Elastic Waveform Inversion of Pressure Field Data

An elastic waveform inversion method for inverting crosswell pressure field data is presented. In this method a low frequency approximation is used to analytically simulate the pressure generated in the fluid filled well. The tube wave in the borehole is not simulated based on the assumption that it can be removed from the field data by median filtering. The inversion method inverts for both Pand S-velocity tomograms at the same time. Therefore it requires fewer data processing procedures and honors the original amplitude information. The field data example shows that this method can provide superior images of the Pand S-velocity structures compared to the traveltime tomogram. The correlation between the Pand S-velocity tomograms is quite reasonable. Comparisons between the tomogram velocity profiles and the sonic logs show a good match. The resolution of the S-velocity tomogram is about the twice that of the P-velocity tomogram. 2 I N T R O D U C T I O N In many crosswell experiments, the hydrophone is used to record the pressure field in a fluid-filled borehole. Zhou et al. (1993) proposed an acoustic waveform inversion method for inverting hydrophone records which don’t contain strong S-wave arrivals. But when strong S-wave arrivals are extant, this inversion method is not valid. The remedy to this problem is to use an elastic waveform inversion method, which is generally applicable to two or three component particle velocity or displacement records (Tarantola et al., 1985; Mora, 1987; Zhou et al., 1994) However it is not straightforward to apply this method to pressure field data and ignoring the borehole effects might prove harmful. So Zhou and Hassanzadeh (1994) presented a divide and conquer strategy to de-complexify the data and invert the Pand S-velocity tomograms separately. Unfortunately there are some drawbacks with that strategy: 1. Skillful data processing procedures are required to separate both the PPand SS-reflections from the original data. The separation is done by FK filtering which usually contaminates the records with coherent noise. It also eliminates many useful parts of the records, such as the truncation of PP-reflections, and the PS-converted waves in the SS-reflections are unable to be eliminated. Consequently, the PSconversions will be treated as coherent noise in the inversion. 2. Scalar waveform inversion is used to separately invert both the Pand Stomograms. The elastic amplitudes must be corrected to match the amplitude distribution of acoustic wave propagation. This rough correction can distort the amplitude information in the original data and may result in an incorrect impedance reconstruction. In this report we apply a full elastic waveform inversion method to the pressure field data. By using a low frequency assumption, we analytically calculate the pressure field in the well from the hypothetical stress distribution on the wall of the well. The inversion method inverts both the Pand S-velocites at the same time to avoid massive data processing. 3 M E T H O D O L O G Y In this section we present the implementation of the general elastic waveform inversion (Zhou et al., 1994) for crosswell pressure field data. 3 . 1 F O R W A R D M O D E L I N G We only disscuss the situation that volume expansion sources and hydrophone receivers are used in the fluid filled source and receiver wells. The source generates the pressure that acts on the wall to generate seismic waves between the wells. Once the seismic waves reach the receiver well, the stresses on the wall generate the pressure in the receiver well which is recorded by the hydrophones. The modeling of seismic wave propagation within the source well can be neglected by inverting the equivalent source on the wall of the source well. The pressure field in the receiver well can be calculated from the stress components on the wall of the well by a low frequency assumption (White and Lessinger,