Estimating local slope in the time-frequency domain: Velocity-independent seismic imaging in the near surface

Seismic reflection processing for multicomponent data is very time consuming. To automatically streamline and shorten this process, a new approach for estimating the local event slope (local static shift) in the time-frequency domain is proposed and tested. The seismic event slope is determined by comparing the local phase content of Stockwell transformed signals. This calculation allows for noninterfering arrivals to be aligned by iteratively correcting trace by trace. Alternatively, the calculation can be used in a velocity-independent imaging framework with the possibility of exporting the determined time and velocities for each common midpoint gather, which leads to a more robust moveout correction. Synthetic models are used to test the robustness of the calculation and compare it directly to an existing method of local slope estimation. Compared to dynamic time warping, our method is more robust to noise but less robust to large time shifts, which limits our method to shorter geophone spacing. We apply the calculation to near-surface shear-wave data and compare it directly to semblance/normal-moveout processing. Examples demonstrate that the calculation yields an accurate local slope estimate and can produce sections of better or equal quality to sections processed using the conventional approach with much less user time input. It also serves as a first example of velocity-independent processing applied to near-surface reflection data.

Imaging near-surface sharp lateral variations with surface-wave methods — Part 1: Detection and location

Near-surface sharp lateral variations can be either a target of investigation or an issue for the reconstruction of reliable subsurface models in surface-wave (SW) prospecting. Effective and computationally fast methods are consequently required for detection and location of these shallow heterogeneities. Four SW-based techniques, chosen between available literature methods, are tested for detection and location purposes. All of the techniques are updated for multifold data and then systematically applied on new synthetic and field data. The selected methods are based on computation of the energy, energy decay exponent, attenuation coefficient, and autospectrum. The multifold upgrade is based on the stacking of the computed parameters for single-shot or single-offset records and improves readability and interpretation of the final results. Detection and location capabilities are extensively evaluated on a variety of 2D synthetic models, simulating different target geometries, embedment conditions, and impedance contrasts with respect to the background. The methods are then validated on two field cases: a shallow low-velocity body in a sedimentary sequence and a hard-rock site with two embedded subvertical open fractures. For a quantitative comparison, the horizontal gradients of the four parameters are analyzed to establish uniform criteria for location estimation. All of the methods indicate ability in detecting and locating lateral variations having lower acoustic impedance than the surrounding material, with errors generally comparable or lower than the geophone spacing. More difficulties are encountered in locating targets with higher acoustic impedance than the background, especially in the presence of weak lateral contrasts, high embedment depths, and small dimensions of the object.

Imaging of fracture zones in the Finnsjön area, central Sweden, using the seismic reflection method

In 1987 the Swedish Nuclear Fuel and Waste Management Co. (SKB) funded the shooting of a 1.7-km long, high‐resolution seismic profile over the Finnsjön study site using a 60‐channel acquisition system with a shotpoint and geophone spacing of 10 m. The site is located about 140 km north of Stockholm and the host rocks are mainly granodioritic. The main objective of the profile was to image a known fracture zone with high hydraulic conductivity dipping gently to the west at depths of 100 to 400 m. The initial processing of the data failed to image this fracture zone. However, a steeply dipping reflector was imaged indicating the field data were of adequate quality and that the problem lay in the processing. These data have now been reprocessed and a clear image of the gently dipping zone has been obtained. In addition, several other reflectors were imaged in the reprocessed section, both gently and steeply dipping ones. Correlations with borehole data indicate that the origin of these reflections are also fracture zones. The improvement over the previous processing is caused mainly by (1) refraction statics, (2) choice of frequency band, (3) F-K filtering, and (4) velocity analyses. In addition to reprocessing the data, some further analyses were done including simulation of acquisition using only the near‐offset channels (channels 1–30) and the far‐offset channels (channels 31–60), and determining the damping factor Q in the upper few hundred meters based upon the amplitude decay of the first arrivals. The data acquisition simulation shows the far‐offset contribution to be significant even for shallow reflectors in this area, contrary to what may be expected. A Q value of 10, determined from observed amplitude decay rates, agrees well with theoretical ones assuming plane wave propagation in an attenuating medium.

The effect of geophone arrays on random noise

For spatially random noise consisting of plane surface waves arriving at a geophone from all directions with equal probability, I compute the noise‐to‐signal ratio (N/S) as a function of the ratio of geophone spacing Δ to noise wavelength λ for linear arrays of 12, 24, 36, and 72 vertical and horizontal geophones. For arrays of M vertical geophones, deviation of N/S from that for pure random noise, [Formula: see text] is marked. As Δ/λ increases, N/S decreases, attaining [Formula: see text] for a value of Δ/λ that defines a coherence distance. As Δ/λ increases beyond the coherence distance, N/S continues to decrease slightly, only to increase again as Δ/λ approaches unity. For linear arrays of 12 to 72 vertical geophones, Δ/λ at the coherence distance is nearly independent of M and is about 0.32. The value of Δ/λ for which N/S = 0.5 changes with M but L/λ, L being the array length defined as MΔ, is independent of M. Introducing a random 14 percent variation into the sensitivities of the individual geophones has a small influence on the coherence distance and the N/S = 0.5 point when the N/S curves for 50 arrays are summed. Introducing a random 14 percent variation into the spatial coordinates of the geophones changes the coherence distance and 0.5 point only slightly but reduces the amount by which N/S fails below [Formula: see text] For arrays of horizontal geophones, there are two N/S curves depending upon whether the horizontal motion is in the plane of incidence of the signal (SV waves) or perpendicular to the plane of incidence (SH waves). Due to the superdirectivity of the array, N/S for SV waves incident on an SV‐wave geophone array is very small for values of Δ/λ greater than about 0.1. The N/S curves for SH waves incident on an SV‐wave array resemble those for the arrays of vertical geophones. Again there is a coherence distance, but the Δ/λ value is twice that for the vertical geophones, indicating the geophones should be separated by about two‐thirds of a wavelength.

Field array performance: Theoretical study of spatially correlated variations in amplitude coupling and static shift and case study in the Paris Basin

Near‐surface propagation anomalies degrade the performance of field arrays. We studied this problem by modeling the signal detected by a field array. In our model, the signal arrival time and amplitude were each varied with distance along the array according to some arbitrary spatial trend. Given the intensity and the correlation distance of the signal variations, both wavenumber selectivity for noise rejection and frequency response for desired signal can be calculated. We begin by describing diagnostic graphs that show an array’s attainable signal bandwidth and noise rejection capability. Next, we discuss the mathematical relationships between the graphs and observable quantities such as correlations, array lengths, geophone spacing, etc. Exponential correlation functions are used in the modeling study for illustrative purposes. The same diagnostics are then generated from measured correlations derived from experimental data acquired in the Paris Basin with a densely sampled geophone spread. We found that the bandwidth diagnostic was useful and easy to calculate for this data set. Data sets with stronger noise waves should allow an accurate calculation of noise rejection capability. The diagnostic graphs can help in choosing the number of channels, array length, and weighting in a particular exploration area.

ENGINEERING SEISMOLOGY APPLICATIONS IN METROPOLITAN AREAS

Seismic refraction investigations in two “noisy” areas differing in geologic environment and field conditions indicate the reliability of such a technique for foundation engineering problems. Shothole conditions and generating media are of great importance. Dense media, clay, and materials within the water‐table are most favorable; fill debris is the least suitable. Seismic noise in the city, usually transient in character, is not an insurmountable problem; a patient instrument operator is a key to success. Several shot locations along an individual spread and a geophone spacing not to exceed 50 ft are standard field procedure for achieving a maximum amount of data.