Volume 38 April 1973

GEOPHYSICS

Number 2

SEISMIC REFRACTION MODELING BY COMPUTERi

J;\MES H. SCOTT*

A computer program has been developed by the U.S. Bureau of Mines for designing a two-dimen- sional, layered earth model as an aid in interpret- ing seismic refraction field measurements. The program requires input data consisting of shot- point and geophone locations, refraction travel- times, and identification of the refraction layer associated with each traveltime. In the program, a first approximation model is generated by a computer adaptation of the delay-time method,

INTRODUCTION

Seismic refraction techniques have been used for many years to map rock layers of interest in problems associated with petroleum exploration, mining, civil engineering, and deep crustal studies. .4 good collection of papers tracing the develop- ment of the technique and presenting various applications has been assembled by Musgrave (1967). Specific discussions of mining applications have been made by Bacon (1966) and Hobson (1970). However, the use of the technique in min- ing applications has been limited by problems such as shortage of access roads, rugged terrain, complex layering, and steep dip, all of which con- tribute to the complexity of making surveys and interpreting results. Many conventional inter- pretation procedures make use of simplifying assumptions and short-cut graphical techniques that cannot be applied with accuracy in mining

followed by a series of improved approximations that are made by use of a ray-tracing procedure. The final result of the program is a model designed to minimize the discrepancy between field- measured traveltimes and computed traveltimes of rays traced through the model. Test applica- tions indicate that the accuracy of interpretation is improved, and that time and effort of the pro- fessional interpreter are greatly reduced by use of the computer technique.

areas with complex multiple layering. The rigor- ous approach, on the other hand, is impractical because it takes too long and is too monotonous for most geophysicists to endure when calcula- tions are performed by hand.

The modeling technique described in this report was developed by the Bureau of Mines in an effort to overcome these interpretational problems. A computer is used to relieve the interpreter of the drudgery of rigorous interpretation and to im- prove the accuracy of the end result by using a ray-tracing procedure to develop a layered earth model that is consistent with field measurement data. Use of the technique gives the interpreter more time to devote to the more interesting and important geologic aspects of seismic refraction interpretation.

Because the details of the computer program have been described by Scott, Tibbetts, and

t Presented at the 41st Annual International SEG Meeting,. November 9, 1971, Houston, Texas. Manuscript re- ceived by the Editor May 15, 1972; revised manuscript received August 21, 1972.

* U.S. Bureau of Mines, Denver, Colorado 80225.

@ 1973 Society of Exploration Geophysicists. All rights reserved.

271

272 Scott

Burdick (1972), the discussion in this paper is limited to general considerations and highlights.

BACKGROUND AND GENERAL APPROACH

The Bureau of Mines developed the computer modeling technique from a modest beginning a few years ago. Because of difficulties associated \vith graphical and desk calculator analysis of seismic refraction data from mining areas with complex multiple layering, an initial effort was made to develop a computer program to perform the calculations by the delay-time method as described by Pakiser and Black (1957). In de- veloping and testing the program, the accurate migration of depth points presented a problem for steeply dipping horizons commonly found in mining areas. To solve this problem, a ray-tracing procedure was added to the computer program to test and correct the estimated migrated position of points representing the locations of ray entry and emergence from the refracting horizon. The ray-tracing procedure took into account the dip of the refracting horizon at the points of ray entry and emergence. The position of the refracting horizon was defined by a series of linked straight- line segments fitted to the points by an averaging and smoothing procedure. Experience with the computer technique indicated that two iterations of ray tracing for each refraction horizon were desirable in converging on a solution in geologi- cally complex areas. With additional use of the program, it was noted that small unavoidable errors often occurred in delineating the base of the near-surface layer, and that these errors were transferred to deeper horizons with magnification because of the increase of layer velocity with layer depth. Subsequently, an error recognition and correction routine was added to the program to adjust the base of the near-surface layer so that these correlated errors in deeper layers would be reduced. After this adjustment was made, one final iteration of ray tracing was added for each refraction horizon beneath the base of the near- surface layer.

Several recent papers have described computer ray-tracing techniques for reflection modeling, velocity computation, and ground-motion esti- mates (Jackson, 1970; Taner et al, 1970; Yacoub et al, 1970j. The refraction ray-tracing and model- ing technique described in this report is unique in that the computer not only simulates ray propa- gation through the model, but it also designs and

adjusts the model itself by using field-measured refraction arrival times as the basic source of in- formation.

BASIC ASSUMPTIONS AND LIMITATIONS

The computer modeling technique is based on the following assumptions. The model is assumed to consist of layers that are continuous and extend from one end to the other of the refraction surve) line. Although layer velocity is assumed to in- crease with layer depth, the “vertical” velocit) associated with slant rays traveling through the layer may be assigned a different value from that of the “horizontal” velocity of critically refracted rays traveling along the interface between two layers, so that, to some degree, velocity anisotropy may be taken into account.

The present program is limited to handling a maximum of 5 layers and 3 inline spreads with up to 7 shotpoints and 48 geophones per spread. These limits can be extended with some sacrifice to computer time if sufficient computer storage space is available. Before a complete depth analy- sis can be made by the computer, the interpreter must identify the refraction layer that is associ- ated with each traveltime. Layers are numbered, starting with layer 1 nearest the surface, and the appropriate number is punched alongside each traveltime entered on a data card. Xumber one indicates a direct arrival through layer 1, number two indicates a refraction along the upper surface of layer 2, and so on, down to the deepest layer.

COMPUTER PROGRAM

The general logical structure of the computer program is described in the following section with emphasis on applications and examples of results.

First the computer reads and stores the input information for a problem. By selecting the exit-0 option of the program, the user may obtain a time-distance printer plot of the observed travel- times for verification of the input data and for making a preliminary appraisal of velocities and layering. An example of such a time-distance plot is given in Figure 1. The figures shows arrival times from shotpoints A, C, and B which are located respectively at the left end, center, and right end of the geophone spread, and from SP L which is offset 629 ft to the left of SP A in line with the spread. Because SP L is far from the spread, its location is not plotted on any of the

Refraction Modeling 273

FIG. 1. Example of program exit 0, showing printer plot of time-distance graph of observed traveltimes.

travekime graphs or depth cross-sections that shotpoint-geophone distances. After the surface follow. layer velocity has been established, the program

Next the program estimates the velocity of the computes an elevation time correction that refers surface layer by averaging the velocities indicated by direct-arrival traveltimes and corresponding

each refraction arrival traveltime to a sloping datum plane represented by a straight line that is

274 Scott

fitted, by the method of least squares, through the improvement in the smoothing of the data the geophone positions. Another time-distance pojnts by comparing Figure 2 with Figure 1. plot with this correction applied can be obtained The refraction velocities of all layers beneath by selecting the exit-l option of the program. An the surface layer are then estimated by a least- example of this plot is given in Figure 2. Notice squares method developed by the Geological Sur-

FIG. 2. Example of program exit 1, showing printer plot of time-distance graph with datum correction applied.

Refraction Modeling 275

vey of Canada (Hobson and Overton, personal communication, 1968). The estimate is made by use of the following formula:

v= BAx; - (ZA&z

ZA.riAti - (ZAxi)(ZAri)/n ’

where V is the desired refraction velocity, Axi is the difference between distances to geophone i from two opposing shotpoints (one on each end of a spread of geophones), At; is the corresponding difference between traveltimes to geophone i from the same two opposing shotpoints, and n is the number of geophones over which the summations are made. To satisfy validity requirements of the method, the traveltimes that are used in the for- mula must represent rays from opposing shot- points that follow the same refraction horizon to a specified geophone.

With the refraction velocity of the deeper lay- ers established, the program next estimates the position of the base of the surface layer by a com- puter adaptation of the delay-time method. De- lay-time depth points are computed for each geo- phone receiving refraction arrivals that represent rays traveling along the interface between layer 1 and layer 2. If more than one depth point is avail- able at a geophone, the depth values are averaged and assigned to a position directly beneath each geophone. For geophones where no refraction in- formation is available, depth points are inter- polated or extrapolated from available points nearby. The position of the base of layer 1 is thus estimated and is represented by a series of straight-line segments connecting points beneath geophones.

The initial depth estimate made by the delay- time method is then tested for validity by a ray- tracing procedure that uses straight-line segments to represent rays. Starting from the delay-time depth points previously established, rays are traced upward to each target geophone from the refracting horizon. The direction of each ray is established from Snell’s law and from considera- tion of the dip of the segmented line representing the refraction horizon at the point of emergence. In a similar manner, rays are traced upward from the points of entry into the refraction horizon to the positions of the explosive charges at the shot- points. The starting points of rays missing the target geophones or shotpoints by more than a

half foot are adjusted, and the rays are retraced iteratively until an accurate position can be established by interpolation. This seldom requires more than two iterations per ray for the first refraction interface (base of layer 1). With the slant ray segment end points thus defined, the total traveltime of the ray from shotpoint to geophone can be computed by adding the timefor ray travel along the horizontal segment to traveltimes for the vertical (slant) segments. Errors resulting from the assumption that all ray segments are straight lines are usually much smaller than errors associated with field data and, therefore, are considered negligible. The traveltimes associated with ray segments are calculated by dividing the ray-segment lengths b) the appropriate velocities. The computed ray traveltimes are then compared with corresponding field-measured traveltimes, and the estimated points of entry and emergence of each ray are adjusted upward or downward to absorb the dis- crepancy, forcing the computed time to be equal to the measured time When this adjustment has been completed for all geophones, new points are established to define the horizon beneath each geophone by averaging or by interpolating avail- able depth points. Experience has ;ndicated that, for the base of layer 1, this second estimate of the position of the refracting horizon is quite accurate and cannot generally be improved by additional iterations of ray tracing and model adjustment.

With the base of layer 1 thus defined, the pro- gram proceeds to strip it away by subtracting the slant-ray-segment times from refraction arrivals representing deeper layers. When this is com- pleted, the user can obtain a plot of the time- distance graph with layer 1 removed by selecting the exit-2 option of the program. The result, an example of which is given in Figure 3, shows addi- tional smoothing because velocity and depth irregularities associated with the surface layer are removed.

This graph is especially helpful to the inter- preter in checking whether he has assigned the correct layer number to traveltimes representing horizons beneath the base of layer 1.

If exit 2 is not selected, the program proceeds to establish the position of deeper refraction hori- zons. With layer 1 removed, the delay-time tech- nique is used again to obtain a first approximation of the base of layer 2. Coordinates are computed for the lower end points of the slant segments of

276 Scott

FIG. 3. Example of program exit 2, showing printer plot of time-distance graph with layer 1 removed.

rays in layer 2. To smooth the scatter of these position of the refracting horizon. For additional

points, the average of the coordinates of points smoothing, a new segmented line is formed by

falling between adjacent geophones is computed. connecting the intersections of each of the line ‘I’hcn the computer connects these average coordi- segments with vertical lines projected downward 11x11~ \rith a sc~grnc~nl~~l line that. apprc~ximates tll(s from tach geophonr Iocatio~~. At this point in the

Refraction Modeling

program the delay-time approximation of the position of the base of layer 2 is considered to be complete.

Xext, the position of the base of layer 2 is tested by tracing rays, computing their traveltimes, and

comparing them with field-measured traveltimes, just as was done for the base of layer 1. The positions of the computed ray end points are adjusted to absorb the discrepancy between com- puted and measured traveltimes, and a segmented

277

278 Scott

FIG. 5. Example of program exit 4, showing printer plot cross-section computed by delay-time approximation followed by one iteration of ray tracing and adjustment.

line is fitted to the points by the averaging and and smoothing are desirable for establishing the smoothing procedure described in the previous position of each interface. Because tests have paragraph. For the base of layer 2 and all deeper indicated that the position generally remains layers, experience has indicated that two sequen- stable after the second pass, additional iterations tial passes of ray tracing, adjustment, averaging, are not considered worthwhile.

After I this operation has been completed for the made of the base oi layer 1. This adjustment is base of layer 2, the same procedure is used to de- needed to remove the effects of small errors in the fine the ! base of layer 3 and then the base of layer position of this shallow horizon that are trans- 4. Whe ‘n computation for the deepest refraction ferred to deeper interfaces with magnification be- horizon has been completed, a final adjustment is cause of increased velocity with depth. Such

Refraction Modeling 279

. ..^._ .“ .^._ . . . _ . “.I..._“.~ . . . . . . . . . . . ____.

FIG. 6. Example of program exit 5, showing printer plot cross-section computed by delay-time approximation followed by two iterations of ray tracing and adjustment.

FIG. 7. Example of program exit 6, showing printer plot cross-section computed by delay-time approximation followed by two iterations of ray tracing, then correction of base of layer 1 for correlated errors, and one final iteration of ray tracing.

+rrors may be caused by record-picking irlaccura- able. The effect of an error in the positioI1 of tht. ties, erroneous assignment of layer numbers to shallow horizon is that all points of ray emergency refraction arrival times, or by missing data at from deeper refracting horizons xi11 be either too some geophones, requiring interpolation of depths shallow or too deep, causing a pattern of corre- from nearby locations where information is avail- lated anomalies to appear on the segmented lines

281

ELEY HO912 TI’E POINT 1 POICT * SP”OS LX!’ LAYERS VCAQOS FT/COL FTlROlr NS/COL ELEV x POS ELEV I PO5 SLOPE IYTCPT __e-- -___ ____-- --_-__ -___-_ -_-_-- _**-e- *-we-- --___- -----s ___*__ ______ ____--

I -6 (1 4 2.5 8.3 1.5 0.0 0.0 0.0 n-0 0.0000 0.0

VELOCllV CAROS

SP.QEAO s, 4 SHOTPOINTS~ I2 GEO~UOYESr ISHIFT . b75.0

SP ELEV x LOC I LOC OEPTM UPHOLE 1 cUDGC 1 END SP __ --_____ ______-- ____.s-_ _______I __--11_1 w_.--.-. .-.-II__

L 2986.9 -704.&l 0.0

A 2PV.S.7 -75.0 0.0 c 2511.7 2'5.0 0.0

0 2549.9 563.0 0.0

2.0

2.0 2.0 :.0

4SRIV.L

92.0 4 ¶b.O . 89.0 . 96.0 4 99.0 . PP.5 4

107.0 a 107.0 a 109.0 l

113.0 4 116.5 4 119.0 4

0.0 0.0 0.0 0.0 0.0 0.0 a.0 0.0

TlycS l FUDGE 1 by0

27.5 2 65.0 3

27.S 2 37.0 2 ::': l :

a.5 2 40.0 2 56.0 2 30.0 2

57.0 4 19.0 2 62.0 6 20.0 2

64.5 6 30.0 2 65.0 6 39.0 2 70.0 0 50.0 2 70.0 4 55.0 3 77.0 4 Lo.0 3

0 0 0 0

c*vtns RECREEIEMTEO

FIG. 8. Example of page 1 of tabular printout (input data) for program exit 6.

that define the deeper horizons. The program detects these correlated errors and repositions the base of layer 1 beneath the geophone in question so that the anomalies are minimized. After this step is completed, the program goes through one final pass of ray tracing and adjustment for each layer beneath layer 1, starting with the base layer 2 and moving downward. This completes the com- putational part of the program, after which results are printed in table and graphical form.

Several intermediate optional exits are avail- able in the depth computation part of the pro- gram. The first one is exit 3, which limits the computation to the delay-time approximation and prints the results in tabular and graphical form after computations are completed for all layers. Figure 4 shows an example of the printed depth cross-section for this option.

Exit 4 limits computation to the delay-time approximation, followed by only one iteration of ray tracing and adjustment for each layer. An

example of the resulting cross-section printer plot is shown in Figure 5.

Figure 6 gives simikdr results for exit 5, which limits the computation to two iterations of ray tracing and adjustment after the delay-time approximation is made for each layer.

Figure 7 shows the results of a full computation obtained by selecting exit 6, which includes the delay-time approximation, two iterations of ray tracing, and adjustment followed by correlated error correction of the base of layer 1, and termi- nated by one final iteration of ray tracing and adjustment for each layer.

It is interesting to note that the degree of scat- ter of refraction ray end points (indicated b> capital letters on the cross-sections) decreases as the program progresses from the delay-time first

. . approxtmatlon through the successive iterations of ray tracing and adjustment illustrated in Figures 4-7.

Figures 8-10 give the tabular printout that

282 Scott

POS fLEV

sp L SP 4 SP c sp 0 .-I_--__ * ‘_“““L’ .._“.‘.L’ “““_.L

b23.3 0 bb9.b 2 735.7 3 735.9 4 2381.2 2QV3.1 2426.3 2393.1

2 POS 000.0 4 723.3 2 780.5 3 773.3 4 ELEV 2385.3 2’93.5 2~33.1 2399.2

3 POS 739.2 4 772.5 2 828.0 3 931.1 4 ECEV 2397.0 2092.2 2442.2 2ao2. L

4 POS 787.4 4 819.3 2 831.0 2 879.7 4 CLEV 2302.0 2Q88.l 2~85.3 2307.9

5 POS 835.8 4 873.0 2 880.0 2 959.5 P

ELEV 2391.5 2aV2.8 ZPVO..$ 2308.0

6 PUS 091.7 4 881.3 P 929.3 2 1006.3 4 ELEV 2005.8 2405.3 2047.0 2P22.8

7 PO5 ELEV

VQl.0 a 2POO.2

942.7 4 972.2 2

24ozt7 24VV,*

1012.9 Q 1021.b 2 2426.0 2501.3

1051.2 0 2430.7

a POS

ELEV 1013.0 4 2427.3

1089.4 4 2006.0

V POS 1065.3 4 1066.2 Q 1071.3 2 1118.1 4 ELEV 2uaV.8 2052,3 2503.7 2467.6

10 POS 1115.3 4 lllb.2 0 1121.4 2 1161.6 4 ELEV 2463.4 2465.9 2508.3 2482.3

11 POS 1172.2 4 1172.1 4 1165.9 3 1182.3 2 ELEV 24A8.5 2488.1 2PV8.2 2514.3

12 Pas llVV,7 4 1198.3 4 1193.5 3 0.0 1 ELEV 250b.2 2502.9 2505.0 0.0

QAY fXD POINTS t3ENEbTH

L.2 RIWT POS 0.0 boo.7 952.9 0.0 .ILE” 010 2494.1 2498.8 0.0

0.0 0.0 V4b.V 1230.0 0.0 0.0 2998.1 25il7.0

0.0 0.0 VVV.3 0.0 0.9 0.0 2058.6 0.0

La3 Ccr?... PO5 0.0 0.0 921.7 0.0 ELtV 0.0 0.0 2452.1 0.0

5b5.1 bP4.5 238R.V 2389.5

J.3 O,T

0.0 0.0

0.0 0.0

0.r) 0.0

0.0 0.0

l22a.o 2~03.7

FIG. 9. Example of page 2 of tabular printout (refraction ray end points) for program exit 6.

=.P s-e

I

C

B

CEO s-v

1

2

3

a

5

6

7

.3

9

10

11

12

POs~rInr. SjRF tLEV _-___--_ __----_.-

roe.: 2‘198.’

95o.c 2511.7

1238.0 25a9.9

.iAvER 2 LLYER 3

DEPTM ELEV !JEPTr( ELEV ______.__I____ _1_---__1.---_

a.6 24.94, I 91.4 2007.3

13.2 2498.5 55.7 2956.0

32.1 2517.0 37.2 2512.1

116.2 23L2.5

105.5 2901.2

13.0 2506.5

075. p 2513.2 27.1 2993.1 93.1 2420. i 123.9 2309.3

725.~ 2500.3 6.a 2093.5 71.7 2028.6 100.5 2393.0

775.c, 2500.5 8.3 2092.7 69.0 2431.1 100.6 2395.9

825.~ 2>02.Y 15.7 2P86.7 6a.a 2938.0 105.4 2397.0

P75.P 2505.9 la.1 2P91.8 60.3 2005.b 103.7 2002.2

925.4 2509.6 12.6 2497.0 57.2 2452.a 108.a 2001.2

975.0 2513.7 13.9 2499.0 54.1 2159.6 102.5 tall.2

ln25.0 2517.4 16.1 2501.3 or.9 2469.5 16.5 2430.9

1075.0 2520.7 17.0 2503.7 35.5 2ae1.9 71.7 2aa9.0

1125.~ 2529.3 21.0 25013.3 35.0 2493.3 62.0 2067.3

1175.3 2538.1 23.8 2514.3 36.1 2502.0 a8.a 2489.7

1200.0 2540.5 29.1 251s.a 38.3 2506.2 40.1 209b.a

PIG. 10. Example of page 3 of tabular printout (smoothed depth points beneath geophones and shotpoints) for program exit 6.

accompanies the printer plot of Figure 7 for pro- end points of entry and emergence

gram exit 6. Figure 9.

To illustrate the accuracy of the model, a

traveltime check is given below for the raypath DISCUSSION AND CONCLUSIONS

283

given in

from SP A to geophone 5 refracted along the top The approach and logical development of the

of layer 2. The calculations are made using ray computer program was heavily influenced by the

Coordinates of ray end points Ray-path segments -

x (W Elev. (ft) Length

(ft) Velocity (ft/sec)

time(msec)

SP A 600.0 2796.i 2.8 1520 1.8

Point of entry 600.7 2494.1 272.5 5900 46.2

Point of emergence 873.2

Geophone 5 875.0

2492.8

2505.9 13.2 1520 a.7

Total model traveltime 56.7 Observed traveltime 56.0

L)iscrepancy 0.7

284 Scott

severe migration problems associatctl \vith steep I ). Ilobson and Anthony Overton of the Canadian and erratic dips found in mining areas. In area> Geological Survey. where dips are relatively gentle and uniform, a

rather good result wmld be expected from the REFERENCES

delay-time approximation alone, or perhaps the Bacon, Lloyal O., 1966, Refraction seismic case histories

delay-time approximation follo\vcd 1,~ only one in mining geophysics, in Mining geophysics, Vol. I: Tulsa, SEG, p. 105-113.

iteration of ray tracing. Subroutines arc used for Hobson, George D., 1970, Seismic methods in mining

each separate operation in the program, so that and groundwater geophysics, in Mining and ground- water geophysics/l967: I.. LV. Morley, editor, Geo-

modification for snecial needs such as this is not logical Survey of Canada, Econ. Geol. Rep. No. 26,

tlitlicult to accomplish. p.-148-176. -

Experience \vitli the program indicates that its Jackson, I’. O., 1970, Seismic ray simulation in a spher-

ical earth: Bull. Seis. Sot. Am.. v. 60. no. 3. n. 1021- greatest benefit is in freeing the gcoph!rsicist of 1025.

the drudgery of hand computation, thus, giving Alusgrave, Albert W., editor, 1967, Seismic refraction

him more time to spend on geologic aspects of prospecting: Tulsa, SEG, 604 p.

I’akiser, I,. C., and Black, R. A., 1957, Exploring for

interpretation, \vhile at the same time providing a ancient channels with the refraction seismograph:

much more accurate interpretation than is possi- Geophysics, v. 22, no. 1, p. 32-47.

ble by hand methods. Scott, James H., Tibbetts, Benton L:, and Burdick,

Richard G., 1972, Computer analysis of seismic re- fraction data: USBM RI. 759.5,95 p.

Taner, RI. Turhan, Cook, Ernest E., and Neidell, ACKNOWLEDGMENTS Norman S., 1970, Limitations of the reflection seis-

Several valuable ideas used in the computer mic method; lessons from computer simulations:

program, particularly in the part dealing with Geophysics,, v. 3.5, no. 4. p. 551-573.

Yacoub, Nazieh K., Scott, James H., and McKeown,

velocity computation, were suggested during dis- I‘. A., 1970, Computer ray tracing through complex

cussions and through correspondence with George geological models for ground motion studies: Geo- physics, v. 35, no. 4, p. 586-602.