Valeri A. Korneev

Scattering of P and S Waves by a Spherically Symmetric Inclusion

Scattering of an arbitrary elastic wave incident upon a spherically symmetric inclusion is considered and solutions are developed in terms of the spherical vector system of Petrashen, which produces results in terms of displacements rather than displacement potentials and in a form suitable for accurate numerical computations. Analytical expressions for canonical scattering coefficients are obtained for both the cases of incidentP waves and incidentS waves. Calculations of energy flux in the scattered waves lead to elastic optical theorems for bothP andS waves, which relate the scattering cross sections to the amplitude of the scattered fields in the forward direction. The properties of the solutions for a homogeneous elastic sphere, a sphere filled by fluid, and a spherical cavity are illustrated with scattering cross sections that demonstrate important differences between these types of obstacles. A general result is that the frequency dependence of the scattering is defined by the wavelength of the scattered wave rather than the wavelength of the incident wave. This is consistent with the finding that the intensity of theP→S scattering is generally much stronger than theS→P scattering. When averaged over all scattering angles, the mean intensity of theP→S converted waves is2Vp2/Vs4times the mean intensity of theS→P converted waves, and this ratio is independent of frequency. The exact solutions reduce to simple and easily used expressions in the case of the low frequency (Rayleigh) approximation and the low contrast (Rayleigh-Born) approximation. The case of energy absorbing inclusions can also be obtained by assigning complex values to the elastic parameters, which leads to the result that an increase in attenuation within the inclusion causes an increased scattering cross section with a marked preference for scatteredS waves. The complete generality of the results is demonstrated by showing waves scattered by the earths core in the time domain, an example of high-frequency scattering that reveals a very complex relationship between geometrical arrivals and diffracted waves.

Seismic low-frequency effects from oil-saturated reservoir zones

We consider the frequency dependence of seismic reflections from a thin (compared to the dominant wavelength), fluid saturated reservoir for the cases of oil and water saturation. Reflections from a thin, water or oil-saturated layer have increased amplitude and delayed travel time at low frequencies if compared with reflections from a gas-saturated layer. This effect was observed for both ultrasonic lab data and seismic field data. One set of field data revealed high correlation of low frequency processed image for two different production horizons represented by fractured shale and sandstone. Another set was processed for the purpose of contouring of oil/water contact, and reveal very good correlation with available well data. The frequency dependent amplitude and phase reflection properties can be used for detecting and monitoring thin liquid saturated layers.

Seismic low‐frequency effects from fluid‐saturated reservoir

The normal incidence of Pelastic wave reflected from a thin porous dry and water saturated layer is considered. The effect of stronger reflections and travel time delays from water saturated layer is observed at low frequencies. We compared the results of laboratory modeling with “frictional-viscous” theoretical model and found that low (< 5) values of attenuation parameter Q and its approximate proportionality to frequency can explain the effect. The values of Q were determined in a separate experiment using recordings of a transmitted field for a thick porous layer, where water saturated layer had attenuation about two times higher then in a dry layer. These findings can be used for detecting and monitoring liquid saturated areas in thin porous layers.

Reconstructing head waves with virtual source method

The original applications of the Virtual Source Method (VSM) concentrate on imaging and monitoring through complex and changing overburden. This can be accomplished by correlating the wavefields recorded by downhole geophones. There are a number of reasons to expect even better results when this concept is extended to using head waves for reservoir imaging and monitoring purposes. The current practice to create virtual source data is to correlate the gated direct arrival at virtual source with total wavefield at receivers. Using a simple acoustic 2D model with two half-spaces having different velocities, we demonstrate the usefulness of correlating the head waves with different types of waves, theoretically and numerically.

Pressure diffusion waves in porous media

Pressure diffusion wave in porous rocks are under consideration. The pressure diffusion mechanism can provide an explanation of the high attenuation of low-frequency signals in fluid-saturated rocks. Both single and dual porosity models are considered. In either case, the attenuation coefficient is a function of the frequency.

Tube-wave monitoring of oil fields

Summary Tube-wave monitoring is a fit-for-purpose downhole imaging and monitoring technique. It aims to detect and characterize time-lapse changes in a cross-well space. In contrast to conventional cross-well seismic it does not require production interruption or reduces it to a minimum. Monitoring relies on tube waves in a well fluid column to carry the seismic signals to and from the reservoir. We present a simple modeling to support the concept and validate experimental data acquired at Stratton and Mallik

Advanced Reservoir Imaging Using Frequency-Dependent Seismic Attributes

Our report concerning advanced imaging and interpretation technology includes the development of theory, the implementation of laboratory experiments and the verification of results using field data. We investigated a reflectivity model for porous fluid-saturated reservoirs and demonstrated that the frequency-dependent component of the reflection coefficient is asymptotically proportional to the reservoir fluid mobility. We also analyzed seismic data using different azimuths and offsets over physical models of fractures filled with air and water. By comparing our physical model synthetics to numerical data we have identified several diagnostic indicators for quantifying the fractures. Finally, we developed reflectivity transforms for predicting pore fluid and lithology using rock-property statistics from 500 reservoirs in both the shelf and deep-water Gulf of Mexico. With these transforms and seismic AVO gathers across the prospect and its down-dip water-equivalent reservoir, fluid saturation can be estimated without a calibration well that ties the seismic. Our research provides the important additional mechanisms to recognize, delineate, and validate new hydrocarbon reserves and assist in the development of producing fields.

Borehole Seismic Monitoring of Injected CO2 at the Frio Site

As part of a small scale sequestration test (about 1500 tonsof CO2) in a saline aquifer, time-lapse borehole seismic surveys wereconducted to aid in characterization of subsurface CO2 distribution andmaterial property changes induced by the injected CO2. A VSP surveydemonstrated a large increase (about 75 percent) in seismic reflectivitydue to CO2 injection and allowed estimation of the spatial extent of CO2induced changes. A crosswell survey imaged a large seismic velocitydecrease (up to 500 m/s) within the injection interval and provided ahigh resolution image of this velocity change which maps the subsurfacedistribution of CO2 between two wells. Numerical modeling of the seismicresponse uses the crosswell measurements to show that this small CO2volume causes a large response in the seismic reflectivity. This resultdemonstrates that seismic detection of small CO2 volumes in salineaquifers is feasible and realistic.

Tube‐wave effects in cross‐well seismic data at Stratton Field

Tube-wave Effects in Cross-Well Seismic Data at Stratton Field Valeri Korneev, Lawrence Berkeley National Laboratory, Jorge Parra, South-West Research Institute, Andrey Bakulin, Shell Int.. Summary The analysis of crosswell seismic data for a gas reservoir in Texas revealed two newly detected seismic wave effects, recorded 2000 feet above the reservoir. The first is that the dominant late phases on the records are the tube waves generated in the source well and later converted into laterally propagating waves through the reservoir in gas/water saturated layers, which convert back to tube- waves in the receiver well. The tube-wave train showed good correlation with multilayered reservoir zone structure, suggesting that the recorded wave field has strong dependence on the reservoir parameters. The second effect is that the recorded field is composed of multiple low- velocity tube-waves. The modeling results suggest that imperfect cementation is the likely cause of this phenomenon. Tube waves Tube waves are traditionally regarded as a source of high amplitude noise in borehole seismic data and much effort typically goes into their suppression and elimination from recordings. Tube waves have very large amplitudes and can propagate long distances without substantial decay. A tube wave is an interface wave for a cylindrical interface between two media, typically a borehole fluid and surrounding elastic rock. Borehole waves were described by Lamb (1898) and were observed in the early twentieth century, as summarized by White (1965). Using trapped (or guided) mode analysis, the classic tube wave can be seen as the lowest order trapped mode (Schoenberg, 1981). Stratton Field Experiment The Stratton field experiment was designed in order to experimentally demonstrate the transmission and detection of guided waves in low-velocity sedimentary layers. The details of data acquisition, processing and low-velocity bed continuity study results can be found in Parra et. al. (2001). The objective of this project was to establish the feasibility and benefit of using interwell guided seismic waves in characterization of Gulf Coast gas reservoirs. Target zones were selected based on geological markers, seismic reflectors and well logs from the upper Frio Formation at the Stratton gas field. It was selected because it is one of the most extensively studied and well-documented producing oil and gas fields on the Gulf Coast. The Stratton field consists mainly of sandstones and shales of the Frio Formation with velocity contrasts on the order of 10% to Packer - at 5100 ft 20%. Three low-velocity intervals were identified, from top to bottom, as the V2, V5, and V12 shale zones, and were recognizable in all the wells. The three wells used to conduct the interwell logging experiments and are located in almost the same vertical plane. The data were collected in the receiver wells Ward159 and Ward145, while sources were placed in the well Ward145 between the receiver wells at three positions, corresponding to the centers of target layers V2 at 3816 ft (A), V5 at 4133 ft (B) and V12 at 4570 ft (C). The source was Texaco’s multiple air-gun array, a tool comprised of three air guns spaced 27 inches apart, which fire simultaneously with each shot. The guided-wave signatures were related to targets arriving in the 0.6 – 0.8 s time interval. The strongest phases in the records, which were arriving later then 0.8 s were not interpreted at the time as being out of scope of the experiment goals. Data sets The Stratton three data sets A145, B145 and C145 consist of 46 records each from the receivers positioned across the target layers. Source well Ward 151 1730 ft Receiver well Ward 145 Source V2 - at 3816 ft Guided, S- , P- waves Receiver line V5 - at 3816 ft Fast and V12 - at 3816 ft slow tube Packer Fast tube wave waves Waves in gas/water saturated permeable layers Fast tube wave Permeable gas/water saturated sandstone Low-velocity dry shale Figure 1. Cross-well experiment scheme and wave paths of the late arrivals.

Spherical Wave Propagation in a Nonlinear Elastic Medium

Nonlinear propagation of spherical waves generated by a point-pressure source is considered for the cases of monochromatic and impulse primary waveforms. The nonlinear five-constant elastic theory advanced by Murnaghan is used where general equations of motion are put in the form of vector operators, which are independent of the coordinate system choice. The ratio of the nonlinear field component to the primary wave in the far field is proportional to ln(r) where r is a propagation distance. Near-field components of the primary field do not contribute to the far field of nonlinear component.