THE USE OF AIRGUN PRESSURE PULSES FOR CALIBRATING A LOW-FREQUENCY STANDARD HYDROPHONE*

A new technique is developed for calibrating a low-frequency hydrophone. The technique involves the use of pressure pulses radiated by the Par 0.65 liter airgun when fired at a fixed depth but with various values of initial chamber pressure. The sensitivity of a low-frequency hydrophone, when determined by the proposed technique, is found to be in agreement with that obtained by using the so-called “impulse method”.     

COMPUTATION OF SIGNATURES OF LINEAR AIRGUN ARRAYS*

Far-field signatures from an airgun array are usually obtained by carrying out extensive field measurements. In order to decrease the need for such measurements, we have developed a method for computing signatures from linear airgun arrays where the distances between the airguns are such that the non-linear interaction among the airguns is negligible. The signature from a single airgun of a given type is computed from the following airgun parameters: airgun chamber volume, chamber pressure, airgun depth and position of the waveshape plate within the chamber. For calibration purposes, a recorded signature for one set of airgun parameters has to be provided for each type of airgun. The signatures are computed by using empirical relations between signature properties and the airgun parameters, and by treating the primary and bubble pulses separately. The far-field signature from a linear airgun array can now be computed by summation of the delayed signatures from the airguns in the array. Practical results are shown for an array with different PAR (Bolt) 1500 C airguns.     

SIGNATURE AND AMPLITUDE OF LINEAR AIRGUN ARRAYS *

During the last few years many airgun arrays have been designed with the objective of generating a short signature of high amplitude. For linear arrays of non-interacting airguns two rules have been derived that may help in the design or evaluation of airgun arrays. To achieve a short pressure pulse, the total available air volume has to be distributed over the individual guns in such a way that the tail of the signal, owing to the added bubble signals, becomes as flat as possible. When we think of ordering airguns according to volume, this flat signal tail can be achieved by designing the volumes such that the difference in bubble times of two adjacent guns is proportional to their volume to the power 2/3. The amplitude expected from a linear array of non-interacting airguns is limited by the physical length of the array. A graph of measured values tends to confirm this relation. No relation has been found between the total volume of an array and its amplitude. The graph also detects inefficient use of available array length of existing arrays.     

LOW-FREQUENCY STANDARD HYDROPHONE * FOR CALIBRATING LINE HYDROPHONE ARRAYS (SEISMIC STREAMERS) AND MARINE SEISMIC SOURCES **

The design of a standard hydrophone with a maximally flat (Butterworth) response in the frequency range 8.0 Hz-1.0 kHz is described. The standard hydrophone has been developed primarily for calibrating line hydrophone arrays (seismic streamers) and marine seismic sources. The standard hydrophone has been used successfully during the past eight years for monitoring the output of a single air gun. It can be used for the calibration of a marine seismic streamer.     

DOWNHOLE PERIODIC SEISMIC SOURCES*

Downhole periodic seismic sources have been proposed as a means for studying fluid zones in hydrothermal/magma systems encountered in deep scientific holes drilled as part of the Continental Scientific Drilling Program. Scientific measurements in these holes will require the use of downhole, nondestructive, high resolution, seismic tools. Downhole periodic seismic sources tested in a shallow geothermal zone showed that a pneumatic oscillator could effectively generate downhole low-frequency (10–100 Hz) seismic waves and that these waves could effectively penetrate a highly fractured formation. An improved version of these downhole sources, capable of swept-frequency operation, is currently under development. This type of downhole seismic source has applications in crustal studies and in the evaluation of petroleum, groundwater and geothermal reservoirs.     

DEVELOPMENT OF MORE EFFICIENT AIRGUN ARRAYS: THEORY AND EXPERIMENT*

Source strength of an airgun array may be increased by:

• — utilizing higher pressure,
• — increasing total array volume,
• — employing more guns,
• — improving gun efficiency.

One measure of gun efficiency is “specific source strength”, P_a*, defined as source strength per unit quantity of air used. Typical units are MPa m/l. Most developments are directed toward increasing gun pressure and/or gun volume to increase source strength of the array. These efforts require that more air compressors be installed onboard the ship. Consequently, a larger ship may be needed for the additional compressors, guns, and auxiliary equipment. A development program was initiated in 1976 to increase source strength of the array without using a larger ship. New guns were designed and built—one for 41.4 MPa and 7.37 liter (6000 p.s.i./450 in³) operation and another with 13.8 MPa and 4.92 liter (2000 p.s.i./300 in³) capability. Experiments were conducted with these new guns (and existing guns) over a range of pressures from 13.8 to 41.4 MPa (2000 to 6000 p.s.i.). Design of the new guns was aided by a mathematical model. The model relates physical dimensions of the airgun to acoustic pressure in the water. It consists of four nonlinear differential equations relating

• — shuttle motion,
• — bubble pressure,
• — chamber pressure,
• — bubble radius.

The last equation is the “free-bubble-oscillation equation” and represents the ideal case of a pressurized bubble released instantaneously in water. The three other equations modify this ideal case; the four equations together model an airgun of the type manufactured by Bolt Associates, Inc.     

TEST RESULTS OF A NEW TYPE OF EFFICIENT SMALL AIRGUN ARRAY*

Recently the author developed and demonstrated (Safar 1980) an efficient method for operating the airgun. The method involves the generation of a short seismic pulse from the pressure bubble pulses radiated by an airgun when fired several times at the same optimum depth but with different chamber pressures. The purpose of this paper is to present and discuss the test results obtained when implementing the same method using a two-dimensional airgun array. The array consists of seven 0.65 liter airguns fired simultaneously at the same depth but with different chamber pressures. It is shown that the far-field pressure pulse radiated by the seven 0.65 liter airgun array is similar to that radiated by the Flexichoc seismic source. It is concluded that the proposed airgun array can be used as a subarray to form an extremely powerful super-long array suitable for deep seismic exploration. The author would like to thank the Chairman and Board of Directors of the British Petroleum Co. Ltd for permission to publish this paper. Thanks are also due to Mike Symes and Lovell Cox for carrying out the field tests and Seismograph Service (England) Ltd for providing the airguns.     

THE SCALING OF AIRGUN ARRAYS,INCLUDING DEPTH DEPENDENCE AND INTERACTIONS*

The article provides a theoretical basis for the extension of the method of scaling law deconvolution to three dimensions using airgun arrays as a sound source. Earlier papers by the author required the dimensions of the scaled sources to be different while the depths and firing pressures were maintained the same in order to preserve the same dynamics of the scaled sources at scaled time. However, this forces the source ghost to be considered as part of the impulse response of the earth rather than as part of the downgoing source wave. And, in fact, the dynamics of the scaled sources are not the same at the same depth because the ghost reflection modulates the behaviour of the oscillating bubbles generated by the airguns, and this modulation does not scale. To force the sources to scale properly, including the ghost interaction, the larger source must be put at greater depth, where hydrostatic pressure is greater, and the initial firing pressure must be adjusted accordingly. Thus, the depth, initial firing pressure and gun volume are all variables. The interaction among guns in scaled airgun arrays also scales exactly if the geometry of an array and the depth of its deployment are scaled by the same factor.     

WAVELET SHAPING AND NOISE REDUCTION *

Approximate deconvolution by means of Wiener filters has become standard practice in seismic data-processing. It is well-known that addition of a certain percentage of noise energy to the autocorrelation of the signal wavelet leads to a filter that does not increase, or even reduces, the noise level on the seismogram. This noise addition will, in general, cause a minimum phase signal to become mixed phase. A technique is presented for the calculation of the optimum-lag shaping filter for a contaminated signal wavelet. The advantages of this method over the more conventional approach are that it needs less arithmetic operations and that it automatically gives the filter with the optimum combination of shaping performance and noise reduction.     

SEISMIC SOURCES FOR SHALLOW REFLECTION SURVEYING*

A standard seismic reflection profile was shot along a disused railway track at Onley, near Rugby, U. K. Four different seismic sources including explosives, the propane/oxygen gas-gun, the Bolt airgun, and the borehole sparker were used and compared with each other in terms of output energy, penetration and resolution. The results indicated that the resolution of the borehole airgun and the gas-gun was slightly higher than that possible with gelignite. Both these sources had an output energy which was equivalent to 30 g of gelignite. The borehole sparker was only useful for obtaining seismic information on the nearsurface weathered layer, since its output power (1 kJ) was very limited. However, McCann and McCann (1982) used a high-power sparker source (14 kJ) on the nearby Grand Union Canal for a wide angle seismic reflection survey and achieved a maximum penetration of 250 m, which is comparable with the results obtained on land with the seismic sources mentioned above. The seismic reflection profile, which was interpreted in the light of borehole information in the area and the results of McCann and McCann (1982), successfully identified the surface of the Palaeozoic rocks. The problem of detecting the presence of thin, high-velocity layers in a seismic refraction survey without the availability of other information to calibrate the seismic section is also highlighted.     

CONTINUOUS CALIBRATION OF MARINE SEISMIC SOURCES*

The success of signature deconvolution in optimizing both signal-to-noise ratio and time resolution in the seismic section depends critically upon obtaining an accurate estimate of the far-field source signature. Various deterministic estimation schemes have been proposed in recent years, most of which involve direct monitoring of source output within the water layer. As an alternative to elaborate and error-prone source monitoring schemes during data acquisition, a simple modification to any source array permits subsequent estimation of far-field signatures directly from reflected signal. The new method requires the inclusion within any chosen source array of a simple point source, the “reference” source. Initial experiments employed a water gun as the reference source, characterized by a concise implosive signature with peak-to-peak amplitude of approximately 2 bar·m within the seismic sprectrum. In operation the reference source is fired shortly before the main array (typically 2 s during initial trials) and the usual record length is extended by a similar amount. Each recorded trace then comprises two results: the subsurface response to the reference source signal followed by the response of the same subsurface to the main array. The disparities in source amplitudes and NMO differentials ensure that interference effects are negligible in the main recording. Time- or frequency-domain methods can be employed to extract the main array signature from the dual dataset or to invert this to some preferred wavelet simultaneously. As an additional benefit the reference source yields excellent high-resolution profiles of the shallow geology.     

MIGRATION IN THE PRESENCE OF NOISE*

It is shown that the so-called Kirchhoff-summation operator is of a very wide-band nature and even contains an evanescent part. As a consequence, discretization may cause serious aliasing errors, particularly for small extrapolation steps. It is proposed to use in all practical cases band-limited versions of the summation operator, the spatial cut-off frequency being determined by the spatial Fourier spectrum of the coherent noise.     

COMBINED SWEEP SIGNALS FOR CORRELATION NOISE SUPPRESSION*

Comparison of both synthetic and field data shows that considerable suppression of correlation noise can be achieved with the Combisweep technique and with the Encoded Sweep Technique. In the first technique, the spectrum is shaped by superposition of linear sweeps with different frequency range; in the second technique, short sweeps of different polarity are combined to form the “alphabet” of a code.     

SEISMIC NOISE MEASUREMENTS IN A GEOTHERMAL AREA*

Generation of electrical power through the use of natural steam obtained from the Earth has the potential to be a significant source of pollution-free power. Successful future exploitation of geothermal power depends upon the development of cost-effective exploration techniques. A field experiment in the Imperial Valley of California indicates that there is a close empirical relationship between hot water deposits at depth and an anomalously high seismic background level at the surface. If this relationship proves to be a general one, it will serve as the basis of a simple and inexpensive method of geothermal exploration.     

OPTIMUM DIGITAL FILTERS FOR SIGNAL TO NOISE RATIO ENHANCEMENT*

One of the main objectives of seismic digital processing is the improvement of the signal-to-noise ratio in the recorded data. Wiener filters have been successfully applied in this capacity, but alternate filtering devices also merit our attention. Two such systems are the matched filter and the output energy filter. The former is better known to geophysicists as the crosscorrelation filter, and has seen widespread use for the processing of vibratory source data, while the latter is. much less familiar in seismic work. The matched filter is designed such that ideally the presence of a given signal is indicated by a single large deflection in the output. The output energy filter ideally reveals the presence of such a signal by producing a longer burst of energy in the time interval where the signal occurs. The received seismic trace is assumed to be an additive mixture of signal and noise. The shape of the signal must be known in order to design the matched filter, but only the autocorrelation function of this signal need be known to obtain the output energy filter. The derivation of these filters differs according to whether the noise is white or colored. In the former case the noise autocorrelation function consists of only a single spike at lag zero, while in the latter the shape of this noise autocorrelation function is arbitrary. We propose a novel version of the matched filter. Its memory function is given by the minimum-delay wavelet whose autocorrelation function is computed from selected gates of an actual seismic trace. For this reason explicit knowledge of the signal shape is not required for its design; nevertheless, its performance level is not much below that achievable with ordinary matched filters. We call this new filter the “mini-matched” filter. With digital computation in mind, the design criteria are formulated and optimized with time as a discrete variable. We illustrate the techniques with simple numerical examples, and discuss many of the interesting properties that these filters exhibit.     

PREDICTION ERROR FILTERS,WHITE NOISE AND ORTHOGONAL COORDINATES*

Optimum filters can be computed using orthogonal coordinates obtained from the eigenvalues and eigenvectors of the autocorrelation matrix. The method is used to obtain unit distance prediction error filters. The output of a unit distance prediction error filter when applied to the input wavelet is an impulse at zero time. The effect on the output of added white noise is easily obtained using the approach through the orthogonal coordinates. The added white noise results in output wavelets which are no longer impulses at zero time. The decrease in time resolution gives a filter that does not increase undesirable high frequency noise as much as filters computed without white noise. Orthogonal coordinates with little signal energy can be omitted from the filter computation resulting in output wavelets resembling those computed using added white noise.     

THE PERFORMANCE OF OPTIMUM STACKING FILTERS IN SUPPRESSING UNCORRELATED NOISE*

Optimum stacking filters based on estimates of trace signal-to-uncorrelated noise ratios are assessed and compared in performance with conventional straight stacking. It is shown that for the trace durations and signal bandwidths normally encountered in seismic reflection data the errors in estimating signal/noise ratios largely counteract the theoretical advantages of the optimum filter. The more specific the filter (e.g. the more frequency components included in its design) the more this is true. Even for a simple weighted stack independent of frequency, the performance is likely to be better than a straight (equal weights) stack only for relatively high signal/noise ratios, when the performance is not critical anyway.     

RESISTIVITY ANALYSIS FOR PLANE-LAYER HALF-SPACE MODELS WITH BURIED CURRENT SOURCES*

Boundary-value problems in steady-state current flow were solved numerically for one and two layers over a half-space. Solutions were obtained for layers of various resistivities where one of the current sources was placed below the surface and the second kept at some finite distance from the drill hole. When a fixed surface dipole receiving pair was used, it was found that as the buried source approached a conductive region, quite good determinations of the depth to the conductor could be made, hence reducing the possibility of extended drilling in “dry” holes resulting from poor surface data and/or interpretation. Numerous models were generated to find the optimum positioning of the two current electrodes for different field situations of this type. It was also found that by placing a current source in the conductive region, better resolution of the lateral extent of a possible ore zone could be obtained, due both to the more rapid convergence of the apparent resistivity to the resistivity of the conductor, and the fact that a smaller separation in the receiving dipole could be used. Numerous analog models were constructed to verify the digital results. Surface and down-hole resistivity field data are compared to show the strength of this technique in delineating structure.     

广义S变换域有色噪声与信号识别方法

为研究广义S变换域有色噪声与信号识别问题,首先推导白噪声在S变换和广义S变换下平均功率谱的统计规律,白噪声的平均功率谱与频率呈线性关系. 然后从理论上定性分析一般的有色噪声功率谱的分布特性,得出在广义S变换域有色噪声的功率谱服从自由度为2的χ2分布的规律, 并用Monte Carle方法进行了验证. 在上述工作基础上,本文提出了利用噪声和有效信号统计特性的差别,在广义S变换域中区分噪声和信号的方法,并用模型数据证明了方法的有效性.