Viability of Using Seismic Data to Predict Hydrogeological Parameters

Ken Mela

Truckee Meadows Community College, 4001 S. Virginia St., Reno, Nev. 89502

Presented at SAGEEP '97, Reno/Sparks, Nevada

ABSTRACT

Design of modern contaminant mitigation and fluid extraction projects make use of solutions from stochastic hydrogelogic models. These models rely heavily on the hydraulic parameters of hydraulic conductivity and the correlation length of hydraulic conductivity. Reliable values of these parameters must be acquired to successfully predict flow of fluids through the aquifer of interest. An inexpensive method of acquiring these parameters by use of seismic reflection surveying would be beneficial. Relationships between seismic velocity and porosity together with empirical observations relating porosity to permeability may lead to a method of extracting the correlation length of hydraulic conductivity from shallow high resolution seismic data making the use of inexpensive high density data sets commonplace for these studies.

INTRODUCTION

Traditional methods of predicting aquifer hydrogeologic parameters of hydraulic conductivity and the correlation length of hydraulic conductivity have required costly techniques involving direct physical contact with the aquifer of interest. Development of a remote sensing tool that could reliably predict these properties would dramatically reduce costs involved in hydrogeologic studies. Benefits would include not only reduced costs but a greater density of data.

Seismic data has long been used in the petroleum industry to predict reservoir characteristics for development of oil and gas fields as well as exploration. Seismic inversion techniques have proven successful in predicting porosity zones at considerably greater depths than the common hydrogeologic study. (Lindseth, 1979) The analysis of high resolution, shallow seismic data in a similar fashion should produce similar results. The accurate prediction of these parameters will benefit the modeling studies used for fluid extraction and contaminant mitigation projects.

As early as 1950 petroleum industry researchers recognized that within lithologically consistent stratigraphic units (all clastics or all carbonates) porosity could be used to predict permeability within field scale areas of interest. (Wylie and Rose, 1950) These methods have been applied with some success in the petroleum industry. (Schlumberger, 1972a,b) This relationship between porosity and permeability leads to the proposed derivation of hydraulic conductivity and correlation length of hydraulic conductivity from seismic reflectivity. We therefore see that seismic reflectivities can be used to estimate acoustic impedances, which estimate seismic velocities, which estimate porosities, resulting in estimated permeabilities. This is the route we wish to examine.

THE METHOD

Standard seismic CMP seismic data processed to retain true relative amplitude information can be used to estimate velocity data. Inversion processing such as this relies on the relationship:
r = ( rho2 v2 - rho1 v1 )/( rho2 v2 + rho1 v1 ) 1)
and the empirical relationship
rho = ( v - 3460 )/( 0.308 v ) 2)
where density is measured in grams per cubic centimeter and velocity is measured in feet per second.

Velocity data extracted in this fashion has been used as a reliable indicator of porosity (Lindseth, 1979). Absolute values of porosity has been derived from velocities measured by sonic logs using the relationship:

phi = (1/v0 - 1/vm)/(1/vf - 1/vm) 3)
where v0 is seismic velocity, vf is velocity of the fluid and vm is matrix velocity.

Porosity values extracted in this manner can be used as predictors of permeability by using the relationship:

sqrt(k) = C phi^3/sw 4)
where k is permability, phi is porosity, sw is irreducible water saturation, and C is an empirical constant after Schlumberger (1972a,b).

Permeability can then be converted to hydraulic conductivity using:

K = k rho g/mu 5)
where K is hydraulic conductivity, rho is density, g is gravitational acceleration, and mu is viscosity of the fluid.

So combining equations 3,4 and 5 seismic velocity derived from equation 1 can be related directly to hydraulic conductivity by:

v0 = vm/(M K^(1/6) + 1 6)
where the constant M is determined by:
M = (mu/(rho g))^(1/6) (sw/C)^(1/3) (vm/vf -1) 7)
These estimates will directly relate seismic velocities to hydraulic conductivities at the outcrop as discussed in subsequent sections.

Within an aquifer on a field sized scale an absolute value for hydraulic conductivity can therefore determined dependant only on parameters that can be expected to be reasonably consistent and one parameter that will vary inversely with hydraulic conductivity.

While direct prediction of absolute values of hydraulic conductivity from seismic data may be difficult due to the presence of the empirical constant C in equations 3 and 6, it should be noted that values for M and vm can be expected to be reasonably constant for a given aquifer on a field sized scale. This absence of great horizontal variation of these parameters within the aquifer of interest may allow extraction of a meaningful correlation length of an aquifer from reflection seismic data. This correlation length may be related to the correlation length of hydraulic conductivity and may be extracted by use of semivariograms. This correlation length of hydraulic conductivity is useful in predicting the dispersivity used in stochastic contaminant transport and flow models (Gelhar et al, 1979).

Correlation length and fractal dimension have been successfully extracted from seismic data from deep crustal reflectors (Pullammanappallil et al., 1996). Recent studies have also established the relationship between horizontal reflectivity correlation length and correlation length of subsurface velocity variations (Levander et al, 1994). Similar techniques are being applied for extracting correlation length from the data examined in this study.

THE FIELD DATA

In July 1996 high resolution seismic data was acquired on a bench of an open pit diatomite mine owned by Eagle Picher near Hazen, Nevada (some 40 miles east of Reno) A Bison 9000 12 channel recording system was used to record nominally 24 fold data with a 3 lb. single jack striking a steel milling ball for a source with 10 summed strikes per record. Twelve foreshot and twelve backshot records at varying offsets were acquired for each geophone setup to achieve 24 fold duplicity. Four lines were acquired, one for a length of 144 feet parallel to the exposed face of the pit at a distance of approximately 50 feet and three lines transverse to the face and the first line, tieing the first line and ending at the face. (fig. 1) From this geometry a reflector from the face can be identified from the transverse lines. A panel of raw data arranged to emulate a VSP shows the reflector (fig. 2).

The parallel line utilized 2 foot geophone spacing and 2 foot source spacing. Geophone setups were recorded into with 12 foreshots and 12 backshots then ``moved along'' 6 stations and the process repeated. Transverse lines were acquired using 1 foot geophone spacing and 2 foot source spacing with sources recorded for the entire distance of the line to an offset of 6 feet from the near geophone.


Fig. 2. A panel of raw data extracted from a transverse line and arranged to emulate a VSP

DATA PROCESSING

Standard CMP data processing will be applied to all four lines. This will result in a standard section for the parallel line with the three transverse lines emulating multifold VSPs. From the three transverse lines, the reflector from the face will be identified. Seismic inversion processing will be applied to the parallel line. A window will be applied to extract data from the reflector of interest which will be the input to a program that will construct semivariograms (Carr, 1995) from several locations. Correlation length for the data will be determined from the semivariogram results. In addition predictions for absolute values (in terms of the factor M discussed above) will be extracted along the length of the reflector. These values can later be checked against permeability values that can be acquired along the length of the face with a permeameter. Both absolute hydraulic conductivity and correlation length can be examined in this fashion.

FUTURE WORK

Direct measurements of permeability, matrix velocity, and irreducible water saturation from the face of the bench will test the validity of determining values of hydraulic conductivity and correlation length determined utilizing this method. With these data gathered not only at this location, but several locations, values for the empirical constant C of equation 3 can be gathered and used in similar studies. Continued use may result in cataloguing of useful values for this constant that may be used in calculating absolute values of hydraulic conductivity in these areas.

SUMMARY

Analysis of high resolution seismic data may lead to useful techniques for determining both absolute values and correlation length of hydraulic conductivity for field sized hydrogeologic studies. Previous work in the petroleum industry demonstrates relationships between seismic velocity and porosity. An empirical relationship between porosity and permeability has also been recognized. While the relationship between porosity and permeability relies on an empirical constant, continued experience with applying these techniques may establish reliable values for this constant for field wide studies.

While predicting absolute values of hydraulic conductivity utilizing these methods will require experience in application of this empirical constant, prediction of correlation length of hydraulic conductivity is independent of the value of this constant and can be confirmed directly by measuring permeability values of the bench face on location and extracting the correlation length from these data.

Establishing the relationship of these hydrogeologic parameters from this study and others will advance the utilization of inexpensive seismic methods to supply these parameters for future hydrogeologic studies.

BIBLIOGRAPHY

Carr, James R., 1995, Numerical Analysis for the Geological Sciences: Englewood Cliffs, NJ, Prentice Hall, 592 pp.

Gelhar, Lynn W., Gutjahr, Allan L., and Naff, Richard L., 1979, Stochastic Analysis of Macrodispersion in a Stratified Aquifer: Water Resources Research, 15, 6, pp. 1387-1397

Levander, Alan R., Hobbs, R.W., Smith, S.K., England, R.W., Snyder, D.B., and Hollinger, K., 1994, The Crust as a Heterogeneous ``Optical'' Medium, or ``Crocodiles in the Mist'': Tectonophysics, 232, pp. 281-297

Lindseth, Roy O., 1979, Synthetic Sonic Logs - A Process for Stratigraphic Interpretation: Geophysics, 44, pp. 3-26.

Pullammanappallil, S.K., Levander, A., and Larkin, Steven, P., 1996, Estimation of Crustal Stochastic Parameters from Seismic Exploration Data: submitted to Jour. of Geophys. Research - July 1996

Schlumberger, Inc., 1972a, Log Interpretation, Charts: Houston.

Schlumberger, Inc., 1972b, Log Interpretation, Vol. 1 - Principles: Houston.

Wyllie, M.R.J., and Rose, W.D., 1950, Some Theoretical Considerations Related to the Quantitative Evaluation of the Physical Characteristics of Reservoir Rock from Electrical Log Data: Jour. Petrol. Technol., 2, pp. 105-118