High-resolution Time-lapse Seismic Velocity Estimation Using Improved Envelope Full Waveform Inversion

An inverse problem is a general framework used to convert observed measurements into information about a physical object or system. Seismic exploration serves as a typical example of an inverse problem, utilizing seismic energy to probe beneath the Earth’s surface and often aiding in the search for valuable deposits of oil, gas, or minerals. Man-made seismic waves are generated at source stations, radiating outward as three-dimensional waves that travel downward into the Earth. Upon encountering changes in the Earth’s geological layering, they produce echoes that travel back up to the surface and are captured by geophones or hydrophones. These recorded seismic waves can be employed to infer physical properties such as P-wave velocity (Vp) and subsurface density. Specifically, Full Waveform Inversion (FWI) is a high-resolution seismic inversion method based on fitting the entire content of seismic waveforms with an optimization objective function to extract physical parameters of the medium sampled by seismic waves. Furthermore, 4D seismic data (seismic data acquired repeatedly at multiple times) can be used to invert the changes in seismic response during the production phase. Likewise, time-lapse FWI using the entire 4D seismic waveform has the potential to reveal high-resolution velocity changes related to reservoir production. However, FWI is a highly nonlinear inverse problem and suffers from a well-known cycle- skipping issue, and heavily depends on low frequencies, long offset data, a good initial velocity model, and accurate source wavelet estimation. Envelope inversion (EI) was proposed to help overcome cycle-skipping issue and recover the long-wavelength background model by fitting the envelop of entire content of seismic waveforms, rather than the waveforms themselves. Nevertheless, some issues like instability of the adjoint source and gradient term make it challenging to use in practice for many seismology applications. In this study, we firstly examine the EI methods with different envelope function exponent p- values from an adjoint source analysis perspective, and reveal the adverse effects of the adjoint source weighting term on the data residuals, which degrade or mute important inversion gradient contributions, especially from reflected or scattered phases in the seismic data. We develop the theory and implementation for an improved envelope inversion (IEI) method by adding an upshift constant (zero-frequency DC bias term) to the seismic waveform data before calculating the envelope functions, which can help solve the instability issue of the adjoint source of EI with power value p = 1. We test the performance of all three methods in detail using the highly realistic SEAM4D model and data, and show the advantages of our new IEI method compared to conventional EI and FWI methods. In addition, we implement IEI on marine seismic data and find that the amplitude mismatching between the modeled and observed data is a critical factor that prevents the successful application of IEI on real data. To match amplitude better, we introduce an amplitude normalization strategy using the amplitude of the head waves as the normalization reference. We demonstrate the successful application of IEI on a 2D marine seismic data example. We estimate a reasonable velocity model with IEI and a high-resolution velocity model with IEI

• FWI using data bandpassed to a maximum frequency content of 24 Hz. In addition, we apply the traditional EI methods with different power values on the envelope and discuss their limitations on the real data example. Furthermore, we implement inversions using different initial velocity models to show the ability of IEI to overcome the cycle-skipping issue and recover low-wavenumber velocity components compared to FWI, including a low-velocity reservoir zone. Finally, time-lapse FWI can introduce inversion artifacts, which might mask the true time- lapse signature within the reservoir zone, especially for the inversion on real data examples. We implement sequential bootstrap time-lapse FWI on the time-lapse marine seismic data from North Australia and observe noticeable inversion artifacts. To better understand these time-lapse FWI artifacts, we implement time-lapse FWI using several seismic data with different frequency bands and observe the distribution of the potential true time-lapse signature and inversion artifacts. On the inverted Vp change models using data with different frequency bands, the distribution of inversion artifacts exhibits inconsistencies, while the inverted Vp change at the reservoir remains consistent. In order to comprehend these observations, we analyze the origin of these time-lapse artifacts from a theoretical perspective and find that a portion of these artifacts may arise from inversion null space and differences in data residuals between baseline and monitoring inversions. Building on these insights, we develop a novel time-lapse FWI method to suppress these inversion artifacts. We use the energy of the inverted Vp change model utilizing data with a lower dominant frequency band as a gradient-weighting term for time-lapse FWI using data with a higher dominant frequency band. The test of the novel time-lapse FWI method on marine data demonstrates its capability to effectively suppress inversion artifacts.