Generalized Reciprocal Method Research Articles

Application of Generalized Reciprocal Method on 2D Seismic Refraction Data in Mt. Manglayang, West Java

The imaging of shallow subsurface structures, weathered rock thickness and velocity propagation distribution of the rocks can be identified by seismic refraction. This method is one of the geophysical exploration methods utilizing refracted wave once it reaches the boundary of subsurface layer. In this research we used the generalized reciprocal method (GRM) as one of the robust processing methods in analyzing subsurface data. This method was chosen due to its accuracy in interpreting shallow subsurface layer with highly undulating refractors by determining time velocity analysis, XY optimum distances, and time depth analysis, then, the expected depth values can be achieved. The acquisition of data for this research was conducted using 13 geophones with forward and reverse sources, the data were then picked to get travel time values and inverted to obtain real geological setting of the earth. The results were interpreted as 2 layers, the first layer had a velocity distribution of 499.289 m/s which was identified as a weathered layer with a thickness of about 4.74 meters, whereas the second layer was interpreted as clay rock with velocity distribution of 1270.433 m/s with the thickness reached up to 16 meters.
 Keywords: generalized reciprocal method, 2D seismic refraction

Integration of GIS with the Generalized Reciprocal Method (GRM) for Determining Foundation Bearing Capacity: A Case Study in Opolo, Yenagoa Bayelsa State, Nigeria

This study addresses the pressing need to assess foundation bearing capacity in Opolo, Yenagoa, Bayelsa State, Nigeria. The significance lies in the dearth of comprehensive geotechnical data for construction planning in the region. Past research is limited and this study contributes valuable insights by integrating Geographic Information System (GIS) with the Generalized Reciprocal Method (GRM). To collect data, near-surface seismic refraction surveys were conducted along three designated lines, utilizing ABEM Terraloc Mark 6 equipment, Easy Refract, and ArcGIS 10.4.1 software. This methodology allowed for the determination of key geotechnical parameters essential for soil characterization at potential foundation sites. The results revealed three distinct geoseismic layers. The uppermost layer, within a depth of 0.89 to 1.50 meters, exhibited inadequate compressional and shear wave velocities and low values for oedometric modulus, shear modulus, N-value, ultimate bearing capacity, and allowable bearing capacity. This indicates the presence of unsuitable, soft, and weak alluvial deposits for substantial structural loads. In contrast, the second layer (1.52 to 3.84 m depth) displayed favorable geotechnical parameters, making it suitable for various construction loads. The third layer (15.00 to 26.05 m depth) exhibited varying characteristics. The GIS analysis highlighted the unsuitability of the uppermost layer for construction, while the second and third layers were found to be fairly competent and suitable for shallow footing and foundation design. In summary, this study highlights the importance of geotechnical surveys in Opolo’s construction planning. It offers vital information for informed choices, addresses issues in the initial layer, and suggests secure, sustainable construction options.

COMPARATIVE ANALYSIS OF STATIC SHEAR MODULUS AND DYNAMIC SHEAR MODULUS DETERMINED BY GEOPHYSICAL AND GEOTECHNICAL INVESTIGATION

Due to the occurrence of earth tremors which leads to the vibrations of foundations and perhaps failure of buildings and roads, it is therefore important to understand and have knowledge of the geomechanical soil properties for foundation design, assessment of risks and suggestion of mitigation plans in engineering structures and road construction. A total of 3 boreholes were drilled with the Standard Penetration Test (SPT) performed and Downhole Seismic Test (DST) carried out in the boreholes located within Assa to investigate the Geomechanical soil properties in the area. For the geophysical survey, the downhole seismic test was carried out to determine the P-wave and S-wave. The results were processed using the generalized reciprocal method (GRM) with the Seisimager program. The results of soil dynamic modulus (shear, young and bulk modulus) and Poisson ratio recorded from DST conducted in BH1, BH2 and BH3 ranges from 7300 KPa to 72390 KPa, 0.31 to 0.41 for the Poisson ratio. Meanwhile, soil static modulus and Poisson’s ratio recorded from SPT conducted in BH1, BH2 and BH3 ranges from 2520 to 44687.0 KPa, 0.20 to 0.55 for the Poisson ratio respectively. The results of this study have shown that there is a wide variation between geomechanical properties derived from geotechnical investigations (static properties) and geophysical investigations (dynamic properties). Based on depth trend analysis, the dynamic and static soil elastic properties all increases with depth. Generally, the dynamic soil properties were significantly higher than the static elastic properties. At shallow depths (<12.0 m), the difference between static and dynamic soil modulus was relatively small, but increased with increasing depth. Meanwhile, the difference between static and dynamic Poisson ratio was high at shallow depth and it decreased with increased depths where they almost overlap. Correlation between the derived static and dynamic properties all revealed positive correlation trends. The strength of the correlation was highest for young modulus (r=0.87) which was closely followed by the shear modulus (r=0.63). Meanwhile, Poisson ratio (r=0.40) and bulk modulus (r=0.23) revealed weak positive correlation trends. The regression models generated from this study were used to derive static elastic properties and compared with the static properties obtained from geotechnical investigation thereby deriving the equations Dynamic Shear Modulus = (1.4207 x Static Shear Modulus) + 5022, Dynamic Young Modulus = (2.0241 x static young modulus) + 5054.8, Dynamic Bulk Modulus = (1.7852 x static bulk modulus) + 15458, Dynamic Poisson’s ratio = (0.1812 x Static Poisson’s ratio) + 0.3154. The results showed fairly good match between static (geotechnical) shear modulus and static (from regression model) shear modulus, static (geotechnical) young modulus and static (from regression model) young modulus. There was no good match obtained for bulk modulus and Poisson ratio generally, except at shallow depth (< 12 m depth) where Poisson ratio revealed a good match.

Application of the Stacked Refraction Convolution Section to 2D Ocean Bottom Seismometer Wide-angle Seismic Data Along the Tamayo Through Basin, Gulf of California

The stacked refraction convolution section can be used as an interpretation tool in wide-angle refraction seismic data generated by air gun shooting and recorded by Ocean Bottom Seismometers (OBS). The refraction convolution section is a full-wave extension of the Generalized Reciprocal Method (GRM), a method frequently used in shallow refraction seismic interpretation, but not applied to deep crustal-scale studies. The sum of the travel times of the waves refracted in the same interface and recorded in a pair of forward and reverse profiles, time-corrected by the reciprocal time, is an estimation close to the two-way travel times of the multichannel seismic reflection sections, but with seismic rays illuminating the interfaces upwards. The sum of seismic traces is obtained with the convolution section. Furthermore, several pairs of convolved forward-reverse refraction recordings of the same area can be stacked together to improve the signal to noise ratio. To show the applicability of the refraction convolution section in OBS deep data, we interpreted the basement structure of the Tamayo Through Basin in the southern Gulf of California, offshore Mexico. We compared the results with both, a multichannel seismic section recorded in the same profile, and the previous interpretations of the same wide-angle seismic data modeled with ray tracing and tomography methods. The basement imaged by the stacked refraction convolution section is similar in geometry to that obtained by seismic reflection processing. The stacked refraction convolution section identifies the full extent of the basement and confirms the location of a nearly constant thickness volcanic layer in the northwestern half of the basin. However, only a small area of volcanic deposits is found in the shallower parts of the southwestern margin. We also show that the convolution process can be used to estimate the occurrence of lateral variations of seismic velocities in the basement, as a further application of the GRM to deep refraction data.

An analytical Generalized Reciprocal Method (GRM) for near-surface seismic refraction investigations

Seismic refraction is one of the active seismic methods that work based on seismic waves that are refracted following the layers of the earth beneath the surface. Seismic refraction surveying is an important tool for determining the geometries and elastic wave propagation velocities of near-surface layer for oil bearing structures. Based on the data acquisition sketch obtained, the acquisition is carried out using the In-Line technique. There are two sources of vibration chosen, namely at the forward and reverse points, the distance between the 5-meter geophone and the distance between the source of the vibration and the geophone of 5 meters. The seismic data processing technique used in this study is the Generalized Reciprocal Method (GRM). This method determines the value of analysis, XY Optimum distance, time-depth analysis value, and depth. In interpreting seismic data, the calculation results that have been made are validated for accuracy using Software. From the research that has been done, it can be known as modeling subsurface structure. There are three layers, the first layer is 6 m-10m deep, while the second layer is 18m-22m deep. In the range of about 0m-20m, the first layer has a velocity of 507.74 m/s, the second layer has a velocity of 1420.43 m/s and the third layer has a velocity of 2522.30 m/s. In the range of about 20m-80m the first layer has a velocity of 550.12 m/s, the second layer has a velocity of 1575.11 m/s and the third layer has a velocity of 2607.45 m/s. In the range of about 80m-100m, the first layer has a velocity of 482.34 m/s, the second layer has a velocity of 1301.09 m/s and the third layer has a velocity of 2400.86 m/s.

Analysis of Near Surface Seismic Refraction for Geotechnical Parameters in Opolo, Yenagoa of Bayelsa State

Three surface refraction seismic profiles were conducted in a site targeted for huge construction in an underdeveloped area in Opolo, Yenagoa city to portray some of the subsurface soil engineering characteristics for the purposes of construction. The Generalized Reciprocal Method (GRM) was used to interpret the acquired P and S-wave. Various shallow rock engineering parameters such as Oedometric modulus, Concentration Index, Material Index, Lame’s constant, Density Gradient, Stress Ratio, Shear modulus, Bearing capacity, and N-value were calculated in other to assess the strength of the subsurface from a geophysical and engineering perspective. The values from the seismic velocity and strength parameters indicates that the bedrock layer (layer 3) of the area studied is characterized by more competent rock quality than layer 1 and 2. Hence, the Opolo site is suggested for construction activities with percussive measures.

The Computation of Attributes from Multi-fold Seismic Refraction Data

Seismic attributes are any measure that helps to better visualize or quantify features of interest in seismic data. Refraction attributes can be readily computed from multifold seismic data using the standard algorithms of the generalized reciprocal method (GRM), a common offset refraction (COR) modification of the GRM, and the refraction convolution section (RCS). The COR GRM algorithms are applied prior to the parameterization of the traveltime data into individual layers. The COR GRM presentations facilitate the efficient quality control and interpretation of large sets of multi-fold data. Furthermore, the COR GRM algorithms can be readily applied to single ended refraction data, which are routinely recorded with marine and land streamers. The time model attribute obtained with the COR GRM algorithm is of comparable accuracy to that computed with the standard multi-fold GRM. However, the COR GRM seismic velocity model is a smoothed version of the fully optimized standard GRM model. The refraction attributes computed from the head wave amplitudes include the multi-fold head coefficient, and a COR equivalent with the amplitude product. Although the COR amplitude product for each offset is of comparable accuracy to the multi-fold head coefficient, it also includes a residual geometric spreading component. Another refraction attribute computed from the head wave amplitudes is the geometric spreading coefficient, which is generally assumed to be two in the far field for plane homogeneous refractors. This parameter is consistent over a wide range of offsets, but varies considerably from less than one to up to four along the seismic traverse The attribute derived from the RCS is bandwidth in octaves. It is proposed that refraction attributes can be employed to derive more useful models of the regolith using multivariate geostatistics. It is concluded that, refraction attributes offer the opportunity of extending the refraction method to new applications.

Non-uniqueness with Refraction Inversion ? A Syncline Model Study

Non-uniqueness occurs with the 1D parameterization of refraction traveltime graphs in the vertical dimension and with the 2D lateral resolution of individual layers in the horizontal dimension. The most common source of nonuniqueness is the inversion algorithm used to generate the starting model. This study generates tomograms with wavepath eikonal traveltime (WET) tomography from starting models obtained with a smooth velocity gradient, the tau-p algorithm and the generalized reciprocal method (GRM) to traveltime data for a syncline (2D) model. The seismic velocity at the region of maximum gradient, taken to be refractor interface, was both ambiguous and anomously low for the smooth velocity gradient and the tau-p starting tomograms. These starting models also produced an artefact with a high seismic velocity in the main refractor. The GRM tomograms accurately reproduced the syncline, together with narrow regions at the thalweg with seismic velocities that are less than and greater than, as well as the true seismic velocities. It is concluded that inversion algorithms, which explicitly identify forward and reverse traveltime data, such as those of the GRM, are required to generate useful starting models in the near-surface where irregular refractors are common. The most likely tomogram can be selected as either the simplest model, or with a priori information, such as head wave amplitudes. The determination of vertical velocity functions within individual layers is also subject to non-uniqueness. Depths computed with vertical velocity gradients, which are the default with many tomography programs, are generally 50% greater than those computed with constant velocities for the same traveltime data. The GRM average vertical velocity provides a more accurate measure of depth estimates, where it can be derived. Non-uniqueness is a fundamental reality with the inversion of all near-surface seismic refraction data. Unless specific measures are taken to explicitly address non-uniqueness, then the production of a single refraction tomogram, which fits the traveltime data to sufficient accuracy, does not necessarily demonstrate that the result is either ?correct? or even the most probable.

Is VIRT an Efficacious Strategy for Refraction Inversion

Visual interactive ray trace (VIRT) inversion is a manual approach to refraction tomography. VIRT tomograms do not detect a major 50 m wide shear zone with a low seismic velocity at Mt Bulga. This failure is attributed to the probable use of a low resolution starting model, specifically the smooth velocity gradient wavepath eikonal traveltime (WET) tomogram, for the VIRT inversion. In this case, the low resolution of the VIRT tomogram is another demonstration of non-uniqueness. Alternatively, a starting model has been generated with the conventional reciprocal method, in which the existence of the low velocity region is unequivocal. In this case, confirmation bias has been employed to remove any expression of the low velocity region. VIRT tomography generates complex velocity models of the weathering from relatively small numbers of traveltimes, indicating that VIRT is overfitting those data. The extensive use of vertical interfaces across which there are large contrasts in seismic velocities is not consistent with standard models of normal weathering profiles. By contrast, VIRT generates simple velocity models in the sub-weathering from many traveltimes, indicating that VIRT is underfitting those traveltimes. Refraction tomograms produced with WET tomography using smoothed and detailed starting models generated with the generalized reciprocal method (GRM) have smaller errors than tomograms obtained with VIRT tomography and with WET tomograms generated with VIRT starting models. VIRT neither improves the accuracy nor the geological verisimilitude of refraction tomograms. Furthermore, VIRT is time consuming and subjective. Although technically, VIRT is efficacious, the alternatives of automatic refraction tomography are more practical, more accurate, and generate more useful tomograms. In the final analysis however, VIRT is simply outdated.

Is accuracy more important than precision in near‐surface refraction seismology?

ABSTRACTThe ubiquity of non‐uniqueness in near‐surface refraction seismology emphasises the importance of making a clear distinction between accuracy, that is, the validity of the model, and precision, that is, traveltime misfit errors. Non‐uniqueness can be resolved by identifying the most probable model within a global model space, based on the generalised reciprocal method (GRM), containing all geologically reasonable seismic velocities. All models within this model space have comparable misfit errors.The strategy involves three elements. First, the XY parameter of the GRM facilitates a more effective differentiation of the various models of the seismic velocities in both the weathered and sub‐weathered regions than is possible with simplistic comparisons of traveltime misfit errors. Second, all valid models of the seismic velocities in the weathered and sub‐weathered regions are restricted to those which employ the same XY value in both regions. Finally, the most probable model employs the optimum XY value, which is that XY value(s) which results in the simplest model of the GRM‐derived seismic velocities in the sub‐weathered region.Under suitable conditions where the refracting interface is sufficiently irregular, the optimum XY value can be measured to a precision of plus/minus half the station spacing. However, where that is either not possible or not undertaken, then a uniform velocity equivalent value can be computed from the cross‐over distance, with an inferred precision of plus/minus the optimum XY value.The significance of non‐uniqueness in any investigation can be demonstrated with two models. The first employs the uniform velocity model equivalent of the optimum XY value, whereas the second employs an XY value equal to the cross‐over distance. These two models represent the end members of the set of models which are consistent with the traveltime data. They span the range of seismic velocities in the weathered layers from uniform or constant values to the hyperbolic cosine function. The latter represents the maximum vertical velocity gradient which is consistent with linear traveltime graphs and which approximates the vertical velocity gradients commonly used in many implementations of automatic refraction tomography.Irrespective of whether the optimum XY value is determined with a precision of plus/minus half the station spacing or plus/minus the optimum XY value, the optimum XY value for uniform layers is commonly one quarter of the cross‐over distance. Therefore, the optimum XY value provides a more precise measure of the accuracy of the seismic velocities than is possible with traveltime misfit errors.

Validating vertical velocity gradients in near-surface refraction seismology

Wavepath eikonal traveltime (WET) refraction tomograms are generated with the generalised reciprocal method (GRM), a novel medium resolution common offset gather (COG) implementation of the GRM, using uniform velocities and vertical velocity gradients, and the low resolution default starting model consisting of smooth vertical velocity gradients. All tomograms have comparable misfit errors, which illustrates the ubiquity of non-uniqueness and the necessity for validating all starting models. Nevertheless, the use of even the maximum vertical velocity gradients in the weathered region does not produce any improvement in the spatial resolution of the seismic velocities in the sub-weathered region with either the default or the COG GRM starting models. Therefore, if a low resolution starting model is used, then the most likely outcome will be a low resolution WET tomogram, irrespective of whether or not vertical velocity gradients are employed. Vertical velocity gradients can be represented as part of a continuum of seismic velocities in the weathered layer, which range from uniform to hyperbolic velocities, and which are consistent with the traveltime data. Acceptable models employ seismic velocities in the weathered and sub-weathered regions computed with the same XY value. In this study, the optimum XY value is representative of uniform seismic velocities, whereas the maximum XY value, which is the average cross-over distance, is representative of default and hyperbolic velocities. Intermediate XY values indicate more moderate vertical velocity gradients and/or undetected layers. WET tomography is largely a smoothing operation which does not improve the spatial resolution of either medium resolution or detailed starting models. A limited number of iterations, usually a maximum of five, can improve the cosmetics of refraction tomograms, whereas repeated applications can result in considerable reductions in spatial resolution, and eventually, low resolution tomograms consisting of essentially featureless parallel quasi horizontal layers.

Resolving complex structure in near-surface refraction seismology with common-offset gathers

Common-offset gathers (COG) have been usefully employed in the processing of seismic reflection data (Fulton and Darr, 1984). COG methods have also been employed to a lesser extent with the processing of seismic refraction data (Coppens, 1985), but their wider application has yet to be fully exploited. This study describes novel COG adaptations of the generalized reciprocal method (GRM) (Palmer, 1981, 2010b). Initially, the COG GRM methods (Palmer, 2012) were developed as simple and convenient methods for the quality assurance of the large volumes of refraction data, which are characteristic of statics computations for high-fold CMP reflection data processing. However, their application to a variety of sets of data has demonstrated a number of additional unanticipated benefits.

Generating starting models for seismic refraction tomography with common offset stacks

Common offset refraction (COR) traveltime attributes are derived from multi-fold data with novel adaptations of the generalised reciprocal method (GRM). COR GRM stacks are generated from a refraction equivalent of common midpoint (CMP) gathers, which are computed at each CMP with the COR GRM algorithms. The COR GRM stacks, which generate detailed spatially varying attributes for each layer detected in the near surface region, provide useful starting models for automatic refraction tomography.The spatial resolution of the depth models of the wavepath eikonal traveltime (WET) refraction tomograms obtained with starting models derived with the COR GRM is similar to the WET tomogram obtained with the standard GRM, whereas the COR GRM seismic velocity model is a smoothed version of the standard GRM model. In all cases, the GRM-derived WET tomograms avoid the generation of undetectable artefacts with common implementations of automatic refraction tomography, which can occur with the use of default starting models consisting of smooth vertical velocity gradients and with the need to minimise misfit errors through over-processing.The COR GRM attributes demonstrate that the traveltime data are consistent with minimal penetration within the sub-weathering, representative of uniform seismic velocities, and that the spatial variations in the time model and seismic velocities are more significant than any variations caused by vertical velocity gradients in the sub-weathered zone. However, the occurrence of vertical velocity gradients in the sub-weathering largely remains unresolved because minimal penetration of the first arrivals can occur even with large vertical velocity gradients, such as the hyperbolic velocity function.The WET tomograms generated with the COR GRM time model and seismic velocity attributes are generally very similar visually to the starting models, even though the misfit errors may differ. It is concluded that COR GRM starting models can frequently be a useful alternative to refraction tomography.

Uncertainty in Near-Surface Refraction Inversion

Uncertainty in the tomographic inversion of near-surface seismic refraction data can be separated into aleatory variability, which describes the misfit errors and epistemic uncertainty, which describes the suite of acceptable models. Common implementations of refraction tomography usually focus on reducing aleatory variability and frequently disregard epistemic uncertainty. In this study, the tomograms generated with three models of the seismic velocities in both the weathering and in the sub-weathering, using the generalized reciprocal method (GRM), are consistent with the traveltime data. However, only one tomogram is consistent with the optimum XY value and the attributes derived from the head wave amplitudes and seismic velocities. This study demonstrates that epistemic uncertainty can be explicitly addressed with the GRM, because the most probable tomogram can be selected objectively from a number of acceptable alternatives. The GRM-based tomogram successfully detects, defines and differentiates narrow regions with low seismic velocities which represent shear zones and a massive sulphide ore body. None of these zones is detected with the tomogram generated with the default starting model using smooth vertical velocity gradients. It is concluded that minimizing epistemic uncertainty through the use of the most appropriate starting model is more important than minimizing aleatory variability.

A General Matrix Model Of Support Department Cost Allocation Methods

<p class="MsoNormal" style="text-align: justify; margin: 0in 0.5in 0pt; mso-pagination: none;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">This paper demonstrates that the direct and step methods for making support department allocations are really special cases of the more general reciprocal method, and that the different allocations can be estimated using the same basic model.<span style="mso-spacerun: yes;">  </span>Simple modification of the matrix of resource consumption between support departments is all that is required to use a matrix algebra approach for all three methods.<span style="mso-spacerun: yes;">  </span>Potential benefits accruing to users and practitioners from the use of these models and areas of possible future research are discussed in the paper.</span></span></p>

Comparing Models GRM, Refraction Tomography and Neural Network to Analyze Shallow Landslide

Detailed investigations of landslides are essential to understand fundamental landslide mechanisms. Seismic refraction method has been proven as a useful geophysical tool for investigating shallow landslides. The objective of this study is to introduce a new workflow using neural network in analyzing seismic refraction data and to compare the result with some methods; that are general reciprocal method (GRM) and refraction tomography. The GRM is effective when the velocity structure is relatively simple and refractors are gently dipping. Refraction tomography is capable of modeling the complex velocity structures of landslides. Neural network is found to be more potential in application especially in time consuming and complicated numerical methods. Neural network seem to have the ability to establish a relationship between an input and output space for mapping seismic velocity. Therefore, we made a preliminary attempt to evaluate the applicability of neural network to determine velocity and elevation of subsurface synthetic models corresponding to arrival times. The training and testing process of the neural network is successfully accomplished using the synthetic data. Furthermore, we evaluated the neural network using observed data. The result of the evaluation indicates that the neural network can compute velocity and elevation corresponding to arrival times. The similarity of those models shows the success of neural network as a new alternative in seismic refraction data interpretation.

Is visual interactive ray trace an efficacious strategy for refraction inversion?

Visual interactive ray trace (VIRT) inversion is a manual approach to refraction tomography. VIRT tomograms neither detect nor define a major 50 m wide zone with a low seismic velocity at Mt Bulga. This failure is attributed to the probable use of a low resolution starting model, specifically the smooth velocity gradient wavepath eikonal traveltime (WET) tomogram, for the VIRT inversion. In this case, the low resolution of the VIRT tomogram is another demonstration of the ubiquity of non-uniqueness.Alternatively, the conventional reciprocal method has been used to generate a starting model, in which the existence of the low velocity region is unequivocal. In this case, confirmation bias has been employed to remove any expression of the low velocity region in the VIRT tomogram.By contrast, WET refraction tomograms produced with smooth and detailed starting models generated with the generalised reciprocal method (GRM) clearly define the 50 m wide zone with the low seismic velocities. The low velocity zone is confirmed with a priori information, specifically the inverted head wave amplitudes and a spectral analysis of the refraction convolution section, and by a posteriori information, specifically numerous closely spaced orthogonal refraction profiles. Furthermore, the GRM tomograms have smaller misfit errors than the tomograms obtained with VIRT tomography and with WET tomograms generated with VIRT starting models.VIRT tomography generates complex velocity models of the weathering from relatively small numbers of traveltimes, indicating that VIRT is overfitting the data. The extensive use of vertical interfaces across which there are large contrasts in seismic velocities is not consistent with standard models of normal weathering profiles, nor is it indicated in the traveltime graphs. By contrast, VIRT generates simple velocity models in the sub-weathering from many traveltimes, indicating that VIRT is underfitting those traveltimes.VIRT neither improves the accuracy nor the geological verisimilitude of refraction tomography. Furthermore, VIRT is time consuming, subjective, and in the final analysis, simply outdated. Although technically, VIRT is efficacious, the alternatives of automatic refraction tomography are more practical, more accurate, and generate more useful tomograms.

A review of shallow seismic methods

Shallow seismic methods have historical roots dating to the 1930s, when limited shallow refraction work was performed using the Intercept-Time (IT) method. Because of high costs and the general lack of appropriate equipment - particularly data-processing equipment and software - the shallow-reflection and surface-wave techniques did not catch on as quickly as the refraction techniques. However, since 1980 substantial progress has been made in the development of all of the shallow seismic approaches. The seismic-reflection method has been used increasingly in applications at depths of less than 30 m, incorporating both the standard Common-Midpoint (CMP) method of the petroleum industry and the Common-Offset (CO) method, which was developed specifically as a low-cost technique for use in shallow surveying. In refraction studies, the Generalized Reciprocal Method (GRM) largely has replaced the classical intercept-time method, and tomographic approaches are rapidly gaining popularity. The Spectral Analysis of Surface Waves (SASW) has been developed by civil engineers, and surface-wave analysis involving many seismograph channels (MASW) recently has shown promise. With any of the shallow seismic methods, however, selecting the appropriate seismic recording equipment, energy sources, and data-acquisition parameters, along with processing and interpretation strategies, often is critical to the success of a project.

Generalized reciprocal method applied in processing seismic refraction data from the basement terrain of Zaria, Northwest Nigeria

A geophysical investigation was carried out at Shika, near Zaria, using seismic refraction method; with the aim of analyzing the data obtained using the generalized reciprocal method (GRM). The technique is for delineating undulating refractors at any depth from in-line seismic refraction data consisting of forward and reverse travel-times. An in-line geometric spread with optimum geophone distance of 25m was used. The result obtained showed that the optimum XY spacing, the upward and downward traveling segments of the rays to each geophone emerged from near the same point on the refractor. This method proved to be particularly well-suited for situations involving large lateral velocity variations and highly irregular refractor surfaces. By using computer processing techniques and advanced interpretational features of GRM, it has been possible to derive a picture of the subsurface layering from the refraction results even in geologically complex environments. However, average velocities of 1356 m/s, 2309 m/s to 2543 m/s and 4065m/s were obtained for the Overburden, weathered Basement and Basement respectively. The borehole log data correlated perfectly with the depth sections as far as the thickness and lithology of the strata from the surface to the basement, is concerned. Subsurface features such as loose ground and low velocity zones were identified and mapped correctly. Finally, it was evident from the processed data that this technique is best suitable for investigating and mapping these geologic features which are of great significance in engineering and geotechnical studies.

Exploiting lateral resolution of near-surface seismic refraction methods

The 1D τ-p inversion algorithm is widely employed to generate starting models with most computer programs that implement refraction tomography. However, this algorithm emphasizes the vertical resolution of many layers, and as a result, it frequently fails to detect even large lateral variations in seismic velocities, such as the decreases that are indicative of shear zones. This study presents a case that demonstrates the failure of the 1D τ-p inversion algorithm to define or even detect a major shear zone that is 50 m or ten stations wide. Furthermore, the majority of refraction tomography programs parameterize the seismic velocities within each layer with vertical velocity gradients. By contrast, the 2D generalized reciprocal method (GRM) inversion algorithms emphasize the lateral resolution of individual layers. This study demonstrates the successful detection and definition of the 50-m wide shear zone with the GRM inversion algorithms. The existence of the shear zone is corroborated by a 2D analysis of the head wave amplitudes and by numerous closely spaced orthogonal seismic profiles carried out as part of a later 3D refraction investigation. Furthermore, a 1D analysis of the head wave amplitudes indicates that a reversal in the seismic velocities, rather than vertical velocity gradients, occurs in the weathered layers. While all seismic refraction operations should aim to provide as accurate depth estimates as is practical, the major conclusion reached in this study is that refraction inversion algorithms that emphasize the lateral resolution of individual layers generate more useful results for geotechnical and environmental applications. The advantages of the improved lateral resolution are obtained with 2D profiles in which the structural features can be recognized from the magnitudes of the variations in the seismic velocities. Furthermore, the spatial patterns obtained with 3D investigations facilitate the recognition of structural features that do not display any intrinsic variation or “signature” in seismic velocities.