begins by noting angularities between reflections (shown in Figure 10.6b and discussed in problem 10.6), which are then used to identify unconformities and other features. Onlap angularities are produced by rising sea level, erosional unconformities by a sea-level fall. During a rise of sea level following a fall, the coastline moves landward (transgresses) unless sedimentation is rapid enough to maintain the coastal position. The interpretation procedure is to first mark the unconformities to define sequences, then map them in three-dimensions, noting changes in the thickness of sequences and the relationship to other sequences, and finally attributing significance to specific sequences.

A fall of sea level, which marks the beginning of a sequence, causes the coastline to move seaward, changing the kinds of sediments deposited, sediments generally becoming coarser as the coastline comes closer. If the sea-level fall moves the coastline below the shelf edge, we expect increased lowstand deposition. Sediments that lie on the slope at the angle of repose will fail more often because storm waves can disturb them more easily, and these sediments will be redeposited farther seaward. During the latter parts of the low-stand as sea level is rising but still below the shelf edge, we expect lowstand progradation resulting in reflections that are more regular and continuous. As sea level rises above its previous level, we expect transgression (landward movement of the coastline) and then less sediment will be available for deposition at seaward locations; this condition will extend into the next highstand. We expect a retrogradational pattern (successive units not reaching as far seaward) during a rapid transgression, then an aggradational one as the transgression comes to an end, and finally progradational as the sequence comes to an end with the next sea-level fall. Thus we expect that cyclical changes of sea level will produce cycles in the depositional patterns. Of course we should not expect the same pattern of seismic facies to be repeated exactly, because conditions will be different during each cycle.

Figure 10.12b.  Interpretation of Figure 10.12a; arrows indicate reflection terminations.

Solution

The following are observations about this single section and tentative suggestions as to their possible meanings. One cannot expect firm conclusions based on a single section.

The major reflection events have been picked in Figure 10.12b and identified by letters. The seafloor reflection is labeled . We see a single peak with about a cycle of forerunner; we interpret this as an embedded wavelet that is nearly zero-phase with standard polarity, although the larger trough following the major peak suggests that the embedded wavelet is not completely zero phase.

The unit is thicker over the right-hand 40% of the section. is a rough surface with a channel cut in it between 2.0 and 4.5 km. We interpret the -to- units as fluvial sedimentation. -to- appears to be progradational. Both and are cut by channels and it appears that the still deeper channel in probably fixed the locations of the shallower channels as far up as ; it is not unusual for channels to localize subsequent channels. The -to- unit thickens to the right with some suggestion of progradation. The source of these sediments appears to be to the right.

At about 9 km there is a listric fault (problem 10.6) either at or at least before . There is a suggestion of onlap onto , and the sediments immediately above it thicken to the right. appears to be out-of-phase with most of the reflections, and there are suggestions of both downlap and onlap onto and of toplap below . , , and indicate progradation. Both and have mounds at the base of their steeper slopes and in places we see both onlap and downlap onto them. , which has been picked discontinuously, may not represent the same horizon. The source of sediments for units below is to the left of the section, in contrast to those above .

Figure 10.12c.  Seismic section in Gulf of Mexico.

and appear to be the best candidates for significant sequence boundaries. Other strong reflections such as , , , and may also be minor sequence boundaries.

The progradation from to may be deltaic. marks a relative sea-level fall that eroded the tops of the -to- sediments. The -to- sediments are mainly lowstand.

10.12b Interpret the Gulf of Mexico section shown in Figure 10.12c, making the same assumptions as with Figure 10.12a.

Solution

There are rather clear evidences of faulting, which must be resolved before stratigraphic interpretation can begin. The reflections are all more-or-less parallel and obvious angularities are few. A number of changes in seismic character (seismic facies) are evident, and these greatly assist in identifying the same horizons across the faults. The most obvious of these are very weak reflection zones underlain by fairly strong reflections that are probably sequence boundaries. These weak-reflection zones are probably predominately shale.

An interpretation of this section is shown in Figure 10.12d with some of the stronger reflections or more obvious seismic facies separations indicated by letters. The general increase in dip to the right below event and the general thickening to the right indicate that the right-hand side of the section was subsiding more rapidly than the left-hand side while the sediments were being deposited. The down-to-the-right synthetic faults are growth faults; the throw increases with time, resulting in thicker units on the downthrown (hanging-wall) sides. Because of the increase of velocity with depth, the throws increase with depth more rapidly than they appear to. The dipping event may be the deep continuation of a listric fault that is soling out.

Figure 10.12d.  Interpretation of Figure 10.12c.

There appear to be two antithetic faults (faults opposite in sense to the more important growth faults), which are associated with the extension involved with rollover anticlines that locally reverse the dip.

The sediments in the Gulf of Mexico are predominently clastics, and this area (in about 200 m of water) was probably marine for a very long time, the coastline being further away during highstands than lowstands. Lowstands generally result in larger volumes of sediments being available for deposition than highstands because more surface is exposed to areal erosion then. Hence, we expect most of this section to be lowstand deposition, and highstands to be thinner with changes more concentrated than in lowstand sediments. Thus sharp changes in physical properties and distinctive reflections will be more probable during the highstand and especially at its end of the highstand. We generally associate the strongest and most continuous reflections with the sequence boundaries; these are indicated by solid lines. The reflections indicated by long dashes are interpreted as the tops of slope-fan units, and those identified by dots as the tops of lowstand prograding sediments. Many of the lettered reflections are probably sequence boundaries, and there are probably more sequence boundaries than have been picked.

The unit between and thins to the right, presumably because the coastline is a long way off to the left and, hence, fewer sediments are available for deposition as one goes to the right. Units often thicken on the downthrown side of growth faults. At times this area was presumably undergoing rapid subsidence because of movement of underlying salt, and some of the thickening is probably the consequence of this.

Often well logs can be interpreted in sequence-stratigraphic terms. A log in a well shown in Figure 10.12d has been interpreted as showing a number of sequence boundaries indicated by the letters , , , , and (the initials of distinctive paleontological species). These generally correspond to the facies changes indicated by the solid lines in Figure 10.12d. Two other sequence boundaries between and are identified in this well, but the resolution of the seismic section does not permit their identification. Event H is probably also a sequence boundary although it was not identified in the well.

10.13 Unconformities

An obvious unconformity () is evident at approximately 1.5 s in Figure 10.13a; precisely where would you position it? Is it associated with the same event at opposite sides of the section?

Figure 10.13a.  Section with angular unconformity (from Yilmaz, 1987).

Background

An unconformity is a surface which at one time was subjected to erosion, either subaerial or submarine, that removed some of the section. An unconformity is characterized by a hiatus, a period of time for which no sediments are present. In stratigraphic interpretation, periods during which sediments were not being deposited are often lumped with erosonal unconformities, because the reason for the missing section may not be evident.

There is a reasonable probability that depositional conditions changed during a hiatus and hence the sections above and below an unconformity are apt to be different. Hence, an unconformity is often marked by a fairly strong reflection, and unconformities often provide the dominant reflections. The reflection patterns above and below an unconformity are often different, and, thus, the dip is apt to be different, especially if the area was tilted during the hiatus. An unconformity is thus often marked by angularities with the unconformity reflection, both below and above the unconformity over at least some portions. Differences between the rocks below and above an unconformity at different locations cause the unconformity reflection to change character and sometimes even polarity. Unconformities may be difficult to recognize if they do not involve a change in dip.

Solution

The left-hand 40% of the section in Figure 10.13a shows a different dip than the right-hand 60%. A hinge-line occurs near that is especially evident at the unconformity but is also evident in the shallower reflections, for example at 0.4 s. Above 1.4 s the reflections on the right side of the section are nearly horizontal and parallel, whereas, on the left side, a number of intervals show thickening to the left.

The interval is somewhat an exception to this as it thins to the left. The character near the top of interval seems to be slightly different from to , possibly suggesting a reef at the shelf edge. Unit also downlaps at its base.

The hinge also appears below the unconformity . Note that the interval on the left portion of this section maintains roughly uniform thickness, although the top of the unit changes its character, whereas interval just below it thickens appreciably to the right. Velocity data might add to the understanding of this hinge and help determine the role of the section between and in what we observe. For example, if this section is low-velocity compactible rock, compaction may be partly the cause of the hinge, and the hinge in the interval may be at least partly a velocity anomaly.

Where the section from to the top of unit subcrops at the unconformity, the unconformity reflection seems to sag and change character somewhat.

Note the changes in below , especially the curved event at the base of . The data at just below the interface between and may indicate another shelf edge or a fault. Changes in the character of the pre-unconformity section also call for explanation. The reason for the rapid thickening to the right of the section below is not clear, nor is the significance of the sharp upward curvature of event at its left end.

10.14 Effect of horizontal velocity gradient

In Figure 10.14a, , , the horizon dips , and the diffracting point is at a vertical depth of 2.00 km, the dipping horizon being midway between and (at the surface). Compare the diffraction curve with what would have been observed on a CMP section if .

Figure 10.14a.  Geometry of problem.

Solution

The curve for the diffracting point below the dipping interface can be solved analytically or graphically by ray tracing. The crest of the diffraction is located beneath where the angle of approach to the surface is ; such a raypath is called an image ray. If we denote the angle between a ray at and the vertical as , then Snell’s law at the interface gives for the image ray the equation


The fact that an image ray approaches the surface vertically is employed in depth migration (see problem 10.16) to accommodate horizontal changes in velocity.

The diffraction curve (solid curve, Figure 10.14c) is not symmetrical and the crest is displaced about 500 m updip from . The right limb is nearly flat because the increased traveltimes at the high velocity is almost compensated for shorter travel distance at the low velocity.

Figure 10.14b.  Ray tracing for the diffracting point .
Figure 10.14c.  Diffraction curves. Solid curve is 2-layer case, dashed is constant velocity case.

The diffraction curve for the constant velocity case (dashed curve, Figure 10.14c) can be calculated using the equations

where is the angle of approach at the surface.

10.15 Stratigraphic interpretation

Interpret the seismic section shown in Figure 10.15a.

Solution

The most striking feature of this section is probably the progradational pattern indicating a source to the right of the section. These prodelta reflections (seaward of a river delta) show both toplap and downlap terminations. Note that these prograding reflections are more continuous at the right and left sides of the section than in the region under the surface channel. There may also be a slight sag in reflections under the channel, and they suffer similar quality deterioration. An interpreter would not interpret these quality changes as having stratigraphic significance.

The thin wedge above that pinches out about midway on the section shows downlap from the left, suggesting a shift in the source of the sediments from the time when the deeper prodelta sediments were being deposited. Downlap is seen onto and reflections below truncate against this reflection; it is probably an unconformity and possibly a sequence boundary.

Figure 10.15a.  Seismic section (courtesy Chevron Oil Company).

Note the change in overall character at reflection ; it is known from well control that separates marine sediments below from nonmarine sediments above. However, the decrease in multiplicity on this CMP section as one goes shallower (because of the mute applied in processing) might also produce a character change.

Dip is gently to the left on this section so the right dip at and below constitutes a dip reversal that may have structural significance.

10.16 Interpretation of a depth-migrated section

What features can be seen in Figure 10.16a?

Background

Problem 10.14 showed the lateral shift of a diffraction curve because of velocity changes in the horizontal direction. Depth migration is a way to remedy this; it involves raytracing through a velocity model that incorporates the horizontal velocity changes. Figure 10.16b shows the velocity model and tracing of image rays (see problem 10.14) for this section. The bending of image rays corrects for the horizontal errors of placement because of the horizontal velocity changes.

Note that depth migration differs from time-to-depth conversion, which does not correct for horizontal velocity changes.

Figure 10.16a.  Depth-migrated seismic section (from Hatton et al., 1981).
Figure 10.16b.  Tracing of image rays through the velocity model.
Figure 10.16c.  Location of features discussed in the text.

Solution

Figures 10.16a,c have about a 2:1 vertical exaggeration and “timing lines” occur at 150-m intervals. Several unconformities can be seen, some showing angularities below and some above them. The most prominent geologic feature is the angular unconformity (Figure 10.16c), which is a strong reflection to the right of 3 km, but it appears weaker and changes character left of 3 km where the depth model (Figure 10.16b) does not show a velocity contrast. Other unconformities can be seen below . Because truncates reflections below it so sharply, we infer that it is erosional, although generally it is not obvious whether unconformities are errosional or nondepositional.

Note the more-or-less uniform leftward thickening of (the unit above ), the thickening not seeming to be related to the sharp folding between 600 m and 2300 m except for the lowest portion of which shows the folding in highly attenuated form. Hence, fold mainly occurred before , but some folding continued into the lower portion of .

is another unconformity; the velocity difference at to the left of 4.3 km is 270 m/s where is present and 630 m/s where is absent. The small portion of above the right-hand syncline bears no obvious correlation with the main body of , so we do not know how they may be related. We see onlap onto and truncation below . and merge at 3.2 km; may have been eroded off to the right of 3.2 km. The pieces of reflection labeled are multiples of the sea-floor reflection, as is evident on a time section but not obvious on the depth section.

The strong event seems rather strange; it cannot be a multiple. It appears to cut across the bedding, especially from 3.0 to 5.0 km, and the folding around 5.2 and 6.6 km is more intense, both above it and below it. It truncates reflections below it, and reflections above it appear to downlap onto it, so it seems to be an unconformity, but the higher intensity of folding above it seems very odd. It might be an out-of-the-plane reflection or perhaps a fault.

There may be a reverse fault at 5.0 km at about 1.2 km depth. The strong reflection also has some of the same problems as and, in addition, it appears to be downthrown to the right at , whereas other events seem to be downthrown to the left. The velocity model has another reverse fault at . The strong event generally parallels , but not exactly, as the section between and thickens and thins.

Thus we see a number of problems with interpreting this section. We would like to do palinspastic reconstruction, that is, flattening successive reflections, as an aid to understanding it. While we do not have the data to do this, we suspect that doing so would show up more inconsistencies and not resolve all of the problems cited above.

10.17 Hydrocarbon indicators

Figure 10.17a displays both peaks and troughs in black so that we can not tell easily the polarity. It shows two lines across a high-amplitude bright spot, presumably indicating a hydrocarbon reservoir. The top of the reservoir is indicated by a single event, but the flat spot on part (i) seems to have three side lobes on either side of the central strongest part, which we pick as a flat spot. What is the maximum reservoir thicknesses shown on each line? Assume 1800 m/s velocity. Why do the reflections from the reservoir top and bottom not converge at the pinchout edge of the reservoirs? Why does the flat spot disappear over the center of the reservoir in (ii)?

Background

Under normal circumstances rock interstices are filled with salt water, but in a reservoir hydrocarbons replace the water in the upper portions because they have lower density. Hydrocarbon-filled rocks almost always have lower velocities and lower densities, than water-filled ones. If the overlying rocks have a higher acoustic impedance than the brine-filled reservoir rocks, the impedance decrease at the top of the reservoir becomes larger when hydrocarbons replace brine, increasing the magnitude of the negative reflection coefficient, thus creating a bright spot. If the overlying rocks have a lower impedance than the brine-filled rocks, the lowering of impedance when hydrocarbons replace brine may lower the reflection coefficient, creating a dim spot, and sometimes may also reverse the polarity.

Figure 10.17a.  Two lines over a reservoir in the North Sea (courtesy of Elf Aquitaine Norge a/s).

Where a fluid contact is present in a reservoir, as at a gas-oil, gas-water, or oil-water interface, there is a positive impedance contrast that may produce a nearly horizontal positive reflection (flat spot) that is distinctive where the bedding reflections are not horizontal. Flat spots, which are sometimes tilted because of overlying velocity changes, are among the best hydrocarbon indicators, but they are often not seen where the resolution is inadequate or where the change in hydrocarbon saturation is gradual. Sometimes other features such as porosity or cementation changes associated with a former horizontal reflector produce a flat spot that is not associated with a current fluid contact.

The change in velocity associated with hydrocarbon-filled rock sometimes produces velocity anomalies beneath a reservoir. The large amplitudes associated with bright spots may result in gain changes in processing that produce decreased amplitudes (amplitude shadows) in the underlying and overlying sections. A lowering of frequency immediately below a reservoir is sometimes seen (low-frequency shadow) and gas leaking from a reservoir into overlying sediments may cause a deterioration of reflections and even a velocity anomaly (gas-chimney effects). One of the most important evidences is to observe the structural conditions that could produce a trap.

All of the hydrocarbon indicators can be caused by situations other than hydrocarbon accumulations, so one cannot rely on any one indicator. However, the case for a hydrocarbon accumulation is considerably strengthened where several indicators are present.

Solution

The strong reflections indicating the reservoir have limited horizontal extent and appear to be located at the top of an anticline, i.e., they are hydrocarbon indicators. The nearly horizontal reflection that cuts across other events, which we interpret as a fluid-contact flat spot, produces a simple positive reflection; we often examine it to learn about the embedded wavelet. In Figure 10.17a(i) it appears to be nearly symmetrical, suggesting that this section is almost zero-phase. We expect the single half-cycle at the top of the reservoir to be a negative reflection because the event is a bright spot. As the negative top-reservoir reflection approaches the positive flat-spot reflection, they interfere and tend to form an antisymmetric 90 wavelet; the top reflection is pushed upward and the flat spot reflection downward because the high frequencies required to show a pinch out are not present.

In Figure 10.17a(ii), the flat spot disappears over the highest part of the reservoir because here the reservoir is completely filled with hydrocarbons so that no hydrocarbon-water contact exists.

The largest time between the centers of the reflections indicating the reservoir top and the flat-spot reservoir base is about 30 ms on (i) and perhaps 40 ms on (ii), giving thicknesses of 27 and 36 m.

10.18 Waveshapes as hydrocarbon accumulation thickens

10.18a Using the minimum-phase wavelet of problem 9.14a [11, 14, 5, –10, –12, –6, 3, 5, 2, 0, –1, –1, 0], determine the waveshapes for a gas-bearing sand encased in shale when the two-way traveltime through the water-sand is 12 ms, the traveltime through the gas-sand portion being successively 0, 2, 4, 6, 8, 10, and 12 ms. Plot the traces side-by-side shifted successively as would be the case for a horizontal gas-water contact. This illustrates a bright-spot–flat-spot situation. Take the reflection coefficients for shale to gas-sand as –0.10, gas-sand to water-sand as +0.15, and water-sand to shale as –0.05. Neglect small time differences because of velocity differences.

Background

Minimum-phase and zero-phase wavelets are discussed in Sheriff and Geldart, 1995, section 9.4 and section 15.5.6, bright spot and flat spot in problem 10.17.

Solution

A two-way traveltime of 12 ms (i.e., for ms where is the sampling interval) corresponds to about 12 m at 2000 m/s velocity. Since we are only interested in the wavelet shape, we scale the reflection coefficients up to –2, +3, and –1 for the shale to gas-sand, gas to water-sand, and water-sand to shale, respectively. Where the water-filled portion of the reservoir thins to zero we have just two contacts, +1 and –1 at the reservoir top and bottom, and the reservoir is six samples thick. Thus,


11, 14, 5, –10, –12, –6, 3, 5, 2, 0, –1, –1, 0
–11, –14, –5, 10, 12, 6, –3, –5, –2, 0 1, 1, 0
11, 14, 5, –10, –12, –6, –8, –9, –3, 10, 11, 5, –3, –5, –2, 0, 1, 1, 0.


Where we have 2-ms round-trip time in the reservoir, we have

–22, –28, –10, 20, 24, 12, –6, –10, –4, 0, 2, 2, 0
33, 42, 15, –30, –36, –18, 9, 15, 6, 0, –3, –3, 0
–11, –14, –5, 10, 12, 6, –3, –5, –2, 0, 1, 1, 0
–22, 5, 32, 35, –6, –24, –35, –15, 6, 16, 14, 5, –6, –5, –2, 0, 1, 1, 0.

For 4-ms round-trip time in the reservoir,

–22, –28, –10, 20, 24, 12, –6, –10, –4, 0, 2, 2, 0
33, 42, 15, –30, –36, –18, 9, 15, 6, 0, –3, –3, 0
–11, –14, –5, 10, 12, 6, –3, –5, –2, 0, 1, 1, 0
–22, –28, 23, 62, 39, –18, –53, –42, 0, 25, 20, 8, –6, –8, –2, 0, 1, 1, 0.


For 6-ms round-trip time in the reservoir,

–22, –28, –10, 20, 24, 12, –6, –10, –4, 0, 2, 2, 0
33, 42, 15, –30, –36, –18, 9, 15, 6, 0, –3, –3, 0
–11 –14 –5 10 12 6 –3 –5 –2 0 1 1 0
–22 –28 –10 53 66 27 –47 –60 –27 19 29 14 –3 –8 –5 0 1 1 0.

For 8-ms round-trip time in the reservoir,

–22, –28, –10, 20, 24, 12, –6, –10, –4, 0, 2, 2, 0
33, 42, 15, –30, –36, –18, 9, 15, 6, 0, –3, –3, 0
–11, –14, –5, 10, 12, 6, –3, –5, –2, 0, –1, –1, 0
–22, –28, –10, 20, 57, 54, –2, –54, –45, –8, 23, 25, 3, –5, –2, 0, –1, –1, 0.

For 10-ms round-trip time in the reservoir,

–22, –28, –10, 20, 24, 12, –6, –10, –4, 0, 2, 2, 0
33, 42, 15, –30, –36, –18, 9, 15, 6, 0, –3, –3, 0
–11, –14, –5, 10, 12, 6, –3, –5, –2, 0, 1, 1, 0
–22, –28, –10, 20, 24, 45, 25, –9, –39, –26, –4, 17, 12, 1, –2, –3, –2, 1, 0.

Where the reservoir is completely gas filled, we have

–22 –28 –10 20 24 12 –6 –10 –4 0 2 2 0
22 28 10 –20 –24 –12 6 10 4 0 –2 –2 0
–22 –28 –10 20 24 12 16 18 6 –20 –22 –10 6 10 4 0 –2 –2 0.

The results are plotted in Figure 10.18a the two outside curves are repetitions of the curves for gas-sand thicknesses of 0 and 12 ms. The first, fairly large trough indicates the top of the gas-filled reservoir and it changes to a peak where water fills the reservoir. The strong horizontal alignment indicates the flat spot and the dipping peak, which gets lost in the tail of the flat spot, the base of the reservoir.

10.18b Repeat using the zero-phase wavelet of problem 9.14e [1, 1, , , , , 10, 17, 10, , , , , 1, 1].

Solution

Where the reservoir is completely filled with brine, the reservoir being six samples thick, we have:

1, 1, –1, –4, –6, –4, 10, 17, 10, –4, –6, –4, –1, 1, 1
–1, –1, 1, 4, 6, 4, –10, –17, –10, 4, 6, 4, 1, –1, –1
1, 1, –1, –4, –6, –4, 9, 16, 11, 0, 0, 0, –11, –16, –9, 4, 6, 4, 1, –1, –1.

Where there is 2-ms round-trip time in the reservoir at the top of the structure, we have:

–2, –2, 2, 8, 12, 8, –20, –34, –20, 8, 12, 8, 2, –2, –2
3, 3, –3, –12, –18, –12, 30, 51, 30, –12, –18, –12, –3, 3, 3
–1, –1, 1, 4, 6, 4, –10, –17, –10, 4, 6, 4, 1, –1, –1
–2, 1, 5, 5, 0, –10, –33, –5, 32, 42, 6, –6, –20, –22, –9, 7, 6, 4, 1, –1, –1.


Figure 10.18a.  Waveshapes as a function of hydrocarbon thickness for a minimum-phase wavelet.

For 4-ms round-trip time in the reservoir,

–2, –2, 2, 8, 12, 8, –20, –34, –20, 8, 12, 8, 2, –2, –2
3, 3, –3, –12, –18, –12, 30, 51, 30, –12, –18, –12, –3, 3, 3
–1, –1, 1, 4, 6, 4, –10, –17, –10, 4, 6, 4, 1, –1, –1
–2, 1, 5, 11, 9, –4, –39, –47, 11, 63, 46, 0, –26, –31, –15, 7, 9, 4, 1, –1 –1.

For 6-ms round-trip time in the reservoir,

–2 –2 2 8 12 8 –20 –34 –20 8 12 8 2 –2 –2
3 3 –3 –12 –18 –12 30 51 30 –12 –18 –12 –3 3 3
–1 –1 1 4 6 4 –10 –17 –10 4 6 4 1 –1 –1
–2 –2 2 11 15 5 –33 –53 –31 42 69 42 –20 –37 –24 1 9 7 1 –1 –1.

For 8-ms round-trip time in the reservoir,

–2, –2, 2, 8, 12, 8, –20, –34, –20, 8, 12, 8, 2, –2, –2
3, 3, –3, –12, –18, –12, 30, 51, 30, –12, –18, –12, –3, 3, 3
–1, –1, 1, 4, 6, 4, –10, –17, –10, 4, 6, 4, 1, –1, –1
–2, –2, 2, 8, 15, 11, –24, –47, –37, 0, 48, 63, 22, –31, –30, –8, 3, 7, 4, –1, –1.
Figure 10.18b.  Waveshapes as a function of hydrocarbon thickness for a zero-phase wavelet.

For 10-ms round-trip time in the reservoir,

–2, –2, 2, 8, 12, 8, –20, –34, –20, 8, 12, 8, 2, –2, –2
3, 3, –3, –12, –18, –12, 30, 51, 30, –12, –18, –12, –3, 3, 3
–1, –1, 1, 4, 6, 4, –10, –17, –10, 4, 6, 4, 1, –1, –1
–2, –2, 2, 8, 12, 11, –18, –38, –31, –6, 6, 42, 43, 11, –24, –16, –6, 1, 4, –2, –1.

If the reservoir is completely gas filled, we have

–2, –2, 2, 8, 12, 8, –20, –34, –20, 8, 12, 8, 2, –2, –2
2, 2, –2, –8, –12, –8, 20, 34, 20, –8, –12, –8, –2, 2, 2
–2, –2, 2, 8, 12, 8, –18, –32, –22, 0, 0, 0, 22, 32, 18, –8, –12, –8, –2, 2, 2.

The results are plotted in Figure 10.18b. The evidences are much the same as in Figure 10.18a despite the change in waveshape.