S. A. Greenhalgh

Finite-difference solution of the eikonal equation using an efficient, first-arrival, wavefront tracking scheme

First‐break traveltimes can be accurately computed by the finite‐difference solution of the eikonal equation using a new corner‐node discretization scheme. It offers accuracy advantages over the traditional cell‐centered node scheme. A substantial efficiency improvement is achieved by the incorporation of a wavefront tracking algorithm based on the construction of a minimum traveltime tree. For the traditional discretization scheme, an accurate average value for the local squared slowness is found to be crucial in stabilizing the numerical scheme for models with large slowness contrasts. An improved method based on the traditional discretization scheme can be used to calculate traveltimes in arbitrarily varying velocity models, but the method based on the corner‐node discretization scheme provides a much better solution.

Prestack multicomponent migration

Prestack elastic migration by displacement potential extrapolation is a mixed, systematic, and function‐blocked vector wavefield migration algorithm. A new wavefield extrapolation method for inhomogeneous media is introduced here according to the following sequence: displacements ← potentials ← extrapolation of the potentials ← displacements, which is relatively accurate and not computer‐time intensive. Traveltimes of both direct downgoing P‐ and S‐waves, which are necessary in elastic migration, are calculated with a modified convolutional acoustic forward modeling program applicable to complex structures. A new image condition based on the time consistent principle is developed. It involves first obtaining an image condition section. Then two images (P P and S S) are obtained from the product of the extrapolated and decomposed P P‐ and S S‐wave displacement amplitudes and the image condition section. All P P‐, P S‐, S P‐ and S S‐waves are considered when the image condition section is calculated. The im...

Linear and parabolic tau -p transforms revisited

New derivations for the conventional linear and parabolic τ-p transforms in the classic continuous function domain provide useful insight into the discrete τ-p transformations. For the filtering of unwanted waves such as multiples, the derivation of the τ-p transform should define the inverse transform first, and then compute the forward transform. The forward transform usually requires a p‐direction deconvolution to improve the resolution in that direction. It aids the wave filtering by improving the separation of events in the τ-p domain. The p‐direction deconvolution is required for both the linear and curvilinear τ-p transformations for aperture‐limited data. It essentially compensates for the finite length of the array. For the parabolic τ-p transform, the deconvolution is required even if the input data have an infinite aperture. For sampled data, the derived τ-p transform formulas are identical to the DRT equations obtained by other researchers. Numerical examples are presented to demonstrate event...

Separation of upgoing and downgoing waves in vertical seismic profiling by contour-slice filtering

The separation of upgoing waves and downgoing waves in vertical seismic profiling is effectively accomplished in the frequency‐wavenumber (f‐k) domain using a new technique of contour‐slice filtering. The response of the filter has no straight edge or boundary and preserves the “natural state” of the spectra. The cutoff contour level can be reduced as low as desirable to remove background noise and other unwanted signals. In this sense it can also be viewed as a noise‐rejection filter. The effectiveness of the process has been clearly demonstrated through synthetic and real examples. Its success with the upgoing waves depends on the degree of coherency of events in the VSP record. To enhance the coherency and to avoid velocity aliasing, we use a novel band‐pass frequency filter which is the result of convolving a boxcar spectral window with a frequency‐shifted Gaussian function.

Shallow seismic reflection investigations of coal in the Sydney Basin

Surface reflection profiling with the Mini‐SOSIE technique successfully mapped shallow coal seam structure in the western Sydney Basin, New South Wales. Several minor faults and zones of fracturing were detected. In regions of thick Triassic sandstone cover, data quality was poor and unsuitable for geologic interpretation. Synthetic seismograms based on nearby borehole and petrophysical control show excellent agreement with the Mini‐SOSIE sections and illustrate the deleterious filtering effects of coal seams and sequences. To establish a phenomenological basis for seismic wave propagation in shallow coal measures, two vertical seismic profiles (VSPs) which used small explosive charges were recorded with high spatial and temporal sampling. Numerous multiple reflections were observed in the downgoing wave display. The isolated upgoing waves were migrated to yield blurred images of the main coal seams. The subsurface velocity function, also deduced from the VSP, shows broad correlation with the geologic log...

Deep Seismic profiling in central Australia

Abstract Deep Seismic profiling undertaken in central Australia comprised expanding spread reflection profiling, long-range refraction work and a small-scale three-dimensional refraction survey, as well as the more usual near-vertical incidence reflection profiling. Scismic reflection sections within the Arunta Block in central Australia show abundant northerly dipping events that are interpreted as reflections from dipping faults, many of which are evident in surface geological mapping. The Redbank Deformed Zone, a major thrust feature, has been imaged to depths of at least 30 km and defines a marked change in reflection character. South of the Redbank Zone, steep, northerly dipping reflections are absent; sub-horizontal basement reflections are prevalent below the Southern Arunta Province and Amadeus Basin. Seismic refraction profiles indicate that the crust is more than 50 km thick below both the boundary between the Southern and Central Arunta Provinces and the northern part of the Amadeus Basin. Expanding reflection spreads and a three-dimensional refraction survey have added fine details to the results in regions of special geological interest and include the resolution of complicated velocity variations in the sedimentary rocks of the northern part of the Amadeus Basin and the measurement of anisotropy in the granulites of the Central Arunta Province adjacent to the Redbank Zone.

Composite boundary‐valued solution of the 2.5-D Green’s function for arbitrary acoustic media

Theoretically, the Green’s function can be used to calculate the wavefield response of a specified source and the Frechet derivative with respect to the model parameters for crosshole seismic full‐waveform inversion. In this paper, we apply the finite‐element method to numerically compute the 2.5-D Green’s function for an arbitrary acoustic medium by solving a composite boundary‐valued problem in the wavenumber‐frequency domain. The composite boundary condition consists of a 2.5-D absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling. A numerical experiment performed for a uniform earth (having a known exact solution) shows the accuracy of the computation in the frequency and time domain. An inhomogeneous medium test, involving an embedded low‐velocity layer, demonstrates that the permissible range of ky at each frequency can be determined rationally from the critical wavenumber value of the medium around the sou...

Attenuating boundary conditions for numerical modeling of acoustic wave propagation

Four types of boundary conditions: Dirichlet, Neumann, transmitting, and modified transmitting, are derived by combining the damped wave equation with corresponding boundary conditions. The Dirichlet attenuating boundary condition is the easiest to implement. For an appropriate choice of attenuation parameter, it can achieve a boundary reflection coefficient of a few percent in a one-wavelength wide zone. The Neumann-attenuating boundary condition has characteristics similar to the Dirichlet attenuating boundary condition, but it is numerically more difficult to implement. Both the transmitting boundary condition and the modified transmitting boundary condition need an absorbing boundary condition at the termination of the attenuating region. The modified transmitting boundary condition is the most effective in the suppression of boundary reflections. For multidimensional modeling, there is no perfect absorbing boundary condition, and an approximate absorbing boundary condition is used.

Orientation of a downhole triaxial geophone

The bearing and elevation of a geophones axes are unknown when a geophone package is placed in a deep exploration borehole. Auxiliary instruments, such as inclinometers, compasses or gyros, may be incorporated into the downhole package to give some indication of local attitude relative to some external reference field, but these solutions may encounter difficulties because small gyros drift, the geomagnetic field may be distorted locally or screened by casing, and inclinometers add to the cost and weight of the downhole receiver. An alternate approach to determining the orientation of a remote tool is to compare its triaxial response to that expected for a known elastic wavefield. The accuracy of the measurement depends on the quality of the geophone-to-formation coupling and on the extent of ones knowledge of the externally impressed wavefield.

Seismic wavefield separation by multicomponent tau-p polarisation filtering

Abstract This paper presents a modified form of controlled direction reception (CDR) filter, to separate P and S waves in a multi-component Seismic profile. The aim of CDR is to enhance the clarity of the section. The essence of the method (in seeking S-wave extinction) is to perform a dot product between the signal vector and the polarisation (slowness) vector during projection of the section into tau-p space, using the P-wave velocity along the array. Alternatively, S waves can be enhanced and all other wave types (including background noise) suppressed by using a conjugate rotation operator and the S velocity profile, in forming the slant stack. A two-dimensional gain function, based on the rectilinearity of particle motion, is then applied in tau-p space as a non-linear boost function in order to enhance strongly polarised arrivals. Synthetic and physical model examples are used to demonstrate the noise rejection properties of the CDR process. and to show how P- and S-wave Seismic sections can be separately obtained.