Flexible 3-D seismic survey design

Flexible 3-D seismic survey design
Gabriel Alvarez Stanford University Victor Pereyra, Laura Carcione Weidlinger Associates Inc. Good Afternoon: I am a third year student with SEP and what I will be presenting today is a continuation of my talk in last year meeting. I will illustrate my methodology in 3-D this time using a relatively simple 3-D subsurface model.

Alvarez, Pereyra, Carcione
Goal Show with a simple 3-D example how to optimize the design of a seismic survey such that it is: Does not compromise the logistics. Locally optimum to illumination. Require many fewer shots than a standard design. I will assume for the purpose of this presentation that we need to design a 3-D seismic survey with a shallow target corresponding to a land prospect in which the sources are expensive and are therefore the deciding factor in the cost of the program. Alvarez, Pereyra, Carcione

Characteristics Flexible: allow survey parameters to change in a systematic way. Exhaustive: exploits all subsurface information as well as logistic and economic constraints. Dips, depths, velocities, presence of fractures, etc Available recording equipment, maps of surface obstacles, etc. This approach is characterized by a few adjectves. The first is that it is flexible, which means that different parameters can be used in response to changes in the subsurface. It is exhaustive, meaning that it exploits all available subsurface information and can incorporate logistcs and cost. Information such as dips, depths, velocities, presence of fractures, etc. On the logistics part available recording equipment, maps of the subsurface and so on can also be incorporated. And the method is illumination based, meaning that target illumination is explicitely considered as the key objective of the design. Illumination-based: uses target illumination as the primary design consideration. Alvarez, Pereyra, Carcione

Design Example Single depth-variable target: m Land prospect. Sources are expensive. I will assume for the purpose of this presentation that we need to design a 3-D seismic survey with a shallow target corresponding to a land prospect in which the sources are expensive and are therefore the deciding factor in the cost of the program. Alvarez, Pereyra, Carcione

Subsurface model View from the inline direction Here is a view of the subsurface model from the dip direction. Reflector 1 corresponds to the topography and reflector 5 corresponds to the objective. The spatial dimensions are 10 km x10 km and the vertical depth is 3 km. Note that there are high dips. Alvarez, Pereyra, Carcione

Subsurface model View from the cross-line direction Here is a view of the model from the strike direction. Again, notice that the model is truly 3-D. Alvarez, Pereyra, Carcione

Target reflector Inline direction Cross-line direction Here we see the target horizon (which was blue in the previous two slides). This view corresponds to the dip direction. Notice again that there is siginificant dip. This is a view from the strike direction. The structure in the middle is the main target of the survey. Alvarez, Pereyra, Carcione

The standard approach Let me show you know the geometry that I would compute with the standard approach. Alvarez, Pereyra, Carcione

Target parameters Minimum depth: 300 m Maximum depth: 3000 m Maximum dip: 60 degrees Minimum velocity: 2000 m/s Maximum frequency: 60 Hz These are the basic parameters that we would use in the standard design strategy. In particular, notice that the target can be very shallow. Also, notice that the dips are high and so is the trace density. Minimum trace density: tr/km2 Alvarez, Pereyra, Carcione

Survey recording patch 500 m 400 m X X X X X X X X X X X X 20 m 8 receiver lines 20 shot salvo 24 fold The basic source and receiver template is chosen orthogonal with the receiver lines represented by the horizontal yellow lines and the source lines represented by the vertical dotted red lines. The template parameters are chosen as shown in the appendix of the paper. A zoom of the are corresponding to this circle is hown here. The distance between the source lines is 500 m and between the receiver lines is 400 m. The source and receiver intervals are 20 m. Here is the schematic of the recording template. There are 8 receiver lines in the patch, 20 shots per salvo. Alvarez, Pereyra, Carcione

Other parameters Max offset inline=2990 m Max offset xline=1590 m Shot density: 100 shots/km2 Aspect ratio: ~2 Number of channels/line: 300 Fold: 24 (6x4) Number of receiver lines: 8 The maximum offset inline is about 3000 m and the maximum offset cross-line is about 1600 m so that the aspect ratio, that is, the proportion of the maximum offsets in the two directions is about 2. We prefer aspect ratios close to one in order to have a better azimuthal distribution. The number of channels per receiver line is 300 and the density of shots is 200 per square kilometer. This number is relatively high. Alvarez, Pereyra, Carcione

Maximum-minimum offset
Problem: Maximum-minimum offset MMO=640 m So far so good, the standard approach has produced parameters that are well within the usual practice, but there is a problem: If we take a look in detail to the bin population we find the situation depicted here: Again the receiver lines are horizontal and the shot lines are vertical. Notice that the minimum possible offset in the central bins is the diagonal of the recording box. Since the sides of the box are 400 m and 500 m this gives a minimum offset for those bins 640 m. This is what’s called the maximum minimum offset. The important point is that those offsets are larger than the target depth and therefore seriously compromise the image of the target. So, what to do? Some bins have minimum offset larger than the target depth. Alvarez, Pereyra, Carcione

Alternatives to solve the problem Halve the receiver- and the source-line intervals. 500 m 400 m 250 m 200 m MMO=320 m. Good. But … Receiver and shot density are doubled. The fold is doubled: 12 x 4 The aspect ratio is doubled: 4 The salvo is halved: 10 Well, there are several ways to deal with this problem. I will illustrate two here. The simplest one is to reduce the distance between the source lines and the distance between the receiver lines. In this case it is easy to simply halve them. This means doing from here to here. Notice that now the MM0 is 320 m. O.K. so we have solved the problem. But of course this solution comes at a price: first notice that both the source and the receiver density have been doubled. This is particularly critical for the sources since the basic assumption was that the sources were expensive. So, doubling the source density could potentially double the cost of the survey, or at least increase it significantly. But not only that, we have also increased the fold to 48 and the aspect ratio to 4 which may not be what we want. Besides, the salvo has been halved so the acquisition is less efficient. Alvarez, Pereyra, Carcione

Alternatives to solve the problem 2. Halve the receiver and source-line interval and use a rectangular bin X X X X X X 20 m 40 m Good. Now the source density doesn’t change. But … The fold is doubled: 12 x 4 The salvo is now one-fourth: 5 The aspect ratio is doubled: 4 The second solution is to use a rectangular bin in addition to halving the source and receiver lines. The aadvantage is that by doubling the source interval we compensate the halving of the source line interval and so the source density does not change. This is good, since again, the sources are assumed to have the highest influence in the cost of the survey. Just as before, however, we end up doubling the fold and the aspect ratio and reducing the salvo to only 5 shots, thus affecting the efficiency of the acquisition. Alvarez, Pereyra, Carcione

Why the need to compromise? Because we are using the same parameters for the entire survey area. We can use different parameters in different parts of the survey: the target is shallow only in a small region. So, the question is, what causes this problem?. Why do we actually need to compromise?. Well, because we are using the same parameters for the entire survey area. Now, a look at the target reflector shows that it is only really shallow in part of the area, so we could use different parameters in different parts of the survey area. Alvarez, Pereyra, Carcione

The proposed approach: subsurface-based design And how to do that?. Wel, this is where the proposed approach comes into play. Alvarez, Pereyra, Carcione

The method in a nutshell Use a subsurface model to trace rays to the surface at uniform opening and azimuth angle. ray tracing Record the emergence position of the rays at the surface. Compute locally optimum spatially-varying geometry. In a nutshell, the method uses a subsurface structural and velocity model to trace rays up to the surface at uniform opening and azimuthal angles as shown here for just a very few points. We record the emergence position of the rays and use them to compute the optimum survey Alvarez, Pereyra, Carcione

Spatially-varying geometry 1. Maintain a standard geometry but allow changes in the parameters (line intervals). 2. Maintain a standard receiver template but allow sources in “arbitrary” positions. 3. Allow sources and receivers to be in “arbitrary” positions. Now, how do we handle the spatial variation of the geometry? Well there are three main ways to do that. The simplest one, and the one that I will show in this example, is to maintain a basic recording geometry, which in this case will be orthogonal and spatially vary the template parameters without changing the template itself. A further step is to maintain a basic receiver template but allow the sources to be in arbitrary positions. This could be useful if we were to use vibrators, for example, which we would like to be along roads which may not be straight. The most ambitious strategy is to allow both sources and receivers to occupy arbitrary positions. Alvarez, Pereyra, Carcione

Model space dimensionality Fixed orthogonal geometry: Only six parameters describe each geometry. Receiver interval Source interval Receiver line interval Source line interval Number of receivers/line Number of receiver lines/patch. Before I go into the details of the method, a word about model space dimensionality. Since I am fixing the recording template as orthogonal, there are only seven parameters that describe a given geometry: receiver interval. source interval, receiver line interval, source line interval, number of receiver lines and number of receivers per line. This of course means that the problem has a very small dimensionality. Notice also that each parameter has only a limited number of acceptable numbers, that is, we are dealing with an integer optimization problem. Each parameter has a limited number of acceptable values (integer optmization). Alvarez, Pereyra, Carcione

Assign source-receiver positions O.K. Now let’s go to the first step, that of assigning each ray emergence position as that of a source or a receiver. This is done in a very simple way as shown here. The two dots represent the emergence position of a pair of dual rays. Dual rays mean rays that originated at the same point, with the same azimuth but with common opening angles equal on each side of the normal. The left panel represents a sparse geometry. The horizontal lines are receiver lines and the vertical lines are source lines. The top point is closest to a source line so it will be assigned to a source whereas the lower point will be assigned to a receiver. The panel on the right shows a similar situation but the geometry is more dense. In this case the upper point is classified as a receiver and the lower point as a source. The upshot is that, for each geometry, the classification is based on which position is close to the point, a source or a receiver. For each geometry: based on ray emergence position being closer to a source or receiver line. Alvarez, Pereyra, Carcione

Preprocessing For each trial geometry: Compute total distance that the rays were moved. Compute shot and receiver density, fold, aspect ratio, offsets, etc. The next step is preprocessing. Rays that fall outside the area of interest or that have too long travel time are discarded. Then the rays are assigned as shown in the previous slide. For each trial geometry, we compute the total distance that the rays were moved, which is a measure of the illumination distorsion. We also compute the shot and receiver density, fold, aspect ratio, maximum offsets and so on. Alvarez, Pereyra, Carcione

Fitness function i: index of trial geometry λ: to balance objectives vs. constraints δ: relative weight of each objective ε: relative weight of each constraint O: objectives (illumination and cost) C: constraints (fold, aspect ratio, MMO, etc) f: fitness value The fitness function for the optimization is multi-objective and constrained as shown here. The first term corresponds to the objectives and the second term to the constraints. Lambda is the factor that balances the optimization of the objectives versus the satisfaction of the constraints. Each objectve and each constraint is assigned a weight (delta and epsilon, respectively) that indicates our expectation of which factor influence the most the solution or which objectives we value the most. Alvarez, Pereyra, Carcione

Objectives and constraints Objectives (to minimize): total distance to adjust the ray emergence positions total number of sources receiver- and source-line cut Constraints: Equipment availability Minimum fold (trace density) Maximum-minimum offset (MMO) Aspect ratio The objectives I used here are total distance moved by the rays, which is a measure of the uniformity of the subsurface illumination. the total number of sources which is a measure of the cost of the survey and the total receiver and source line cut which may also influence the cost of the survey. The constraints are of two types: logistic, represented by the equipment availability and geophysical represented by the minimum fold, the aspect ratio and in this particular case the maximum minimum offset. Alvarez, Pereyra, Carcione

Splitting the survey area 10 km Shallow zone: depths <400 m (<5 km2) Mid zone: depths (400,700) m (<10 km2) Deep zone: depths >700 m (>85 km2) To actually do the opimization I used the emergence positions of the normal rays to subdivide the survey area into three zones. Zone 1 corresponds to target depths less than 400 m, the second zone to target depths between 400 and 700 meters and the third zone to target depths greater that 700 m. Acquisition within the red rectangle will be done with dense parameters, within the green rectangle with less dense parameters and in the rest of the are with sparse parameters. Alvarez, Pereyra, Carcione

Shallow zone Weights-objectives Weights-constraints δ1 Illumination δ2 Sources δ3 Line-cut ε1 MMO ε2 Channels ε3 A-ratio Fold 0.7 0.25 0.05 0.4 0.2 0.1 C1 C2 C3 C4 < 400 2000,3000,5000 1-3 24-36 These are the relative weights that I used for each of the objectives and the constraints in each zone. The detail of the numbers is probably not too important, but notice that they are different in each zone. Alvarez, Pereyra, Carcione

Results for shallow zone 320 m 180 m X X X X X X 20 m 9 shots Max offset xline=1070 m Max offset inline=1590 m Shot density: 156 shots/km2 Aspect ratio: ~1.5 Number of channels/line: 160 Fold: 30 (5x6) Number of receiver lines: 12 In the first zone the basic template consists of 12 receiver lines. The maximum offset inline is 1590 m, which is short, but corresponds to the area where the target is shallow. The maximum crossline offset is 1070. The source and receiver line intervals are 320 m and 180 m respectively. The receiver and shot intervals are 20 m and the salvo consists of 9 shots. The fold is 5x6, the aspect ratio is 1.5 and the shot density is 156 Alvarez, Pereyra, Carcione

Mid zone Weights-objectives Weights-constraints δ1 Illumination δ2 Sources δ3 Line-cut ε1 MMO ε2 Channels ε3 A-ratio Fold 0.6 0.3 0.1 0.2 C1 C2 C3 C4 2000,3000,5000 1-3 24-36 These are the relative weights that I used for each of the objectives and the constraints in each zone. The detail of the numbers is probably not too important, but notice that they are different in each zone. Alvarez, Pereyra, Carcione

Results for mid zone 440 m 360 m X X X X X X 20 m 18 shots Max offset xline=1790 m Max offset inline=2640 m Shot density: 114 shots/km2 Aspect ratio: ~1.5 Number of channels/line: 260 Fold: 30 (6x5) Number of receiver lines: 10 In zone 2 the maximum offset inline is now 2640 m, the maximum offset xline is 1790 m and the source and receiver line intervals are 440 m and 360 m respectively. The source and receiver intervals are still 20 m but the salvo is now 18 shots. Notice that the fold is again 30, the aspec ratio is still 1.5 but the density of shots is only 114. Alvarez, Pereyra, Carcione

Deep zone Weights-objectives Weights-constraints δ1 Illumination δ2 Sources δ3 Line-cut ε1 MMO ε2 Channels ε3 A-ratio Fold 0.6 0.3 0.1 0.4 0.2 C1 C2 C3 C4 2000,3000,5000 1-2 24-32 These are the relative weights that I used for each of the objectives and the constraints in each zone. The detail of the numbers is probably not too important, but notice that they are different in each zone. Alvarez, Pereyra, Carcione

Results for deep zone 720 m X X X X X X 20 m 36 shots Max offset xline=3590 m Max offset inline=3590 m Shot density: 70 shots/km2 Aspect ratio: ~1 Number of channels/line: 360 Fold: 25 (5x5) Number of receiver lines: 10 Finally, in zone 3 the maximum offset inline is equal to the maximum offset crossline and is 3590 m, which is O.K. because this corresponds to the area where the target is deep. The source and receiver line intervals are 720 m and the salvo is now 36 shots. The fold is 25, very close to the original 24. The aspect ratio is 1 and the shot density is only 70. Alvarez, Pereyra, Carcione

Summary of optimum geometry Zone dr ds drl dsl nrl Shallow 20 180 320 12 Mid 360 440 10 Deep 720 drl: receiver-line distance dsl: source-line distance nrl: number of receiver-lines dr: receiver interval ds: source interval This table summarizes the main parameters for the three zones Alvarez, Pereyra, Carcione

Stats of optimum geometries Zone Fold Aspect ratio Maxmin offset Source density 1 5x6 1.5 (1590,1070) 156 2 6x5 (1790,2630) 114 3 5x5 1.0 (3590,3590) 70 Alvarez, Pereyra, Carcione

A look at the logistics Logistics are not compromised because: for each source (salvo) the receiver template is standard orthogonal, the receiver-line interval in zone 2 is half that in zone 3 and in zone 1 is half that in zone 2, the sources are along continuous lines as usual. The standard approach to 3-D design can be summarized as an effort to keep the same parameters for all the survey area, again, irrespective of changes in the subsurface. As a result, compromises must be usually made between economic and logistic considerations on one hand and geophysical requirements on the other hand. Alvarez, Pereyra, Carcione

The bottom line The geometry is locally optimum from the illumination point of view. The average source density is about half than with the standard approach. Logistics are not compromised. The bottom line is that not only was the design optimized for illumination, given the restriction of the orthogonal geometry, but we did that with less than half the source density required by the standard approach. Alvarez, Pereyra, Carcione

Additional remarks 1. We emphasized reflector depth, but we can also use reflector dip, curvature, etc. 2. Different geometries may be combined to form the final geometry. 3. Can estimate the local acquisition effort. This will help in dealing with surface obstacles. Let mention quickly some other points that I believe are important in my strategy; I used depth as the discriminating factor, but dip, velocities, fracture trends, etc could also be used. Different geoemtries may be combined to form the resulting geometry We can compute an acquisition effort map that can be used in dealing with surface obstacles Speacking of obstacles, surface maps can be used at the design stage to constrain the positions of sources and receivers. 4. Surface maps should be used at the design stage to further constrain the position of sources and receivers. Alvarez, Pereyra, Carcione

Conclusions The standard seismic survey design is too rigid because of the assumption that the subsurface is featureless. Relaxing this assumption allows the design to be flexible, illumination based, locally optimum in terms of the required acquisition effort. In conclusion, the standard design is too rigid because it knows nothing about the subsurface. Relaxing this assumption allows the design to be more flexible, illumination-based and locally optimum. Alvarez, Pereyra, Carcione

Thank you for your attention. I will be happy to entertain your questions. Thank you very much for your attention. Alvarez, Pereyra, Carcione

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