Question 1.Our printed circuit board is a multi layer card . It has one layer of an uninterrupted low impedance ground plane, so that the voltage difference between different ground points are small. Would it be possible to connect the analog ground and the digital ground to the same ground plane? 2.We found out that sclock and sdata lines have rise rime of more than 200 nanosecond. What is the reason for that? Is it aloud to use 1 K Ohm pull up resistor in order to get shorter rise time for these signals? Answer 1. The analog and digital ground pins of the AD7872 should be connected to the same ground plane. The problem exists when there is a lot of other noisy logic on the board which is also connected to this same ground plane. Then, the well known phenomena of ground bounce will increase the noise on the conversion result. How serious this is depends on how noise the digital logic is. 2. SCLK and SDATA are open-drain outputs and require pull up resistors (2k for SCLK, 4k7 for SDATA). This is noted in the pin function description.

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AD7872 Production
The AD7871 / AD7872 are fast, complete, 14-bit analog-to-digital converters (ADC). They consist of a track-and-hold amplifier, successive approximation...
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AD7872 on Analog.com