A non-reflecting wave equation through directional wave-field suppression and its finite difference implementation

The acoustic wave equation describes wave propagation directly from basic physical laws, even in heterogeneous acoustic media. When numerically simulating waves with the wave equation, contrasts in the medium parameters automatically generate all scattering effects. For some applications - such as propagation analysis or certain wave-equation based imaging techniques - it is desirable to suppress these reflections, as we are only interested in the transmitted wave-field. To achieve this, a modification to the constitutive relations is proposed, yielding an extra term that suppresses waves with reference to a preferred direction. The scale-factor $$\alpha$$ α of this extra term can either be interpreted as a penetration depth or as a typical decay time. This modified theory is implemented using a staggered-grid, time-domain finite difference scheme, where the acoustic Poynting-vector is used to estimate the local propagation direction of the wave-field. The method was successfully used to suppress reflections in media with bone tissue (medical ultrasound) and geophysical subsurface structures, while introducing only minor perturbations to the transmitted wave-field and a small increase in computation time.

MATHEMATICAL MODELING OF ELASTIC WAVE PROPAGATION IN A BODY WITH A DEFECT

The solution of the dynamic problem of calculation the wave field of displacements on the surface of an elastic half-space caused by the opening of an internal crack under the action of torsional forces is presented. Based on the solutions of the boundary integral equations, the nature of the change in the amplitude-frequency characteristics of elastic oscillations on the surface of a rigid body depending on the size of the defect is shown.

On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system

Consider an inverse problem of determining two stochastic source functions and the initial status simultaneously in a stochastic thermoelastic system, which is constituted of two stochastic equations of different types, namely a parabolic equation and a hyperbolic equation. To establish the conditional stability for such a coupling system in terms of some suitable norms revealing the stochastic property of the governed system, we first establish two Carleman estimates with regular weight function and two large parameters for stochastic parabolic equation and stochastic hyperbolic equation, respectively. By means of these two Carleman estimates, we finally prove the conditional stability for our inverse problem, provided the source in the elastic equation be known near the boundary and the solution be in a prior bound set. Due to the lack of information about the time derivative of wave field at final moment, the stability index with respect to the wave field at final time is found to be halved, which reveals the special characteristic of our inverse problem for the coupling system.

Seismic Wave Field Anomaly Identification of Ultra-Deep Heterogeneous Fractured-Vuggy Reservoirs: A Case Study in Tarim Basin, China

Ultra-deep (7500–9000 m) Ordovician tight limestone heterogeneous fractured-vuggy reservoir is an important target of FuMan Oilfield in Tarim Basin. The strike-slip fault controlled reservoir is related to formation fracture and dissolution caused by geological stress. The seismic wave-field anomaly characteristics with different energy and irregular waveform are displayed in the seismic profile. Accurate identification of fractured-vuggy reservoirs wrapped in tight limestone is the direct scheme to improve production efficiency. Therefore, a new combination method flow of seismic wave-field anomaly recognition is proposed. In this process, the seismic data must be preprocessed initially, and on this basis, robust formation dip scanning is carried out. Secondly, the dip data is applied to the transverse smoothing filter to obtain the formation background data. Eventually, the seismic wave-field anomaly data is the residual between background data and original seismic data. This method has been applied in blocks with different structural characteristics and can effectively improve the resolution of strike-slip fault controlled reservoirs. Based on the results, the drilling success rate is increased to more than 95%, and the high-yield rate of oil tests is increased to 75% in 2021. Multiple applications indicate that the method is robust and can be popularized.

Components and Tidal Modulation of the Wave Field in a Semi-Enclosed Shallow Bay

The wave field in coastal bays is comprised of waves generated by far-off storms and waves generated locally by winds inside the bay and regionally outside the bay. The resultant wave field varies spatially and temporally and is expected to control morphologic features, such as beaches in estuaries and bays (BEBs). However, neither the wave field nor the role of waves in shaping BEBs have been well-studied, limiting the efficacy of coastal protection and restoration projects. Here we present observations of the wave field in Tomales Bay, a 20 km long, narrow, semi-enclosed embayment on the wave-dominated coast of Northern California (USA) with a tidal range of 2.5 m. We deployed pressure sensors in front of several beaches along the linear axis of the bay. Low-frequency waves (4 * 10^-2 * 2.5 * 10*^-1 Hz or 4 - 25 s period) dissipated within 4 km of the mouth, delineating the "outer bay" region, where remotely-generated swell and regionally-generated wind waves can dominate. The "inner bay" spectrum, further landward, is dominated by fetch-limited waves generated within the bay with frequency >= 2.5 < 10*-1 Hz. The energy of both ocean waves and locally-generated wind waves across all sites were modulated by the tide, owing to tidal changes in water depth and currents. Wave energies were typically low at low tide and high at high tide. Thus, in addition to fluctuations in winds and the presence of ocean waves, tides exert a strong control on the wave energy spectra at BEBs in mesotidal regions. In general, it is expected that events that can reshape beaches occur during high wind or swell events that occur at high-tide, when waves can reach the beaches with less attenuation. However, no such events were observed during our study and questions remain as to how rarely such wind-tide concurrences occur across the bay.