Direct Wave Arrivals Research Articles

Processing of random roadway source signals based on a cross-correlation algorithm in the deconvolution domain

Advanced seismic detection technology utilising random roadway sources is advantageous method adapting to the development of dynamic intelligent technologies for the detection of hidden and disastrous geological structures. However, roadheaders generate complex signals, that are continuous and random with seismic wavelets that are wider and longer than conventional source wavelets, and these complex wavelets cannot be directly subjected to data processing. To address this problem, based on two basic techniques, namely, deconvolution and cross-correlation, a cross-correlation algorithm in the deconvolution domain is proposed to process continuous random roadheader signals, convert those signals into normal-impulse seismic data, and extract the arrivals of direct and reflected waves and other information. First, the feasibility of the algorithm is explained based on a derivation of theoretical formulas. Then, to verify the applicability of the algorithm to the processing of actual data, a random signal from a tamping source is processed; the continuous random signals are successfully converted into impulse signals, and the extracted in-phase direct waves are clear with good continuity. Moreover, the continuous random signal processing results are compared with an active source signal, and good consistency is found, verifying the effectiveness of the algorithm. Finally, an application analysis of the algorithm is carried out using an actual acquired roadheader source signal. After implementing the algorithm, the random roadheader signal is successfully converted into a normal-impulse seismic signal, and the direct wave arrivals are extracted. Based on the arrival times of the direct waves, the longitudinal wave velocity of the coal seam is calculated as 1918 m/s, which is consistent with the actual velocity. A comprehensive analysis of the test results confirms that the cross-correlation algorithm in the deconvolution domain is both feasible and effective and that the processed seismic signals can be used for subsequent processing and interpretation.

Designing an exploration-scale OBN: Acquisition design for subsalt imaging and velocity determination

Direct wave arrivals are the most robust signals to determine velocity. They have been used for almost a century in hydrocarbon exploration. This is because the arrival time is explicitly available and provides a direct measurement of the average velocity of the subsurface raypath. To acquire these direct arrivals in a seismic experimental setting, it is necessary that the waves turn back to the surface after they start traveling into the earth. As is well known, it is possible to turn waves back up if they encounter faster propagation velocities than previously experienced. Using these simple concepts, we show how it is possible to design a seismic acquisition to measure subsalt velocities when the salt cover is very thick and potentially not homogeneous. Until now in marine seismic surveying, the physical limitations of the earth meant that the use of direct wave arrivals was restricted to relatively shallow depths of investigation. By combining the application of node technology with a well-established physical phenomena (i.e., refraction in the basement), it is possible to retrieve subsalt velocities from seismic surveys.

Direct Modeling of the Mechanical Strain Influence on Coda Wave Interferometry

AbstractCoda waves interferometry (CWI) aims at tracking small changes in solid materials like rocks where elastic waves are diffusing and so intensively sampling the medium, making the technique more sensitive than those relying on direct wave arrivals. Its application to ambient seismic noise correlation, referred to as ambient noise interferometry, has found a large range of applications over the past years like for reservoir monitoring or regional fault evolution. Physically, the changes in phases observed are typically interpreted as small variations of seismic velocities. However, this interpretation is questionable. The goal of the present work is to show from a direct numerical modeling that deformation signal also exists in CWI measurements which might provide new outcomes for the technique. For this purpose, we model seismic wave propagation within a diffusive medium using a spectral element approach (SPECFEM2D) during an elastic deformation of the medium. The mechanical behavior is obtained from a finite element approach (Code_Aster) keeping the mesh grid of the sample constant during the whole procedure to limit numerical artifacts. CWI of the late wave arrivals in the synthetic seismograms is performed using both a stretching technique in the time domain and a frequency cross‐correlation method. Both show that CWI is sensitive to the heterogeneity of the elastic deformation field in addition to the isotropic volumetric deformation and independently of nonlinear acoustoelastic effects. Implications for strain monitoring of reservoirs are discussed.

Noise suppressing and direct wave arrivals removal in GPR data based on Shearlet transform

We present a new application of Shearlet transform (ShT) for ground penetrating radar (GPR) to remove the direct wave arrivals and suppress random noise. In fact, the reflecting waves from the underground targets and the direct wave arrivals are sometimes overlapped when the targets are buried shallowly, which influences the arrival-time detection and the target-position location. Random noise is also one of the influencing factors. In this paper, ShT is introduced to remove the direct wave arrivals and suppress random noise. The original GPR data is transformed to ShT domain by using multi-scale and multi-direction properties of ShT. The direct wave arrivals and the remaining GPR signal are effectively separated. While we eliminate the direct wave arrivals, the GPR signal is not damaged. In ShT domain, GPR data can be expressed sparsely. The GPR signal is described by big Shearlet coefficients, but random noise is described by small ones. So we can use the threshold method depending on different scales and directions in ShT domain to suppress random noise. The GPR signal's signal to noise ratio (SNR) is enhanced. The synthetic and field GPR data verify the effectiveness of direct wave arrivals removal and random noise suppression based on ShT.

Estimation of Sea Surface Temperature (SST) Using Marine Seismic Data

Not much attention is given to direct wave arrivals in marine seismic data that are acquired for petroleum exploration and prospecting. These direct arrivals are usually muted out in routine seismic data processing. In the present study, we process these direct arrivals to accurately estimate soundspeed in near-surface seawater and invert for sea surface temperature. The established empirical equation describing the relationships among temperature, salinity, pressure and soundspeed is used for the inversion. We also discuss processing techniques, such as first-break picking and cross-correlation for the estimation of soundspeed, that are well known among petroleum-industry geophysicists. The accuracy of the methods is directly linked to the data quality and signal processing. The novelty in our approach is in the data conditioning, which consists essentially of spectral balancing based on a wavelet transform that compensates for spherical spreading and increases the signal-to-noise (S/N) ratio. The 2D seismic data used in this paper are from the offshore Krishna-Godavari Basin east of India. We observe a significantly higher soundspeed of 1545 m/s for near-surface water than the commonly used value of ~1500 m/s. The estimated temperature (from velocity) is about 30 °C. Interestingly, the estimated temperature matches well with the temperature recorded in the CTD profile acquired in the study area during the month of May, the month corresponding to the acquisition of seismic data. Furthermore, the estimated temperatures during different times of data acquisition correlate well with the expected diurnal variation in temperature.

Reflection of compressional and Rayleigh waves on the edges of an elastic plate with quadratic nonlinearity

Previous ultrasonic studies have demonstrated that measurements of material nonlinearities can provide a means for detecting early signs of fatigue damage using both compressional (P) and Rayleigh (R) surface waves. However, these experimental studies have typically been limited to the direct wave arrival between the source and receiver in simple geometries where no reflection occurs. In particular, the degree of material nonlinearity is often quantified by the ratio of the cumulative amplitude of the first harmonic to that of the fundamental for the direct arrival only. Hence a practical question arises over the interpretation of ultrasonic measurements of material nonlinearities in the presence of reflected nonlinear waves. Thus, this article investigates the reflection problem of P or R waves at the edge of a homogeneous plate with quadratic nonlinearity using both a theoretical formulation, based on perturbation analysis, and direct numerical simulations using a Cellular Automata formulation. The numerical approach is first validated against an existing theoretical formulation for reflecting nonlinear P waves. It is then used to simulate the nonlinear reflection of R waves at a plate's edge for which no closed-form formulation is presently available.

Estimation of direct-arrival velocity using the linear moveout velocity analysis method with applications from eastern Saudi Arabia

Estimation of near-surface models from refraction data conventionally involves picking of arrival times for the direct and head waves. However, it is often difficult to pick the direct wave automatically on shot records if the direct-wave arrival is not a first arrival. The linear moveout velocity analysis method is proposed here to overcome this difficulty. The method is applied to help estimate the depth to the watertable at three locations in the eastern province of Saudi Arabia. The data consist of three shot records acquired in coastal sabkhas with a very shallow watertable, making it possible to check the analysis results. Conventional automatic picking algorithms failed to pick the direct arrivals in these records because the direct arrivals always come after other arrivals. The proposed method is used to estimate the direct-arrival velocities in these records and the depths to the watertable are estimated. Comparison of estimated and true water depths shows that the error was within 8%. In addition, the direct-wave velocities estimated by the proposed method showed almost perfect agreement with results from a previous study in two of the tested areas in which manual picking of the direct-wave arrivals was used.

An optimization of the inverse scattering multiple attenuation method for OBS and VC data

The inverse scattering multiple attenuation (ISMA) algorithm for ocean‐bottom seismic (OBS) data can be formulated in the form of a series expansion for each of the four components of OBS data. Besides the actual data, which constitute the first term of the series, each of the other terms is computed as a multidimensional convolution of OBS data with streamer data, and aims at removing one specific order of multiples. If the streamer data do not contain free‐surface multiples, we found that the computation of only the second term of the series is needed to predict and remove all orders of multiples, whatever the water depth. As the computation of the various terms of the series is the most expensive part of ISMA, this result can produce significant savings in computation time, even in data storage, as we no longer need to store the various terms of the series. For example, if the streamer data contained free‐surface multiples, OBS seismic data of 6‐s duration, corresponding to a geological model of the subsurface with 250‐m water depth, require the computation of five terms of the series for each of the four components of OBS data. With the new implementation, in which the streamer data do not contain free‐surface multiples, we need the computation of only one term of the series for each component of the OBS data. The saving in CPU time for this particular case is at least fourfold.The estimation of the inverse source signature, which is an essential part of ISMA, also benefits from the reduction of the number of terms needed for the demultiple to two because it becomes a linear inverse problem instead of a nonlinear one. Assuming that the removal of multiple events produces a significant reduction in the energy of the data, the optimization of this problem leads to a stable, noniterative analytic solution.We have also adapted these results to the implementation of ISMA for vertical‐cable (VC) data. This implementation is similar to that for OBS data. The key difference is that the basic model in VC imaging assumes that data consist of receiver ghosts of primaries instead of the primaries themselves. We have used the following property to achieve this goal. The combination of VC data with surface seismic data, which do not contain free‐surface multiples, allows us to predict free‐surface multiples and receiver ghosts as well as the receiver ghosts of primary reflections. However, if the direct wave arrivals are removed from the VC data, this combination will not predict the receiver ghosts of primary reflections. The difference between these two predictions produces data containing only receiver ghosts of primaries.

Attenuating primaries and free‐surface multiples of vertical cable (VC) data while preserving receiver ghosts of primaries

Marine vertical cable (VC) data contain primaries, receiver ghosts, free‐surface multiples, and internal multiples just like towed‐streamer data. However, the imaging of towed‐streamer data is based on primary reflections, while the emerging imaging algorithms of VC data tend to use the receiver ghosts of primary reflections instead of the primaries themselves. I present an algorithm for attenuating primaries, free‐surface multiples, and the receiver ghosts of free‐surface multiples while preserving the receiver ghosts of primaries. My multiple attenuation algorithm of VC data is based on an inverse scattering approach known, which is a predict‐then‐subtract method. It assumes that surface seismic data are available or that they can be computed from VC data after an up/down wavefield separation at the receiver locations (streamer data add to VC data some of the wave paths needed for multiple attenuation). The combination of surface seismic data with VC data allows one to predict free‐surface multiples and receiver ghosts as well as the receiver ghosts of primary reflections. However, if the direct wave arrivals are removed from the VC data, this combination will not predict the receiver ghosts of primary reflections. I use this property to attenuate primaries, free‐surface multiples, and receiver ghosts from VC data, preserving only the receiver ghosts of primaries. This method can be used for multicomponent ocean bottom cable data (i.e., arrays of sea‐floor geophones and hydrophones) without any modification to attenuate primaries, free‐surface multiples, and the receiver ghosts of free‐surface multiples while preserving the receiver ghosts of primaries.

Synthesis of scattered energy density for nonspherical radiation from a point shear-dislocation source based on the radiative transfer theory

It is well known that S-coda wave amplitudes of local earthquakes smoothly decay with increasing lapse time and asymptotically converge to a common master curve irrespective of their epicentral distances. This property is thought to be the conceptual basis for the conventional coda normalization method, which has often been used for the estimation of amplitude attenuation and site amplification factors around the world. We note that it has also been widely accepted that the common decay curve is independent of the radiation pattern especially at long lapse times. However, there have been few theoretical attempts to clarify the way how S-coda wave envelopes neglect the radiation pattern of the source with increasing lapse time. Focusing on this problem, we try to formulate the multiple scattering process in a scattering medium for an impulsive radiation from a point-shear dislocation source on the basis of the radiative transfer theory. We assume that the inhomogeneous medium in a 3-D space is represented by a homogeneously random distribution of point-like scatterers and, for simplicity, that scattering is isotropic. The master equation is written in the form of a convolution integral equation for the energy density, which corresponds to the mean square seismogram amplitude. Introducing the spherical harmonics expansion for nonspherical radiation from the source, in addition to the Fourier transform in space and the Laplace transform in time, we are able to solve the integral equation in each spherical harmonics mode analytically. The inverse Fourier-Laplace transformation gives the spatiotemporal change in energy density for each spherical harmonics mode. As the order of spherical harmonics mode increases, the corresponding energy density decreases more rapidly with increasing lapse time. The energy density faithfully reflects the nonspherical radiation pattern of a point-shear dislocation immediately after the direct wave arrival. However, the direction dependence diminishes as lapse time increases, and the energy density asymptotically converges to that for a spherically symmetric radiation, which corresponds to the lowest spherical harmonics mode. At a distance of the mean free path from the source, the difference between the maximum energy density and the minimum energy density at the same lapse time becomes less than 3% when the lapse time exceeds twice the travel time of the direct wave.

Multiple Isotropic Scattering Model IncludingP-SConversions For the Seismogram Envelope Formation

SUMMARY High-frequency seismogram envelopes of local earthquakes are well characterized by the scattering nature of the randomly inhomogeneous lithosphere. In addition to direct P- and S-wave phases, incoherent wave trains are found not only in the S coda but also between the P and S phases. This implies the importance of scattering with conversions between P and S. the contribution from scattering increases with increasing hypocentral distance or lapse time because of multiple scattering processes. the multiple scattering contribution has been extensively studied mathematically especially for the S coda by supposing isotropic scattering. Here, extending the isotropic scattering assumption for scattering in conversion between two different wave velocities, we formulate the multiple scattering process for spherical radiation from a point source and derive the space time distribution of the energy density in 3-D space on the basis of energy transport theory. We confirm conservation of the total energy in the case of no intrinsic absorption, which assures the self-consistency of the formulation. A hybrid method, combining the analytical solutions corresponding to single scattering and numerical calculations for multiple scattering with order greater than, or equal to, two, is proposed to synthesize the spacetime distribution of the energy density. Synthesized time traces give a good explanation of the rather smooth and gradual increase in amplitude of wave trains often observed between P and S phases and the larger amplitude of the S coda. the envelope characteristics, except for short time windows around the direct wave arrivals, are well characterized by multiple scattering irrespective of the change in source duration time.

Application of a wave transform to pressure transient testing in porous media

Solutions to the diffusion equation for nonuniform media are difficult to obtain in a form that can be easily evaluated. Often the solutions are written as the inverse Laplace transform of an inverse Fourier transform. In this paper, I show that the wave transform of Bragg and Dettman (1968) coupled with the Cagniard-de Hoop method for solving the wave propagation problem results in simplified solutions to the problem of pressure transient testing in linear composite reservoirs. The potential usefulness of an inverse wave transform, which would transform measured pressure data (smooth) into a wave signal propagating at the ‘velocity’ of the square root of the diffusivity, is demonstrated by a synthetic example. In the example, diffusivity of the source region is estimated from the ‘time’ of the direct wave arrival, while diffusivity of a second, higher diffusivity region is estimated from the ‘velocity’ of the head wave. In the wave domain the time-like variable has units of (time)1/2 which makes the units of ‘velocity’ equal to L T-(1/2). I also demonstrate, using synthetic data, that it is difficult, but perhaps possible, to invert the wave transform numerically.

Diffraction of elastic waves by defects in plates: Calculated arrival strengths for point force and thermoelastic sources of ultrasound

This paper applies geometrical ray theory to the calculation of the surface displacements generated by point force and thermoelastic sources of ultrasound in plates containing planar defects. The calculation includes direct wave arrivals, waves undergoing back-wall reflection with or without mode conversion, and waves diffracted by the crack-tip. Ultrasonic B-scan data are also simulated so that comparison can be made with experimental data. It is shown that the thermoelastic source, which can be generated by a pulsed laser, is particularly well suited to defect detection by the ultrasonic time-of-flight technique.

Seismic exploration of the continental shelf off the west coast of India

Some recent observations in connection with seismic exploration of the continental shelf off the west coast of India are described. A single ship with a single sono-buoy was used. Five shots were fired at distances up to six miles from the sono-buoy. Roughly, the depth of the ocean was about 80 fathoms, and a negative temperature gradient existed. The exact times of shots were calculated from the observed arrival of direct waves. The loose sediments are surmised to be about 2.8 km thick, and seismic velocity in these sediments is found to be 1.2 miles per second. The depth of sediments has been calculated from assigning a broad maximum in the records to reflection from the bottom of the loose sediments.